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Multi-robot strategies for adaptive sampling with autonomous underwater vehicles

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Multi-robot strategies for adaptive sampling with autonomous underwater vehicles

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Content Multi-Robot Strategies for Adaptive Sampling
with Autonomous Underwater V ehicles
b y
Stephanie Kemna
A Dissertation Presen ted to the
F A CUL TY OF THE USC GRADUA TE SCHOOL
UNIVERSITY OF SOUTHERN CALIF ORNIA
In P artial F ulllmen t of the
Requiremen ts for the Degree
DOCTOR OF PHILOSOPHY
COMPUTER SCIENCE (CS)
Decem b er 2018
Committee :
Prof. Gaura v S. Sukhatme Committee Chair, USC CS
Prof. Nora A y anian USC CS
Prof. Da vid A. Caron USC Biology
Cop yrigh t 2018 Stephanie Kemna
Abstract
Biologists and o ceanographers are sampling lak es and o ceans w orldwide, to obtain data on
natural phenomena therein. F or example, measuring the abundance of algae to understand and
explain p oten tially harmful algal blo oms. T ypical metho ds of sampling are (a) taking ph ysical
w ater samples and sensor measuremen ts from b oats, (b) deplo ying sensor pac k ages on buo ys, do c ks
or other static h uman-built structures, and more recen tly (c) running pre-programmed missions with
aquatic rob ots. W e p osit that the use of rob ot teams could signican tly impro v e cost- and time-
eciency of lak e and o cean sampling, allo wing p ersisten t and ecien t mapping of the w ater column
at ner spatial and temp oral resolution. A dditionally , these systems ma y b e able to in telligen tly
gather data without needing signican t amoun ts of prior information.
W e en vision a scenario where one or t w o groups of biologists or o ceanographers come together
for monitoring a lak e, bringing their autonomous v ehicles with biological sensors. Our fo cus
is on impro ving sampling eciency , and en vironmen tal mo deling p erformance, through the use
of (decen tralized) co ordination approac hes for m ulti-rob ot sampling systems. This dissertation
in v estigates adaptiv e sampling tec hniques for single- and m ulti-rob ot deplo ymen ts. W e start with
an adaptiv e formation con trol approac h, where the v ehicles adapt their formation shap e based
on geometric constrain ts. This do es not consider the qualit y of data that is collected. Subsequen t
c hapters address adaptiv e informativ e sampling. In adaptiv e informativ e sampling, the rob ots adapt
their tra jectory online, in resp onse to sampled data, while utilizing information-theoretic metrics
to nd informativ e sampling lo cations. Through sim ulation studies w e sho w the b enets that can
b e obtained from emplo ying adaptiv e informativ e sampling approac hes. W e include eld results
to demonstrate the feasibilit y of running adaptiv e informativ e sampling on b oard an autonomous
underw ater v ehicle (A UV).
F or the m ulti-rob ot case, w e sho w the b enets that can b e obtained from adding data sharing
b et w een v ehicles, and w e explore the trade-o of surface-based (Wi-Fi) comm unications v ersus
underw ater (acoustic) comm unications. In terms of co ordinating m ultiple v ehicles, w e dev elop ed an
explicit co ordination approac h, based on dynamic estimation of V oronoi partitions, whic h sho ws
p oten tial for impro ving mo deling p erformance in the early stages of mo del creation. W e also
dev elop ed a metho d that addresses ho w to b est start adaptiv e sampling runs when no prior data is
a v ailable. Finally , w e studied implicit co ordination through async hronous surfacing with a surface-
based data h ub. W e sho w that p erformance across surfacing strategies is similar, though there is
v ariation in p erformance consistency , and some metho ds sho w p oten tial for greatly reducing the
n um b er of surfacing ev en ts needed.
Ov erall, this dissertation dev elop ed sev eral metho ds for adaptiv e informativ e sampling with
A UV s, fo cusing on m ulti-rob ot co ordination and eld deplo ymen t constrain ts. The results sho w
the b enets and p oten tial of incorp orating data sharing and co ordination strategies in to adaptiv e
sampling routines for m ulti-rob ot systems.
2
Contents
P age
List of Figures 7
List of T ables 10
1 In tro duction & Motiv ation 13
1.1 In tro duction to aquatic rob ots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2 In tro duction to algal blo oms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3 In tro duction & motiv ation for our researc h . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Thesis statemen t, con tributions & future w ork . . . . . . . . . . . . . . . . . . . . . . 19
1.5 PhD publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Co ordinated Sampling through F ormation
Con trol 22
2.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Related w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Approac h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Sim ulation of the ASV sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Cho osing the formation shap e . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.3 Cho osing the p osition in the formation . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Implemen tation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 Beha viors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.2 A coustic comm unications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.3 Exp erimen tal set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 F uture w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 An In tro duction to Informativ e A daptiv e
Samplng 34
3.1 Informativ e Sampling & A daptiv e Informativ e Sampling . . . . . . . . . . . . . . . . 34
3.2 Gaussian Pro cess regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 P ath planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 Related w ork in informativ e (adaptiv e) sampling . . . . . . . . . . . . . . . . . . . . 37
3
Stephanie Kemna A daptiv e Sampling with A UV s
4 Single-Rob ot A daptiv e Informativ e Sampling 41
4.1 Sim ulation set-up & Implemen tation . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 Single A UV results; la wnmo w er vs. adaptiv e . . . . . . . . . . . . . . . . . . . 43
4.3 Discussion & F uture w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5 Field T esting of Single-Rob ot A daptiv e Informativ e Sampling 44
5.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2 Mo deling Approac h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.3 Related W ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.4 Field T esting Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4.1 The autonomous underw ater v ehicle . . . . . . . . . . . . . . . . . . . . . . . 47
5.4.2 Lo cation and exp erimen tal set-up . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.4.3 Ground truth & analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.5 Field T esting Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.6 Field T esting Discussion, Conclusion & F uture W ork . . . . . . . . . . . . . . . . . . 52
6 Multi-Rob ot A daptiv e Informativ e Sampling:
Data Sharing 54
6.1 Related w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.2 Approac h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.3 Exp erimen tal set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.3.1 Sim ulated comm unications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.3.2 Sim ulation exp erimen ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.4.1 Multiple A UV s; la wnmo w er vs. adaptiv e parallel vs. adaptiv e timed data
sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.4.2 Multiple A UV s; timed data sharing vs. acoustic comm unications . . . . . . . 58
6.4.3 Multiple A UV s; deteriorating acoustic comm unications . . . . . . . . . . . . . 58
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.6 F uture w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
7 Multi-Rob ot A daptiv e Informativ e Sampling:
Co ordination 61
7.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.2 Related W ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.3 Approac h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.3.1 Dynamic V oronoi partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.3.2 Data sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.4 Implemen tation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.5.1 T w o A UV s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.5.2 Three A UV s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4 CONTENTS
A daptiv e Sampling with A UV s Stephanie Kemna
7.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.7 F uture w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8 Pilot Surv eys for A daptiv e Informativ e Sampling 70
8.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
8.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.2.1 Gaussian Pro cess Regression for Mo del Creation . . . . . . . . . . . . . . . . 72
8.2.2 P ath Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
8.2.3 In tegrated Pilot Surv eys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.3 Exp erimen tal set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
8.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8.4.1 Ro ot Mean Squared Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8.4.2 Hyp erparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8.5 Discussion & F uture w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
9 Multi-Rob ot A daptiv e Informativ e Sampling:
Async hronous Surfacing Strategies 83
9.1 In tro duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
9.1.1 Related w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
9.1.2 Con tributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
9.2 Metho d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
9.2.1 Mo deling Approac h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
9.2.2 Async hronous Surfacing Metho ds . . . . . . . . . . . . . . . . . . . . . . . . . 85
9.3 Exp erimen tal Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
9.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
9.5 Discussion & F uture w ork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
9.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
10 Discussion 94
11 P oten tial F uture Researc h Directions 96
12 A c kno wledgemen ts 99
13 References 101
14 App endix 110
14.1 Field trials results - nal predictiv e mean and v ariance . . . . . . . . . . . . . . . . . 111
14.1.1 F ull runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
14.1.2 Half runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
14.1.3 Chloroph yll half runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
14.2 Async hronous surfacing strategies results . . . . . . . . . . . . . . . . . . . . . . . . . 115
14.2.1 Median RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
CONTENTS 5
Stephanie Kemna A daptiv e Sampling with A UV s
14.2.2 RMSE b o xplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
14.2.3 Cum ulativ e v ariance b o xplots . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
14.2.4 Num b er of surfacing ev en ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
14.2.5 Final HP optimization GP size . . . . . . . . . . . . . . . . . . . . . . . . . . 135
14.2.6 First surfacing ev en t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6 CONTENTS
List of Figures
1.1 Examples of A UV s and ASV s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2 Example A UV mission soft w are: w a yp oin ts and la wnmo w er surv ey . . . . . . . . . . 15
2.1 Explanation of maxim um formation width. . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 F ormation bank examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Sim ulation lak e setting: San ta F e Reserv oir. . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Leader-follo w er formation con trol tra jectories. . . . . . . . . . . . . . . . . . . . . . 30
2.5 A daptiv e formation con trol tra jectories. . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 A daptiv e formation con trol, with dynamic assignmen t, tra jectories. . . . . . . . . . 31
2.7 Three A UV s and one failing, formation con trol tra jectories. . . . . . . . . . . . . . . 32
4.1 Example surv ey area in a lak e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Example grid sim ulated data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 RMSE & NLL for 1 A UV, la wnmo w er vs. adaptiv e. . . . . . . . . . . . . . . . . . . 43
5.1 USC’s EcoMapp er A UV. Photographer: Luk e Fisher . . . . . . . . . . . . . . . . . . 47
5.2 A UV eld testing set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3 Bath ymetry ground truth: in terp olated data from (unrelated) A UV missions run
b et w een August 2012 and Marc h 2017. Mission area outline sho wn in white. . . . . 49
5.4 Example full run bath y , `GP: predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 50
5.5 Example half run bath y , `GP: predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 50
5.6 Example half run Chloroph yll, `GP: predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.7 RMSE curv es for all bath y runs, predictions at ev ery 600s. . . . . . . . . . . . . . . 51
6.1 RMSE & NLL for 2 A UV s, la wnmo w er vs. adaptiv e. . . . . . . . . . . . . . . . . . . 57
6.2 RMSE & NLL for 2 A UV s, timed data sharing vs. acoustic comm unications. . . . . 58
6.3 RMSE & NLL for 2 A UV s, acoustic comm unications at dieren t throughput lev els. 59
7.1 Scenario 1: single blo om . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.2 Scenario 2: dual blo om . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
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Stephanie Kemna A daptiv e Sampling with A UV s
7.3 RMSE for 2A UV s, scenario 1, timed data sharing vs. dynamic V oronoi. . . . . . . . 66
7.4 NLL for 2A UV s, scenario 1, timed data sharing vs. dynamic V oronoi. . . . . . . . . 66
7.5 RMSE for 2 A UV s, scenario 2, timed data sharing vs. dynamic V oronoi. . . . . . . . 67
7.6 NLL for 2 A UV s, scenario 2, timed data sharing vs. dynamic V oronoi. . . . . . . . . 67
7.7 RMSE for 3 A UV s, scenario 1, timed data sharing vs. dynamic V oronoi. . . . . . . . 68
7.8 NLL for 3 A UV s, scenario 1, timed data sharing vs. dynamic V oronoi. . . . . . . . . 68
7.9 RMSE for 3 A UV s, scenario 2, timed data sharing vs. dynamic V oronoi. . . . . . . . 68
7.10 NLL for 3 A UV s, scenario 2, timed data sharing vs. dynamic V oronoi. . . . . . . . . 68
8.1 Determining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
8.2 Example tra jectories for dieren t ‘temp erature’ . . . . . . . . . . . . . . . . . . . . 75
8.3 Six scenarios with generated data. Theoretically the data can represen t an ything,
in this w ork the ‘data v alue’ represen ts Chloroph yll, g{L. . . . . . . . . . . . . . . 76
8.4 RMSE b o xplots pilot surv eys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
8.5 HP b o xplots pilot surv eys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
9.1 Calculation time function tting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
9.2 GMM and GP sampled scenarios, for async hronous surfacing exp erimen ts . . . . . . 89
9.3 Median RMSE for scenario a) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 90
9.4 Median RMSE for scenario e) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 90
9.5 RMSE b o xplots for scenario a) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 90
9.6 RMSE b o xplots for scenario e) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 90
9.7 Cum ulativ e v ariance b o xplots for scenario a) for A UV 2 . . . . . . . . . . . . . . . . 90
9.8 Cum ulativ e v ariance b o xplots for scenario e) for A UV 2 . . . . . . . . . . . . . . . . 90
14.1 F ull run, `GP , Marc h 31 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
This is the same as Figure 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
14.2 F ull run, `GP , April 28, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 111
14.3 F ull run, `GP , July 21, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 111
14.4 Half run, `GP , Marc h 31, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
This is the same as Figure 5.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
14.5 Half run, `GP , April 28, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 112
14.6 Half run, `GP , Ma y 18, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 112
14.7 Half run, `GP , Ma y 24, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 113
14.8 Half run, `GP , July 7, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . . 113
14.9 Half run, GP, July 21, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 113
14.10 Half run, `GP , Aug. 8, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t). . 113
14.11 Half run, `GP , Apr. 28, 2017. Pred. mean
Yx
(left) and v ariance
2
Yx
(righ t). . . . 114
14.12 Half run, `GP , Ma y 18, 2017. Pred. mean
Yx
(left) and v ariance
2
Yx
(righ t). . . . . 114
8 LIST OF FIGURES
A daptiv e Sampling with A UV s Stephanie Kemna
14.13 Half run, `GP , Ma y 24, 2017. This is the same as Figure 5.6. . . . . . . . . . . . . . 114
14.14 Half run, `GP , July 7, 2017. Pred. mean
Yx
(left) and v ariance
2
Yx
(righ t). . . . . 114
14.15 Median RMSE for scenario a) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 115
14.16 Median RMSE for scenario b) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 116
14.17 Median RMSE for scenario c) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 116
14.18 Median RMSE for scenario d) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 117
14.19 Median RMSE for scenario e) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 117
14.20 Median RMSE for scenario f ) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 118
14.21 Median RMSE for scenario a) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 119
14.22 Median RMSE for scenario b) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 119
14.23 Median RMSE for scenario c) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 120
14.24 Median RMSE for scenario d) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 120
14.25 Median RMSE for scenario e) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 121
14.26 Median RMSE for scenario f ) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 121
14.27 RMSE b o xplots for scenario a) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 122
14.28 RMSE b o xplots for scenario b) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . 122
14.29 RMSE b o xplots for scenario c) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 123
14.30 RMSE b o xplots for scenario d) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . 123
14.31 RMSE b o xplots for scenario e) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 124
14.32 RMSE b o xplots for scenario f ) for A UV 1 . . . . . . . . . . . . . . . . . . . . . . . . 124
14.33 RMSE b o xplots for scenario a) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 125
14.34 RMSE b o xplots for scenario b) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . 125
14.35 RMSE b o xplots for scenario c) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 126
14.36 RMSE b o xplots for scenario d) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . 126
14.37 RMSE b o xplots for scenario e) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 127
14.38 RMSE b o xplots for scenario f ) for A UV 2 . . . . . . . . . . . . . . . . . . . . . . . . 127
14.39 Cum ulativ e v ariance b o xplots for scenario a) for A UV 1 . . . . . . . . . . . . . . . . 128
14.40 Cum ulativ e v ariance b o xplots for scenario b) for A UV 1 . . . . . . . . . . . . . . . . 128
14.41 Cum ulativ e v ariance b o xplots for scenario c) for A UV 1 . . . . . . . . . . . . . . . . 129
14.42 Cum ulativ e v ariance b o xplots for scenario d) for A UV 1 . . . . . . . . . . . . . . . . 129
14.43 Cum ulativ e v ariance b o xplots for scenario e) for A UV 1 . . . . . . . . . . . . . . . . 130
14.44 Cum ulativ e v ariance b o xplots for scenario f ) for A UV 1 . . . . . . . . . . . . . . . . 130
14.45 Cum ulativ e v ariance b o xplots for scenario a) for A UV 2 . . . . . . . . . . . . . . . . 131
14.46 Cum ulativ e v ariance b o xplots for scenario b) for A UV 2 . . . . . . . . . . . . . . . . 131
14.47 Cum ulativ e v ariance b o xplots for scenario c) for A UV 2 . . . . . . . . . . . . . . . . 132
14.48 Cum ulativ e v ariance b o xplots for scenario d) for A UV 2 . . . . . . . . . . . . . . . . 132
14.49 Cum ulativ e v ariance b o xplots for scenario e) for A UV 2 . . . . . . . . . . . . . . . . 133
14.50 Cum ulativ e v ariance b o xplots for scenario f ) for A UV 2 . . . . . . . . . . . . . . . . 133
LIST OF FIGURES 9
List of T ables
2.1 P arameters for the leader-follo w er and formation-switc hing sim ulations. . . . . . . . . 29
3.1 Literature review comparison based on mo deling and path planning approac hes. . . . 39
3.2 Literature review comparison based on planning c haracteristics and researc h fo cus. . 40
5.1 Final log-h yp erparameters estimated on b oard the v ehicle at the end of ev ery adaptiv e
sampling run: log length scale l, and the log of signal and noise standard deviations. 52
6.1 Reduced acomms throughput, empirical data. . . . . . . . . . . . . . . . . . . . . . . 58
8.1 RMSE outliers, pilot surv eys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
8.2 HP outliers, pilot surv eys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
9.1 A v erage n um b er of surfacing ev en ts, with one standard deviation, a v eraged o v er all
scenarios, o v er b oth v ehicles, o v er all 30 sim ulation runs. . . . . . . . . . . . . . . . . 91
9.2 A v erage n um b er of samples in nal GP for h yp erparameter optimization, with one
standard deviation, a v eraged o v er all scenarios, o v er b oth v ehicles, o v er all 30 sim u-
lation runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
9.3 A v erage time of rst surfacing ev en t with standard deviation, a v eraged o v er all
scenarios, o v er b oth v ehicles, o v er all 30 sim ulation runs. . . . . . . . . . . . . . . . . 91
14.1 A v erage n um b er of surfacing ev en ts for A UV 1 . . . . . . . . . . . . . . . . . . . . . . 134
14.2 A v erage n um b er of surfacing ev en ts for A UV 2 . . . . . . . . . . . . . . . . . . . . . . 134
14.3 A v erage size do wnsampled GP at nal HP optimization for A UV 1 . . . . . . . . . . 135
14.4 A v erage size do wnsampled GP at nal HP optimization for A UV 2 . . . . . . . . . . 135
14.5 A v erage time of rst surfacing ev en t for A UV 1 . . . . . . . . . . . . . . . . . . . . . 136
14.6 A v erage time of rst surfacing ev en t for A UV 2 . . . . . . . . . . . . . . . . . . . . . 136
10
Abbreviations and Conventions
In this w ork w e discuss adaptiv e informativ e sampling. In prior publications this has at times
b een called informativ e adaptiv e sampling. Ho w ev er, w e b eliev e that the correct order is to place
adaptiv e rst, giv en that ‘informativ e sampling’ in and of itself is a researc h area, and can b e
executed b oth in a non-adaptiv e, o-line, manner, as w ell as an adaptiv e, on-line, manner. In parts
of this thesis, where w e ha v e copied text from prior publications, w e ha v e switc hed the ordering to
t this con v en tion.
F or those of y ou who get confused b et w een A UV and UA V, here is the rather simple guideline
for ho w those abbreviations w ork:
AxV Autonomous V ehicle
AA V Autonomous A erial V ehicle
A GV Autonomous Ground V ehicle
ASV Autonomous Surface V ehicle (V essel)
A UV Autonomous Underw ater V ehicle
UxV Unmanned V ehicle
UA V Unmanned A erial V ehicle
UGV Unmanned Ground V ehicle
USV Unmanned Surface V ehicle (V essel)
UUV Unmanned Underw ater V ehicle
The w ord gliders is often used to reference underw ater gliders, whic h are a subset of A UV s. The
w a v e glider is of course an ASV.
The w ord dr ones is t ypically used to refer to UA V s, and these da ys also for AA V s. W e will not use
it to refer to underw ater v ehicles.
Other abbreviations used in this do cumen t:
11
Stephanie Kemna A daptiv e Sampling with A UV s
CTD Conductivit y , T emp erature, Depth
D VL Doppler V elo cit y Log
FSK F requency-shift Keying
GP Gaussian Pro cess
GPS Global P ositioning System
IMU Inertial Measuremen t Unit
INS Inertial Na vigation System
IvP In terv al Programming
`GP log-Gaussian Pro cess
MDP Mark o v Decision Pro cess
MOOS Mission-Orien ted Op erating Suite
NLL Negativ e Log Lik eliho o d
PRM Probabilitic Road Map
RR T Rapidly-exploring Random T ree
RMSE Ro ot Mean Squared Error
TDMA Time Division Multiple A ccess
TSP T ra v eling Salesp erson Problem
12 LIST OF T ABLES
1 | Introduction & Motiv ation
The o c e an is the lifeblo o d of Earth, c overing mor e than 70 p er c ent of the planet’s surfac e,
driving we ather, r e gulating temp er atur e, and ultimately supp orting al l living or ganisms.
Thr oughout history, the o c e an has b e en a vital sour c e of sustenanc e, tr ansp ort, c ommer c e,
gr owth, and inspir ation.
Y et for al l of our r elianc e on the o c e an, 95 p er c ent of this r e alm r emains unexplor e d, unse en
by human eyes.
NO AA, How much of the o c e an have we explor e d?
Biologists and o ceanographers are sampling lak es and o ceans w orldwide, to obtain data for the
biology and en vironmen tal phenomena they are in terested in. Applications include w ater qualit y
monitoring, ecosystem mo deling, o cean mo deling, studying harmful algal blo oms, etc. T ypical
metho ds of sampling are (a) taking ph ysical w ater samples and sensor measuremen ts from b oats,
and (b) deplo ying sensor pac k ages o of buo ys, do c ks or other man-made underw ater structures.
T ypical sensors record conductivit y (salinit y), temp erature, depth (pressure) - these three are often
com bined in a CTD sensor, pH, dissolv ed o xygen, turbidit y , c hloroph yll (Chl) measuring algae
concen trations, blue-green algae, and nitrate. Note that all of these sensors are m y opic, i.e. they
are taking sp ot measuremen ts, in-place, without a sensor range. These metho ds of data collection
tend to b e time and cost in tensiv e, and they pro vide only limited data. The use of rob ot teams
could signican tly impro v e cost- and time-eciency of lak e and o cean sampling, allo wing p ersisten t
and ecien t mapping of the w ater column in ner resolution. A dditionally , these systems ma y b e
able to in telligen tly gather data without needing a lot of prior information.
1.1 Introduction to aquatic robots
T ypical aquatic rob ots include autonomous underw ater v ehicles (A UV s) and autonomous surface
v ehicles (ASV s). Figure 1.1 sho ws a couple of examples of commercially a v ailable A UV s and ASV s,
as w ell as USC’s A UV and ASV. A UV s, and ASV s with winc hed sensors, can b e used to create data
slices of the w ater column, b oth v ertically and horizon tally , of, for example, temp erature, salinit y
or uorescence resp onses.
W e w ould lik e to p oin t out some k ey c haracteristics and diculties of (w orking with) A UV s.
First of all, t ypical metho ds for lo calization and comm unication can not b e used when A UV s
op erate underw ater. This is b ecause electromagnetic w a v es (e.g. optical, radio) are absorb ed b y
the w ater column. The only reliable medium in whic h an y data can b e transmitted underw ater is
through mec hanical w a v es, most imp ortan tly acoustic. This has impacts on v ehicle lo calization and
13
Stephanie Kemna A daptiv e Sampling with A UV s
Figure 1.1: Examples of prop elled autonomous underw ater v ehicles (A UV s, left) and autonomous
surface v ehicles (ASV s, righ t). A UV s from top to b ottom: YSI EcoMapp er (YSI Incorp orated and
OceanServ er, 2008), Iv er3 (OceanServ er, 2013), REMUS-100 (K ongsb erg Maritime, 2016), Bluen-
9 (Bluen Rob otics, 2017), Ga via Scien tic (T eledyne Marine, 2017), Girona-500 (Carrera et al.,
2013). ASV s from top to b ottom: USC’s ASV, Heron (Clearpath Rob otics, 2017), C-enduro (ASV
Global, 2017).
14 CHAPTER 1. INTR ODUCTION & MOTIV A TION
A daptiv e Sampling with A UV s Stephanie Kemna
comm unication. When the v ehicles are underw ater, they can not receiv e GPS signals or use Wi-Fi
comm unications. F or lo calization, they use de ad-r e ckoning tec hniques, whic h estimate the v ehicle
p osition based on prior GPS estimates, and its estimation of its o wn mo v emen ts (direction and
distance tra v eled). Sensors used for dead rec k oning include inertial measuremen t units (IMUs), and
Doppler V elo cit y Logs (D VLs). An IMU t ypically incorp orates accelerometers and gyroscop es, to
detect rates of acceleration and rotation. A D VL sends an acoustic signal to the b ottom of the lak e,
sea or o cean, and, b y using the Doppler eect, the v ehicle can th us calculate its o wn sp eed o v er
ground. The D VL can greatly increase dead rec k oning precision, but is also an exp ensiv e system and
therefore not alw a ys a v ailable on (small) A UV s, and can only b e used when A UV s op erate in w ater
shallo w er than the range of the D VL signal. In general, b ecause of these lo calization tec hniques, it
is useful to command the A UV s mostly through mo v emen ts that k eep the system stable, suc h as
straigh t lines.
Note that A UV s are t ypically trimmed to b e sligh tly p ositiv ely buo y an t. This is done as a
safet y measure, suc h that, if an ything go es wrong with the v ehicle (barring leaks), it will end up
somewhere on the surface. Ho w ev er, this also means that in order to sta y underw ater, the v ehicle
needs to k eep mo ving con tin uously . Therefore, y ou can not stop an A UV in the middle of a mission,
other than b y running small maneuv ers. Commercial o-the-shelf A UV s and ASV s often come with
soft w are to command them through w a yp oin ts or la wnmo w er surv eys. W a yp oin ts are lo cations in
latitude and longitude (and depth), whic h the v ehicle transits to w ards in a straigh t line mo v emen t.
La wnmo w er surv eys are sequences of w a yp oin ts, whic h lead the v ehicle to v ertically , or horizon tally ,
go up and do wn an area, t ypically in order to completely co v er it. Figure 1.2 sho ws an example of
t w o missions planned using w a yp oin ts (left) and a la wnmo w er surv ey (righ t).
Figure 1.2: Examples of A UV mission soft w are sho wing mission planning through w a yp oin ts (left)
and a la wnmo w er surv ey (righ t) (OceanServ er, 2009).
The la wnmo w er mo v emen ts are t ypically sequences of w a yp oin ts, whic h are tra v ersed un til the
full la wnmo w er is completed. In the case of w a yp oin t con trol, when the A UV reac hes a w a yp oin t,
CHAPTER 1. INTR ODUCTION & MOTIV A TION 15
Stephanie Kemna A daptiv e Sampling with A UV s
it w ould need to b e giv en a next w a yp oin t. The v ehicle can b e giv en a sequence of w a yp oin ts, or
it can calculate new w a yp oin ts. T o a v oid surfacing ev en ts, the v ehicle can b e commanded to k eep
going to w ards, or circle, a w a yp oin t un til a new one is giv en or calculated.
Commercial o-the-shelf A UV s come with soft w are that allo ws the user to set w a yp oin ts or
program set missions suc h as la wnmo w ers. This can usually b e done through the man ufacturer’s
mission planning soft w are. Some v ehicle man ufacturers allo w y ou to buy the A UV with an additional
computer on b oard, whic h, if an in terface is pro vided, can b e used to send directions to the primary
v ehicle computer. The secondary computer is often called the pa yload computer, after additional
pa yload, e.g. sensors, that can b e added to the v ehicle and handled via the secondary computer.
F urthermore, the primary computer and secondary computer are often called the fr ontse at and
b ackse at computer, resp ectiv ely . Y ou can think of this as in a cab: the driv er sits in the fron t seat
and kno ws ho w to driv e the car, but the high lev el directions come from the passenger in the bac k
seat. The fron tseat computer has the A UV man ufacturer’s soft w are, and runs all lo w lev el con trol
algorithms to handle v ehicle con trol e.g. roll, pitc h, and y a w con trol. P oten tially the fron tseat
can also handle obstacle a v oidance and simple path planning. The bac kseat computer can send
directions at dieren t lev els of abstraction, for example b y sending w a yp oin ts (tak e me to the
airp ort!), or b y sending directions through sp eed/heading/depth or lo w er lev el motor commands
(go left here ... no w go righ t at the next trac ligh t).
In order to comm unicate with an A UV when it is underw ater, one needs to install an acoustic
mo dem on the A UV. Dep ending on the frequency used for comm unications, the size of the mo dem
transducers can b e substan tial. Higher frequency mo dems ha v e smaller transducers and can ac hiev e
greater bandwidth but are limited to op erate o v er short ranges (e.g. up to 1km), while lo w er
frequency mo dems can ha v e greater ranges (up to 8km), they are limited in bandwidth and need
bigger transducers. In this w ork w e assume a base lev el acoustic mo dem, suc h as the WHOI
MicroMo dem, whic h, with FSK
1
rate 0, can send messages of 32 b ytes (W o o ds Hole Oceanographic
Institution, 2017). Note that t ypically acoustic mo dems are set up suc h as to not transmit at the
same time, to a v oid in terference of signals. In order to determine time slots for sending, one should
consider the tra v el time of the signal, whic h in w ater is appro ximately 1500mzs.
The reliabilit y of acoustic comm unications dep ends on the ph ysical medium, the w ater column,
as w ell as on in terference eects. Sources of deterioration of acoustic signals include the state of
the ph ysical medium (e.g. sea state, thermo clines or p ycno clines
2
, m ulti-path eects), and external
sound sources (suc h as sea state, shipping noise, and snapping shrimp). In general, it is practically
imp ossible to get a comm unication c hannel that is 100% reliable for the whole duration of an y A UV
mission. This, com bined with the bandwidth constrain ts, also mak es it infeasible to remote-con trol
A UV s.
1
FSK: F requency Shift Keying, a frequency mo dulation tec hnique used to enco de information b y c hanging the
frequency of the signal.
2
Thermo clines and p ycno clines are la y ers in a w ater b o dy where the temp erature or densit y , resp ectiv ely , increases
rapidly with depth. These la y ers can b e so pronounced that acoustic signals reect o of them.
16 CHAPTER 1. INTR ODUCTION & MOTIV A TION
A daptiv e Sampling with A UV s Stephanie Kemna
1.2 Introduction to algal blooms
The main application area for our rob otic sampling eorts, c hosen for this thesis, is the sampling
and monitoring of algal blo oms. Algal blo oms are of in terest b ecause they can b e harmful to the
en vironmen t. There are t w o w a ys in whic h algal blo oms can b e damaging: First, there are so-called
harmful algal blo oms (HABs). Some t yp es of algae or cy anobacteria (often called blue-green algae,
though actually bacteria) can pro duce to xic substances. These to xic substances can cause sic kness
or death to sh, marine mammals, animals and h umans. When a blo om of to xic-pro ducing algae
forms, this is called a HAB. Secondly , non-to xic algal blo oms can cause problems to the en vironmen t
and underw ater life b y creating lo w or zero o xygen conditions. When algae die, they are brok en
do wn b y bacteria. This pro cess uses o xygen. T ypically this breakdo wn happ ens near the b ottom of
a lak e or the o cean, where there can b e anoxic , i.e. zero o xygen, zones. A t times, blo oms of algae
are so abundan t, that almost all the o xygen in the w ater column is used in the breakdo wn of the
algae, whic h can lead to sh, or other marine life, dying due to the w ater b ecoming hyp oxic , i.e.
the amoun t of dissolv ed o xygen in the w ater is less than 1:4ml{l (Stauer et al., 2012). In order
to b etter understand ho w algal blo oms form, spread, mo v e through the w ater column, and cease
existing, w e are in terested in mo deling algal blo oms.
Algal blo oms can b e of dieren t spatial exten t, dep ending on man y factors, including the size
and depth of the w ater b o dy , the orien tation of the w ater b o dy , wind stress and w ater curren ts. F or
relativ ely small lak es, algal blo om ranges are on the order of tens of meters
3
. F or larger lak es and
the o cean, w e could exp ect length scales ranging from h undreds of meters to tens of kilometers, for
example: Hedger et al. (2003) sho w ed spatial exten ts up to h undreds of meters in the coastal o cean,
in a ba y o of Scotland. do Rosario Gomes et al. (2008) sho w ed spatial exten ts of tens of kilometers
in the North Arabian Sea. Bro wn and Y o der (1994) ev aluated blo oms of Co ccolithophorids, a t yp e
of ph ytoplankton, in the w orld’s o ceans with spatial exten ts of thousands of kilometers. And most
recen tly , algal blo oms in the North P acic at h undreds to thousands of kilometers
4
. The latter are
exceptionally large. More commonly o the coast of California, there are blo oms that range up to
tens of kilometers in North-South spatial exten t, and up to a few kilometers o shore
3
. Kno wing
the spatial exten t one can exp ect for algal blo oms in the w ater b o dy one w an ts to monitor, can help
in deciding what mo del parameters to use.
Note that so far w e ha v e only discussed the horizon tal (‘x, y’) exten t of algal blo oms. Algal
blo oms can also v ary in terms of v ertical (‘z’) exten t. F urthermore, algal la y ers can b oth b e presen t
at the surface and in the w ater column. In most cases, the v ertical exten t is orders of magnitude
smaller than the horizon tal exten t. Subsurface algal la y ers, also called subsurface maxima, often
are near thermo clines, the depth of whic h can v ary with time of da y , mon th or season. A subsurface
maxima can b e found b y sampling with a CTD or Chl sensor at man y depths, or running a short
A UV-based yoyo mission, where the A UV tra v els from w ater surface to sev eral meters o the b ottom,
sampling the w ater column. In case of subsurface blo oms, it is hard to c haracterize the blo om from
surface or remote-sensing measuremen ts. A UV s are ideal systems to sample within the blo om for
extended p erio ds of time. In this thesis, w e assume that there is a single subsurface algal la y er, and
our mo del is trying to capture the exten t and shap e(s) of the blo om(s) at that subsurface maxima.
3
Based on con v ersations with Prof. Da vid A. Caron.
4
https://www.climate.gov/news- features/event- tracker/record- setting- bloom- toxic- algae- north- pacific
CHAPTER 1. INTR ODUCTION & MOTIV A TION 17
Stephanie Kemna A daptiv e Sampling with A UV s
1.3 Introduction & motiv ation for our research
While aquatic rob ots with en vironmen tal sensors pro vide w a ys of c heap data collection, the v ehicles
themselv es are still relativ ely costly for most scien tic end-users. A t the same time, m ulti-rob ot
approac hes can reduce the time required to explore or map an area. W e en vision a scenario where
one or t w o groups of biologists or o ceanographers come together for monitoring a lak e, bringing
their autonomous v ehicles with biological sensors. T o this end, our approac hes are aimed at using
small groups of (small) A UV s. Our fo cus is on impro ving sampling eciency , and en vironmen tal
mo deling p erformance, through the addition of decen tralized m ulti-rob ot co ordination approac hes.
As explained in the previous section, the standard metho ds of running surv eys on A UV s are
running la wnmo w er surv eys or pre-sp ecied sequences of w a yp oin ts. These surv ey metho ds ma y
not guaran tee that the end-user gets the most informativ e data within the time limits of v ehicle
endurance. Therefore, w e are also in terested in adaptiv e informativ e sampling; i.e. adapting
the v ehicle tra jectory online based on sampled data, while incorp orating information-theoretic
metrics to seek out the most informativ e sampling lo cations. Chapter 3 to 9 discuss our researc h
eorts in adaptiv e informativ e sampling, and sho w the p oten tial of using these approac hes. Our
sim ulation studies sho w impro v ed p erformance running single A UV adaptiv e informativ e sampling
o v er running standard la wnmo w er surv eys. Chapter 5 in v estigates the feasibilit y of running the
adaptiv e informativ e sampling on b oard an A UV, and w e sho w results from our eld trials. F or
m ulti-rob ot approac hes, w e rst sho w the b enets of simple data sharing, and explore the trade-o
b et w een surface (Wi-Fi) comm unications and underw ater (acoustic) comm unications. Then, w e
discuss a m ulti-rob ot co ordination approac h based on dynamic V oronoi partitioning, whic h sho ws
impro v emen ts o v er data sharing. A t this p oin t w e tak e a brief detour to in v estigate pilot surv eys:
metho ds of starting adaptiv e sampling runs collecting represen tativ e data for the mo del b efore
the v ehicle adapts to this data. Finally , w e discuss and compare m ultiple strategies for m ulti-
rob ot adaptiv e informativ e sampling, whic h compare the V oronoi-based approac h to data sharing
strategies that use a surface-based data h ub.
18 CHAPTER 1. INTR ODUCTION & MOTIV A TION
A daptiv e Sampling with A UV s Stephanie Kemna
1.4 Thesis statement, contributions & future work
Our thesis statemen t is as follo ws:
The addition of multi-r ob ot c o or dination str ate gies to adaptive sampling impr oves a multi-r ob ot
system’s eld mo deling p erformanc e.
W e sho w that this is true for systems under the follo wing constrain ts:
Minimal comm unication: Keep underw ater comm unication to a minim um, and do not assume
constan t or p erfect comm unication.
Decen tralization: Keep an y approac h decen tralized, if p ossible. There will not b e a cen tral
con troller, whic h could b e a single p oin t of failure or lead to comm unication o v erhead.
Robust systems: Dev elop approac hes whic h will con tin ue to w ork ev en if some v ehicles fail
during execution.
Little to zero prior data: Dev elop approac hes whic h can b e used for deplo ymen ts in lak es and
o ceans where w e ha v e not sampled b efore, and for whic h w e do not necessarily kno w what w e
will nd.
Our con tributions include:
dev elopmen t of an adaptiv e formation con trol approac h for a team of heterogeneous v ehicles,
whic h is decen tralized and robust to v ehicles failures (Chapter 2, (Kemna et al., 2015)),
a comparativ e study regarding the comm unication medium for data sharing in m ulti-rob ot
adaptiv e informativ e sampling (Chapter 6, (Kemna et al., 2016)),
an activ e m ulti-rob ot co ordination approac h for m ulti-rob ot adaptiv e informativ e sampling,
whic h is decen tralized, robust to v ehicle failures, and a w are of comm unication constrain ts
(Chapter 7, (Kemna et al., 2017)).
eld testing results demonstrating the feasibilit y of single-A UV adaptiv e informativ e sampling,
and prop osed metho d for ev aluating eld exp erimen ts (Chapter 5, (Kemna et al., 2018a)),
dev elopmen t of an approac h for designing pilot surv eys, to collect represen tativ e data for
mo del initialization if no prior data is a v ailable (Chapter 8, (Kemna et al., 2018b)),
dev elopmen t of surfacing strategies for m ulti-rob ot adaptiv e informativ e sampling with a
surface-based data h ub (Chapter 9,(Kemna and Sukhatme, 2018)).
CHAPTER 1. INTR ODUCTION & MOTIV A TION 19
Stephanie Kemna A daptiv e Sampling with A UV s
1.5 PhD publications
This w ork is in large part a stitc hing together of publications pro duced during the course of m y
PhD studies. Chapter fo otnotes will p oin t out what publication w as used for eac h c hapter. F or
clarit y , all publications, including those not discussed in this thesis, are listed here in c hronological
order:
Stephanie Kemna, Da vid A. Caron, and Gaura v S. Sukhatme, Constrain t-induced formation
switc hing for adaptiv e en vironmen tal sampling. IEEE/MTS Oc e ans Genova , Ma y 2015.
Stephanie Kemna, Da vid A. Caron, and Gaura v S. Sukhatme, A daptiv e Informativ e Sampling
with Autonomous Underw ater V ehicles: A coustic v ersus Surface Comm unications. IEEE/MTS
Oc e ans Monter ey , Septem b er 2016.
Stephanie Kemna, John G. Rogers I I I, Carlos Nieto-Granda, Stuart Y oung, and Gaura v S.
Sukhatme, Multi-Rob ot Co ordination through Dynamic V oronoi P artitioning for Informa-
tiv e A daptiv e Sampling in Comm unication-Constrained En vironmen ts. IEEE International
Confer enc e on R ob otics and A utomation , Ma y 2017.
Stephanie Kemna, Oliv er Kro emer, and Gaura v S. Sukhatme, Pilot Surv eys for A daptiv e
Informativ e Sampling. IEEE International Confer enc e on R ob otics and A utomation , Ma y
2018.
Christopher Denniston, Thomas R. Krogstad, Stephanie Kemna, and Gaura v S. Sukhatme,
Planning Safe P aths with A UV s through Hazardous En vironmen ts. Submitted to IEEE OES
A utonomous Underwater V ehicle Symp osium 2018.
Nic holas F ung, John G. Rogers I I I, Stephanie Kemna, Carlos Nieto-Granda, Gaura v S. Sukhatme,
Henrik I. Christensen, Multi-rob ot co ordination for adaptiv e informativ e sampling in struc-
tured en vironmen ts. Submitted to IEEE/RSJ International Confer enc e on Intel ligent R ob ots
and Systems 2018.
Stephanie Kemna, Hrur K. Heiarsson, and Gaura v S. Sukhatme, On-b oard A daptiv e
Informativ e Sampling for A UV s: a F easibilit y Study . T o app ear in IEEE/MTS Oc e ans
Charleston , Octob er 2018.
Stephanie Kemna, and Gaura v S. Sukhatme, Surfacing strategies for m ulti-rob ot adaptiv e in-
formativ e sampling with a surface-based data h ub. T o app ear in IEEE/MTS Oc e ans Charleston ,
Octob er 2018.
20 CHAPTER 1. INTR ODUCTION & MOTIV A TION
A daptiv e Sampling with A UV s Stephanie Kemna
Posters:
Stephanie Kemna, Da vid A. Caron and Gaura v S. Sukhatme. "Measuring Ocean Phenomena
with Autonomous Underw ater V ehicles", CRA-W Graduate Cohort p oster session, 2013.
Stephanie Kemna, Da vid A. Caron and Gaura v S. Sukhatme. "Decen tralized A daptiv e
Informativ e Sampling using Autonomous Underw ater V ehicles", IEEE RAS Summer Sc ho ol
on Multi-Rob ot Systems, Singap ore, June 2016.
Stephanie Kemna, Gaura v S. Sukhatme. "Multi-Rob ot Co ordination through Dynamic V oronoi
P artitioning for Informativ e A daptiv e Sampling in Comm unication-Constrained En vironmen ts",
Southern California Rob otics Symp osium (SCR) p oster session, 2017.
Nic holas F ung, John G. Rogers I I I, Stephanie Kemna, Carlos Nieto-Granda, Gaura v S. Sukhatme,
Henrik I. Christensen, Multi-rob ot task allo cation for collab orativ e adaptiv e informativ e sam-
pling in structured en vironmen ts. W orkshop on Informativ e P ath Planning and A daptiv e
Sampling, at IEEE International Confer enc e on R ob otics and A utomation , Ma y 2018.
And at USC computer science’s ann ual researc h review, 2013-2017:
2013 "Measuring Ocean Phenomena with Autonomous Underw ater V ehicles"
2014 "In v estigations in to detecting diurnal migration of algae using autonomous underw ater v ehi-
cles"
2015 "Constrain t-induced formation con trol for autonomous v ehicles in adaptiv e en vironmen tal
sampling"
2016 "Informativ e adaptiv e sampling using autonomous aquatic v ehicles"
2017 "Multi-Rob ot Co ordination through Dynamic V oronoi P artitioning for Informativ e A daptiv e
Sampling in Comm unication-Constrained En vironmen ts"
CHAPTER 1. INTR ODUCTION & MOTIV A TION 21
2 | Coordinated Sampling through F ormation
Control
This c hapter discusses a formation con trol approac h for co ordinated sampling of lak es. It considers
ho w to direct a team of heterogeneous v ehicles, balancing the pros and cons of dieren t w ell-kno wn
formation con trol approac hes.
This c hapter is mostly a reprin t of Constrain t-induced formation switc hing for adaptiv e en viron-
men tal sampling (Kemna et al., 2015).
2.1 Introduction
W ater qualit y monitoring b y taking w ater samples and sensor measuremen ts from b oats is time and
cost in tensiv e, and pro vides only limited data. The use of rob ot teams could signican tly impro v e
eciency of lak e sampling, allo wing p ersisten t and ecien t mapping of the lak e in ner resolution,
without needing a lot of prior information. T ypical aquatic rob ots include autonomous underw ater
v ehicles (A UV s) and autonomous surface v ehicles (ASV s).
The use of a heterogeneous team of rob ots ma y also b e required, giv en cost and sensor con-
strain ts. F or example, most commercial o-the-shelf small A UV s (e.g. (K ongsb erg Maritime, 2016,
OceanScan-MST, 2018, OceanServ er, 2013, 2014, YSI Incorp orated and OceanServ er, 2008)), out-
tted for (biological) sampling of the underw ater en vironmen t, do not ha v e forw ard lo oking sonar.
Unless accurate maps of the underw ater en vironmen t are a v ailable, they ma y collide with the sea
or lak e o or, underw ater moun ts, or other underw ater ob jects (e.g. wrec ks, mines, trash). Instead
of increasing individual A UV capabilities, a team of A UV s or ASV s with dieren t sensors could
b e used. In this w ork, w e assume a group of small homogeneous A UV s, equipp ed with biological
sensors, used in com bination with an ASV, whic h has sensors to measure the en vironmen t and
detect obstacles (e.g. laser, sonar, cameras).
Ho w ev er, curren tly there is no commercial o-the-shelf solution for deplo ying a group of au-
tonomous v ehicles (AxV s) to sample a lak e. One cannot deplo y all v ehicles with the touc h of one
button, and ha v e them sample the lak e, without needing further in teraction. This ho w ev er is exactly
what w e w an t to ac hiev e, and leads us to examine formation con trol approac hes.
W e presen t an adaptiv e formation con trol approac h, in whic h w e com bine ideas from the three
main formation con trol approac hes (Beard et al., 2001): b eha vior-based, leader-follo w er and virtual
structures formation con trol. W e exploit the reactiv e and adaptiv e nature of b eha vior-based systems,
This c hapter is mostly a reprin t of Constrain t-induced formation switc hing for adaptiv e en vironmen tal
sampling (Kemna et al., 2015).
22
A daptiv e Sampling with A UV s Stephanie Kemna
tak e a leader-follo w er set-up for simplifying commanding and con trol and to reduce comm unication
o v erhead, and include ideas from virtual structures for sampling in consisten t formation shap es.
An autonomous surface v ehicle (ASV) is deplo y ed as a leader. This v ehicle can b e running a pre-
planned tra jectory (i.e. to optimize co v erage) or it can b e remote-con trolled b y a scien tist. A group
of A UV s form an underw ater formation that follo ws the leader, able to adapt to an y constrain ts
passed on b y the ASV. This leader-follo w er, formation con trol approac h reduces the need for user
in v olv emen t. The A UV s spatially distribute themselv es whenev er (lak e) constrain ts allo w, while
aiming for consisten t tra jectories. This w ork sho ws the p oten tial of adaptiv e formation con trol
to w ards accessible rob otic lak e sampling.
2.2 Related work
T o deplo y a team of rob ots, one approac h w ould b e to deplo y and command eac h rob ot separately ,
i.e. plan an optimal sampling tra jectory for eac h. Benets can include optimalit y and stabilit y
guaran tees. Ho w ev er, these stabilit y guaran tees ma y not scale with addition or remo v al of rob ots,
or ma y not hold v alid when the rob ot encoun ters unmo deled circumstances. F urthermore, t ypically
when a group of rob ots is deplo y ed, eac h with their o wn plan, they all need to b e individually
o v erseen b y an op erator, and (new) commands need to b e send to eac h individually . Alternativ ely ,
one could con trol a team of rob ots through formation con trol, whic h w ould allo w commanding and
monitoring the formation, rather than eac h rob ot individually .
There are three main approac hes for formation con trol (Beard et al., 2001): b eha vior-based (Balc h
and Arkin, 1998, Bro oks, 1986), leader-follo w er (Cui et al., 2010, Soares et al., 2013, Stilw ell and
Bishop, 2000), and virtual structures (Lewis and T an, 1997, T an and Lewis, 1996). Beha vior-based
approac hes (including sw arming and o c king (Olfati-Sab er, 2006, Reynolds, 1987)) t ypically w ork
w ell in dynamic en vironmen ts due to their reactiv e nature, and can easily com bine dieren t ob jectiv e
functions, to include for example obstacle a v oidance. Ho w ev er, it ma y also mak e it more dicult
to understand and explain their actions, since the o v erall b eha vior is emergen t from what subset of
b eha viors migh t b e activ e at an y time. This in turn dep ends on what the v ehicles encoun ter,
including dynamic ob jects. W e w ould lik e to tak e the exibilit y , and the easy in tegration of
dieren t ob jectiv es, from b eha vior-based approac hes, but y et b e more restricted in co ordination
and mo v emen ts to ha v e more certain t y on exp ected b eha vior.
In leader-follo w er approac hes, t ypically there is one leader, and all follo w ers reference themselv es
to the leader (Cui et al., 2010). Although there are exceptions, e.g. (Rego et al., 2014, Soares et al.,
2013) uses t w o leaders and one follo w er. This mak es it easy to con trol a whole group, since y ou
only need to con trol the leader. A p oten tial do wnside is that the leader also b ecomes a single p oin t
of failure, whic h is hard to a v oid in this set-up, unless the leader can b e dynamically assigned.
A t the same time, the leader do es not adjust its execution to the follo w er v ehicles, whic h means
that the follo w ers could sta y b ehind or ‘lose’ the leader. F or range/b earing leader-follo w er set-ups,
there is no explicit co ordination b et w een the follo w er v ehicles, eac h rob ot only lo oks at where it is
with resp ect to the leader. This means there are no guaran tees ab out the relativ e distances and
mo v emen ts b et w een the follo w er v ehicles. F or example, if y ou w an t the formation to b e in the shap e
of a (rigid) diamond, there are no guaran tees that this will happ en, since the follo w er v ehicles do
not c hec k where the other follo w er v ehicles are. This could p oten tially lead to collision b et w een
CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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23
Stephanie Kemna A daptiv e Sampling with A UV s
follo w er v ehicles. Giv en our heterogeneous v ehicle set-up, giv en limited a v ailabilit y of sensors and
a-priori information, and giv en that commanding one v ehicle w ould b e easier for scien tists using it,
w e will use a leader-follo w er set-up for co ordination b et w een v ehicles. Ho w ev er, w e lo ok at virtual
structures for more guaran tees on consisten t b eha vior.
In virtual structures, the idea is to treat the formation as a (rigid) structure, where all v ehicles
reference to one another. Therefore, the o v erall b eha vior of the team is co ordinated, and eac h
v ehicle adjusts its p osition all the time based on ev ery one’s p erformance. Ho w ev er, requiring to
main tain the structure can restrict p ossible applications or complicate mo v emen ts, e.g. when trying
to a v oid obstacles. F urthermore, the con tin uous referencing to, and p oten tial negotiating with, other
v ehicles ma y lead to a comm unication o v erhead. W e w ould lik e to incorp orate the ideas of virtual
structures, without requiring the v ehicles to strictly follo w it, and without creating an y o v erhead to
comm unications.
F or autonomous underw ater v ehicle (A UV) formation con trol, the main limitation is on comm u-
nication. Leader-follo w er formation con trol therefore b ecomes an ob vious c hoice, b ecause follo w er
v ehicles only need to kno w the lead v ehicle’s (relativ e) lo cation (Edw ards et al., 2004, P orri et al.,
2006). Most A UV formation con trol approac hes fo cus on leader-follo w er con trol, man y addressing
v ehicle con trol from a con trols p ersp ectiv e (Cui et al., 2010, Rego et al., 2014, Stilw ell and Bishop,
2000). W e argue that the mo del-based guaran tees of stabilit y ma y not alw a ys p ort o v er to real w orld
settings, i.e. if mo dels are incomplete, or when v ehicles encoun ter unforeseen circumstances. W e
are in terested in dev eloping formation con trol approac hes that w ork irresp ectiv e of exact v ehicle
dynamics, the t yp e of A UV, or the exact amoun t of v ehicles. T o the b est of our kno wledge,
there are few examples com bining ideas from all three aforemen tioned formation con trol approac hes
(e.g. (Beard et al., 2001, Eren et al., 2005)), in order to utilize all b enets. This c hapter discusses an
approac h that in tegrates ideas from all aforemen tioned approac h to dev elop a exible, but consisten t,
approac h to formation con trol for autonomous v ehicles.
2.3 Approach
The rst step in the formation con trol is to determine the allo w able formation width b y the ASV. The
ASV broadcasts
1
the calculated allo w able width to the underw ater v ehicles. When the A UV s receiv e
the formation width constrain t, they c ho ose an allo w ed formation from a bank of p ossible formations.
This bank con tains formations that are deemed v alid for generating consisten t tra jectories, from
whic h one is c hosen. Eac h v ehicle then determines their p osition in the formation, b y solving
the Hungarian metho d for the assignmen t problem (Kuhn, 1955). And this is sen t to a w a yp oin t
b eha vior to c hange the v ehicle’s route. This section will briey discuss eac h individual comp onen t
in more detail.
2.3.1 Simulation of the ASV sensor
The detection of lak e outline is sim ulated to calculate the allo w able formation width. It runs only
on the surface v ehicle, sim ulating for example a sonar or laser moun ted on the ASV. This could b e
1
Note that, giv en that comm unication happ ens via the acoustic c hannel, messages are alw a ys heard b y all v ehicles.
One option is to address eac h message to a subset of v ehicles, suc h that the others w ould discard the message. Ho w ev er,
w e ma y as w ell b enet from this, and let ev ery one use the information receiv ed.
24 CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
CONTR OL
A daptiv e Sampling with A UV s Stephanie Kemna
implemen ted in man y w a ys. Because the sensor mo del is not the fo cus of this approac h, w e use a
simple circular sector mo del, dened b y the sensor range and the width at the sensor horizon. In
this case w e use a sensor range of 30 meters, and a sensor horizon width of 70 meters, eectiv ely
leading to a sensor co v erage width of ca. 100 degrees.
The allo w able formation width is calculated from the in tersection of the sensor horizon and the
lak e outline p olygon. Giv en that all formation shap es are assumed to b e cen tered on the ship main
axis (v ehicle heading, see Section 2.3.2), w e calculate the lengths of the in tersection on eac h side
of the ASV heading. The minim um of these forms half the allo w able formation width, as sho wn in
Figure 2.1. Curren tly , no other obstacles are mo deled in the sim ulation, but a similar in tersection
approac h could b e used for p olygonal obstacles.
lake outline
intersection
½ max formation width
ASV
ASV heading
sensor_range
sensor_width
Figure 2.1: The maxim um formation width is calculated from the minim um half of the in tersection
b et w een the sensor horizon and lak e outline.
This is the only information that is delib erately shared for formation con trol. It is merged
in to the v ehicle’s status message, whic h is already broadcast
1
to all v ehicles, for in ter-v ehicle
collision a v oidance and to pro vide information to the command and con trol cen ter, th us pro ducing
no comm unication o v erhead.
2.3.2 Cho osing the formation shape
Once the allo w able formation width is kno wn, the v ehicles need to c ho ose whic h formation should
b e tak en. This is done on eac h A UV, meaning ev ery one determines for themselv es the formation
shap e, based on the n um b er of underw ater v ehicles (whic h can b e deduced from the receiv ed status
messages) and the receiv ed allo w able formation width. Th us implemen ting decen tralized formation
con trol.
A formation b ank w as created to store the p ossible formations. V ehicles can only tak e on a
formation that is in the formation bank. This guaran tees that the formation tak es on a desired
CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
CONTR OL
25
Stephanie Kemna A daptiv e Sampling with A UV s
(virtual) structure, e.g. for the sak e of measuring data along geometrically consisten t tra jectories.
Curren tly , all formations are in 2D, addressing only the planar distribution of the v ehicles. This is
paired with a constan t depth or y o y o depth b eha vior on the A UV s.
Figure 2.2 sho ws the p ossible formations for t w o and three A UV s. These formations w ere hand
c hosen for their abilit y of pro viding consisten t tra jectories. F ormations are dened b y their reference
p oin t (star), the n um b er of v ehicles, and a pre-dened in ter v ehicle distance. The formation reference
p oin t is at a pre-dened follo w range b ehind the lead v ehicle. Preference is giv en to formations that
are spread out across the horizon tal axis, to guaran tee the acquisition of dieren t samples (i.e. not
all sampling along the same tra jectory), assuming forw ard mo v emen t of the lead v ehicle.
follow
range
int er
vehi cl e
dis ta nce
}
Figure 2.2: F ormation bank: p ossible formations for 2 (left) and 3 (righ t) A UV s follo wing an ASV.
The star sho ws the formation reference p oin t. P ositions within eac h formation are determined from
the formation reference p oin t, giv en the follo w range and the in ter v ehicle distance parameters.
The allo w able formation width is sen t b y the ASV at the momen t it is calculated via the in ter-
v ehicle acoustic comm unications. This is t ypically receiv ed to o early on the A UV s to b e used, giv en
the sensor range and follo w range distances b et w een when the constrain t is measured and when
the formation will b e there. Therefore, the constrain t initially is stored on ev ery v ehicle, with an
estimated time for when it will need to b e acted up on. Similarly , the receiv ed lead v ehicle p osition
is stored, with an estimated time when the formation reference p oin t needs to b e at this lo cation.
A t ev ery iteration, the pro cess pSelectF ormation c hec ks if there is a stored constrain t, and a new
shap e needs to b e tak en.
F or eac h formation, the p ossible p ositions in the formation are calculated from the formation
reference p oin t:
p
i
p
fc
R
hdg
t
i
(2.1)
where p
i
is the new p osition for A UV i (in the global reference frame), p
fc
is the calculated
p osition of the formation reference p oin t (star in Figure 2.2), R
hdg
is the 2x2 rotation matrix where
is lead v ehicle heading, and t
i
is the translation v ector for the p osition i in the formation (A UV
sym b ols in Figure 2.2), referenced b y the formation reference p oin t. Whic h p osition eac h v ehicle
should tak e, out of all calculated p ositions in the formation, is describ ed in the next section.
26 CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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A daptiv e Sampling with A UV s Stephanie Kemna
2.3.3 Cho osing the p osition in the formation
The next step is to calculate whic h p osition in the formation should b e tak en b y the A UV. One
simple approac h w ould b e to assign a static p osition in the formation, whic h is what w ould t ypically
b e done in a leader-follo w er setting (Balc h and Arkin, 1998). Ho w ev er, if v ehicles are added or
remo v ed, then ev ery one will need to b e assigned a new p osition. Alternativ ely , auction metho ds can
b e used to allo w v ehicles to c ho ose their p osition in the formation, e.g. (Mic hael et al., 2008). But
these t ypically require the v ehicles to negotiate, th us pro ducing comm unication o v erhead, and giv en
the slo w sp eed of underw ater comm unications, also dela ys in actions. Another alternativ e approac h
to solving the task assignmen t problem migh t b e to use lo cal searc hing and task sw aps (Liu and
Mic hael, 2010), ho w ev er this metho d still has a comm unication o v erhead compared to the fully
decen tralized Hungarian Metho d.
Giv en that the n um b er of v ehicles can c hange, and giv en that tra v el distances to dieren t
p ositions in the formation ma y dier dep ending on when the formation is c hanged, this should b e
solv ed at ev ery formation c hange, rather than pre-assigned. Solving whic h v ehicle go es where, is a
v arian t of the (task) assignmen t problem. T o solv e it, eac h A UV uses the Hungarian metho d (Kuhn,
1955), to nd an optimal assignmen t. As the cost metric, the Euclidean distance b et w een the A UV’s
curren t p osition and the a v ailable p ositions in the formation is used. The p osition assignmen t is
th us solv ed in a decen tralized manner.
If the v ehicles w ere to solv e the assignmen t problem with the same information, w e w ould b e
guaran teed an optimal assignmen t. Ho w ev er, due to the inheren t dela ys of acoustic comm unications
(not ev en considering p oten tial message loss), the v ehicles ma y b e solving a dieren t problem, whic h
migh t lead to them c ho osing the same lo cation. T o alleviate this problem, the v ehicles not only
solv e the assignmen t problem when the formation shap e c hanges, but at an y time new information
is receiv ed.
2.4 Implementation
2.4.1 Behaviors
T o in v estigate formation con trol for a team of A UV s, follo wing an ASV, w e set up a sim ulation using
the MOOS-IvP middlew are (Benjamin et al., 2010). MOOS-IvP is a commonly used middlew are
for (aquatic) rob otics and pro vides man y pro cesses for aquatic rob otics sim ulations. It includes a
b eha vior-based arc hitecture. F or com bining b eha vior outputs, w e rely on an in terv al programming
(IvP) solv er, used for m ulti-ob jectiv e optimization (Benjamin et al., 2010) (an alternativ e to e.g.
the n ull-space-based approac h (An tonelli et al., 2008)).
F or the main v ehicle con trol, w e use w a yp oin t b eha viors for b oth the ASV and A UV. The ASV
w a yp oin t can b e calculated b eforehand, hand-pic k ed, or assigned on the go. The A UV w a yp oin ts
are calculated as p er Section 2.3.2 and Section 2.3.3. The ASV uses a standard w a yp oin t b eha vior
with constan t sp eed (Benjamin et al., 2010). F or the A UV s, w e w an ted to allo w the A UV s to sp eed
up and slo w do wn. T o enable this, w e implemen t a linearly decreasing sp eed when nearing the
CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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27
Stephanie Kemna A daptiv e Sampling with A UV s
w a yp oin t:
v
$
'
&
'
%
v
min
if d
w
r
c
v
min
p
dwrc
rvrc
pv
max
v
min
qq if r
c
d
w
r
v
v
max
if r
v
d
w
(2.2)
wherev
min
minim um sp eed, v
max
maxim um sp eed, r
c
capture radius, r
v
sp eed radius, are b eha vior
parameters, and d
w
is the calculated (Euclidean) distance to the w a yp oin t.
F or safet y , the A UV s run (in ter-v ehicle) collision a v oidance b eha viors, suc h that they will not
collide with eac h other or the ASV. The ASV is not trying to a v oid collision with the A UV s. W e
assume all A UV s indep enden tly run depth con trol, and use a constan t depth b eha vior (similar
to (Soares et al., 2013)). This could b e replaced with other depth b eha viors, e.g. a y o y o. F or
the sim ulations describ ed here, the underw ater v ehicles w ere running at a depth of 10 m (assuming
o v erall deep er lak e depth, and the use of a safet y b eha vior that implemen ts minim um altitude).
The A UV s ha v e no safet y b eha vior to sta y in a certain op eration area, since w e assume they do not
kno w the lak e outline.
2.4.2 A coustic communications
W e sim ulate acoustic comm unications using gob y-acomms (Sc hneider, 2014). The dev elop ed sim u-
lation encompasses t w o autonomous underw ater v ehicles and one autonomous surface v ehicle. The
v ehicles are set up to comm unicate via a (static) time division m ultiple access (TDMA) sc heme,
assuming sync hronized clo c ks, with time slots of 3 seconds: one second for transmission, one for
one-w a y tra v el (assumed range max. 1km, no ac kno wledgemen ts), and one second as a buer.
This allo ws eac h v ehicle to send one message ev ery 9 seconds. W e mak e minimal assumptions
on acoustic comm unications: a maxim um comm unication range of 500 m and the abilit y to send
only 32-b yte messages, whic h should b e easily ac hiev able with a small, high frequency , short-range
acoustic mo dem, suc h as the 25kHz WHOI MicroMo dem (F reitag et al., 2005, Gallimore et al.,
2010), or the Ev oLogics S2CR 18/34 (Ev oLogics Gm bH, 2014). Ho w ev er, w e do assume decen t
acoustic comm unications giv en this conguration, and no loss of messages.
2.4.3 Exp erimen tal set-up
The sim ulation is run for a lak e setting, in this case the East part of the San ta F e reserv oir, see
Figure 2.3.
The dicult y in this scenario is a natural passage. Note that this is only one example of a
complex en vironmen t. Other examples where similar adaptiv e formation b eha vior will b e required
are, including but not limited to: oating platforms in a lak e, underw ater moun ts, buo ys, shing
b oats, or other obstacles that ma y b e hard or imp ossible to lo cate a priori. W e compare the
p erformance of the dev elop ed adaptiv e formation con trol approac h to standard leader-follo w er
con trol, using MOOS-IvP’s trail b eha vior (Benjamin et al., 2010). And w e also compare it to
formation switc hing with a static assignmen t, instead of using the Hungarian metho d. T o get
comparable follo w range and in ter-v ehicle distance, w e use the parameters as dened in T able 2.1.
Ev ery sim ulation starts with all v ehicles in the East corner of the lak e.
28 CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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A daptiv e Sampling with A UV s Stephanie Kemna
100m
Figure 2.3: East part of San ta F e Reserv oir, with op eration area (y ello w p olygon), lead v ehicle
w a yp oin ts (y ello w balls) and lead v ehicle tra jectory (white). Note; the follo w er v ehicles are not
a w are of the op eration area.
Approac h P arameter V alue
Leader-
follo w er
trail range 30 m
trail angle
(A UV 1)
130 degrees
trail angle
(A UV 2)
230 degrees
F ormation-
switc hing
follo w range 30 m
2A UV s in ter v ehicle
distance
50 m
F ormation-
switc hing
follo w range 30 m
3A UV s in ter v ehicle
distance
25 m
T able 2.1: P arameters for the leader-follo w er and formation-switc hing sim ulations.
2.5 Results & Discussion
Figure 2.4 to Figure 2.6 sho w p ost-mission plots for sim ulations of leader-follo w er, adaptiv e forma-
tion con trol with static assignmen t and adaptiv e formation con trol with dynamic assignmen t. Note
again that the A UV s are not a w are of the lak e outline. In the case of standard leader-follo w er con trol,
the A UV s run outside of the lak e b oundaries, whic h w orks in this sim ulation, but the v ehicles w ould
ha v e stranded in a real scenario. In b oth cases of the adaptiv e formation con trol, all v ehicles get
through the passage without problems.
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29
Stephanie Kemna A daptiv e Sampling with A UV s
Figure 2.4: Leader-follo w er formation con trol. V ehicles start from (arro ws) and return to (arro ws)
the East corner of the lak e.
Figure 2.5: A daptiv e formation con trol, static assignmen t. V ehicles start from (arro ws) and return
to (arro ws) the East corner of the lak e.
30 CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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A daptiv e Sampling with A UV s Stephanie Kemna
Figure 2.6: A daptiv e formation con trol, dynamic assignmen t. V ehicles start from (arro ws) and
return to (arro ws) the East corner of the lak e.
Figure 2.5 and Figure 2.6 sho wing resp ectiv ely static and dynamic p osition assignmen t, with
formation switc hing, sho w v ery similar b eha vior. This is exactly what w e w an t to ac hiev e. W e can
argue that the static assignmen t with formation switc hing is the optimal b eha vior, giv en switc hing.
Ho w ev er, w e kno w it will not b e able to deal with adapting to failures of v ehicles, hence w e need
the dynamic assignmen t. One more thing to note is that the dynamic assignmen t allo ws v ehicles
to switc h out p ositions, if this is more adv an tageous. An example w e can see when w e compare
the v ehicles’ b eha vior in the left b ottom corner of the righ t part of the lak e (at ca. 1150, 175) in
Figure 2.5 and Figure 2.6. When p osition assigmen t is determined with the Hungarian metho d,
v ehicles will go to the p osition that is closest for them, this allo ws them to switc h out and a v oid
unnecessary idling (for A UV2).
Figure 2.7 sho ws the p ost-sim ulation plot for the scenario where 3 A UV s start, and one is tak en
out in the middle of the mission (*). A t this p oin t the 2 v ehicles ha v e to reorganize. A UV2, whic h
w as tak en out, w as measuring East of the leader v ehicle tra jectory and either A UV1 or A UV3 no w
has to tak e this p osition. Comparing to Figure 2.2, they need to switc h from the middle 3A UV
conguration to the leftmost 2A UV conguration. It tak es a little while for the v ehicle to totally
reorganize. This is partly due to them ha ving to gure out that one v ehicle is no longer there,
and then to switc h o v er. Ho w ev er, from Figure 2.7 it is clear that after the transition through the
passage, the v ehicles settle to b e distributed around the leader tra jectory .
CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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31
Stephanie Kemna A daptiv e Sampling with A UV s
Figure 2.7: Three A UV s, one fails. V ehicles start from (arro ws) and return to (arro ws) the East
corner of the lak e.
2.6 F uture work
The curren t w ork has discussed adapting formations based on a formation bank. W e b eliev e using
a formation bank is not scalable to large groups of v ehicles. F uture w ork could include deriving
la ws for creation of formations. F urthermore, all formations so far ha v e b een cen tered on the ASV
heading. Ho w ev er, there ma y b e cases where one could shift the formation, rather than switc h
to a completely dieren t formation. Other more exible and scalable approac hes to determining
formation shap es and p osition of the formation reference p oin t could b e dev elop ed.
There curren tly also is no noise in v ehicle lo calization. Ho w ev er, since the underw ater v ehicles
could b e inexp ensiv e v ehicles without exp ensiv e inertial na vigation systems (INS), there will b e
some noise and drift in the p osition estimates o v er time. This not only impacts the solving of the
assignmen t problem (c hoice of the p osition in formation), but also in ter-v ehicle collision a v oidance.
F or the collision a v oidance, the v ehicles use the via acomms receiv ed p ositions, estimated on b oard
eac h v ehicle. If this estimate is far o from the real lo cation, v ehicles ma y actually crash in to eac h
other while trying to a v oid a wrong lo cation. Metho ds to impro v e this could include incorp orating
co op erativ e lo calization (Bahr et al., 2009, F allon et al., 2010) or b eacon-based (long-baseline, ultra-
short baseline) na vigation metho ds.
Finally , it w ould b e v ery in teresting to include ev aluation metrics in to the problem form ulation.
F or example, if the goal is to gather the most amoun t of information ab out a particular sp ecies of
algae in the w ater column, the exact tra jectory of the v ehicles ma y not matter as m uc h as ho w m uc h
information they are obtaining at p ossible sampling lo cations. The curren t w ork has pro vided a
32 CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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A daptiv e Sampling with A UV s Stephanie Kemna
go o d framew ork to start in v estigating all these dieren t kinds of topics related to adaptiv e formation
con trol for heterogeneous aquatic rob ot teams.
2.7 Conclusion
This c hapter describ ed a new metho d for adaptiv e formation con trol. By com bining ideas from
dieren t formation con trol approac hes, w e dev elop ed a exible metho d, whic h allo ws v ehicles to
switc h b et w een formations, giv en en vironmen tal constrain ts. The heterogeneous team set-up enables
easy deplo ymen t and con trol of the rob ots, allo wing scien tists to con trol a whole team of rob ots b y
only con trolling one. F or lak es and o ceans, the bath ymetry or lo cation of (dynamic) ob jects ma y
not b e kno wn a priori. In suc h cases, the presen ted approac h will mak e it p ossible to safely deplo y
a team of rob ots to sample the en vironmen t, without requiring con tin uous sup ervision or remote
con trol. Results conrm the p oten tial of the presen ted approac h. V ehicles can eectiv ely c hange
b et w een formations, without cen tralized con trol and without comm unication o v erhead.
CHAPTER 2. COORDINA TED SAMPLING THR OUGH F ORMA TION
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33
3 | An Introduction to Informative Adaptive
Samplng
In the previous c hapter w e discussed an en vironmen tal sampling approac h whic h used a team of
heterogeneous rob ots for sampling a lak e, in formation. While the results sho w ed the approac h
to b e an eectiv e and robust approac h for formation con trol, a deep er question arises: In ho w
far do w e care ab out the exact mo v emen ts of the v ehicles, v ersus the data they gather?. In our
applied researc h, w e should nev er forget the end user and their problems and desires. In the case of
en vironmen tal sampling, the end user is a biologist, o ceanographer or other en vironmen tal scien tist,
who is most in terested in the measuremen ts made as a data pro duct. In most cases, they will not
care m uc h ab out ho w w e con trol our rob ots, as long as w e giv e them the most informativ e data on
what they are trying to observ e or mo del. T o that end, the fo cus of this thesis is shifting to the
eld of informativ e sampling.
In informativ e sampling, w e use information-theoretic metrics in our motion planning to deter-
mine the most informativ e sampling lo cations for the mo del that the v ehicles are trying to construct.
This c hapter pro vides a brief history of informativ e sampling, and explains the basic concepts. It
serv es as an in tro duction to the subsequen t c hapters, i.e. Chapter 4 - 7. In those c hapters w e will
not rep eat this theory , and will only describ e related w ork not discussed y et and relev an t to those
c hapters.
3.1 Informative Sampling & Adaptive Informative Sampling
Single-rob ot informative sampling w as pioneered b y Guestrin, Krause, and Singh (Guestrin et al.,
2005, Krause et al., 2005, Singh et al., 2007). Their approac h w as to use Gaussian Pro cess (GP)
regression (Rasm ussen and Williams, 2006) to mo del the en vironmen t. On top of that, they used
information-theoretic criteria, suc h as m utual information (Guestrin et al., 2005), to determine
whic h p ossible sampling lo cations w ould b e most informativ e for the GP mo del. Section 3.2 will
further explain the ideas b ehind this approac h. They used these found sampling lo cations in sev eral
approac hes; for deplo ying sensor systems (Krause et al., 2005) and with a path planning approac h
for commanding (m ultiple) rob ots (Singh et al., 2007). Their approac h w as fully o-line: First they
w ould mak e, or ha v e, a GP mo del, and then they w ould use the mo del to plan where to deplo y
sensors or rob ots.
This c hapter incorp orates Theory and Related W ork sections regarding Gaussian Pro cess regression from Kemna
et al. (2016), Kemna et al. (2017), and Kemna and Sukhatme (2018).
34
A daptiv e Sampling with A UV s Stephanie Kemna
When path planning happ ens on-line, during execution, and new data is incorp orated, then this
is called adaptive sampling . Lo w et al. (2008) extended up on the w orks of Guestrin, Krause and
Singh, b y dev eloping an online, adaptiv e approac h, i.e. adaptive informative sampling . He used
a dynamic programming approac h for path planning, based on data gathered so far. Singh et al.
(2009b) also extended their former approac hes in to a nonm y opic adaptiv e informativ e path planning
approac h. They ac hiev ed adaptiv e sampling b y com bining their former sensor placemen t approac h
with a path planning approac h based on recursiv e greedy (Chekuri and PÆl, 2005), and a replanning
strategy .
Lo w et al. (2008) used b oth Gaussian Pro cesses (GPs) and log-Gaussian Pro cesses (`GPs)
for mo deling the en vironmen t. `GPs are a v ariation on GPs, where the data is assumed to
follo w a lognormal distribution, rather than a normal distribution. In the case of en vironmen tal
sampling, it should b e noted that measuremen ts tak en in a eld with biological phenomena suc h as
hotsp ots, i.e. a eld with a couple areas of high v alue measuremen ts, t ypically follo w a log-normal
distribution (Cro w and Shimizu, 1988). Therefore the `GP is a b etter t for the kind of mo dels w e
are in terested in. On top of the `GP mo del, Lo w used the exp ected sum of p osterior v ariances and
p osterior map en trop y as information-theoretic criteria (Lo w et al., 2009c). A dynamic programming
approac h w as used in single- and m ulti-rob ot path planning.
As is clear from these seminal w orks, the t ypical steps in adaptiv e informativ e sampling are as
follo ws:
1. Construct a mo del of the en vironmen t, using e.g. a m ultiv ariate normal distribution, Ba y esian
regression, Gaussian Pro cess regression, or a linear com bination of a set of basis functions.
2. Cho ose an information-theoretic metric for the mo del, e.g. sum of p osterior v ariances, en trop y ,
or m utual information.
3. Cho ose a path planning approac h, e.g. lo cal greedy , global greedy , recursiv e-greedy (Chekuri
and PÆl, 2005), dynamic programming, Mark o v Decision Pro cess (MDP), Rapidly exploring
Random T ree (RR T), Probabilistic RoadMap (PRM), etc.
Section 3.4 lists related w orks and their c hoices for eac h of these steps.
3.2 Gaussian Process regression
Gaussian Pro cess (GP) regression (Rasm ussen and Williams, 2006) is a common metho d for creating
en vironmen tal mo dels of sampled spatial data (Lo w et al., 2009c, Singh et al., 2007), kno wn in
geostatistics as Kriging. GP regression is a non-parametric mo deling tec hnique, where the GP is
completely sp ecied b y its mean function (i.e. prior) and its co v ariance matrix (i.e. k ernel). In GP
regression a signal is estimated b y estimating its mean and v ariance, based on measuremen ts z at
lo cations (inputs) x, where xPR
2
. Let Z
x
denote a GP . The GP is initialized with a prior mean
and co v ariance matrix, also kno wn as the k ernel. The estimates of the mean and v ariance, t ypically
called the pr e dictive or p osterior mean and v ariance, are calculated as (Rasm ussen and Williams,
2006):

Z
X
kpX

;XqkpX;Xq
1
z (3.1)
CHAPTER 3. AN INTR ODUCTION TO INF ORMA TIVE AD APTIVE
SAMPLNG
35
Stephanie Kemna A daptiv e Sampling with A UV s

2
Z
X
kpX

;X

qkpX

;XqkpX;Xq
1
kpX;X

q (3.2)
where kp;q is the GP’s k ernel, X are the training inputs, and X

are the test inputs.
While a GP (and `GP) is a non-parametric mo del, its p erformance is aected b y h yp erpa-
rameters, whic h are the k ernel’s parameters. These are t ypically estimated from the data using
gradien t-based optimization (Rasm ussen and Williams, 2006). W e refer to ? for a more detailed
explanation of GP regression.
In this w ork, w e use the standard approac h of taking a zero-mean prior and a squared exp onen tial
co v ariance function, or k ernel (Rasm ussen and Williams, 2006). The SE co v ariance function is giv en
b y (Rasm ussen and Williams, 2006):
kpx;x
1
q
2
f
expt
1
2l
2
|xx
1
|
2
u (3.3)
where x and x
1
are t w o training sample lo cations, xPR
2
,
2
f
is the signal v ariance (or amplitude),
and l is the k ernel’s length scale.
2
f
and l are h yp erparameters. W e com bine the SE k ernel
with a white noise k ernel, to b etter mo del the exp ected noise in the data. This k ernel has one
h yp erparameter
2
n
, the noise v ariance.
F or h yp erparameter optimization w e use resilien t bac kpropagation (Blum and Riedmiller, 2013)
for the early w ork, Chapter 4, 6, and 7, and the conjugate gradien t metho d for the later w ork
in Chapter 5, 8, and 9. F or the w ork in Chapter 4 and Chapter 6 w e run a pilot surv ey for
initial h yp erparameter optimization, whic h is a lo w resolution la wnmo w er, run b oth v ertically and
horizon tally o v er the surv ey area. F or the w ork in Chapter 7 w e do not run a pilot, the v ehicles
start with going to a random lo cation in the surv ey area. The rst h yp erparameter optimization is
done at the rst surfacing ev en t. F or Chapter 5 w e used a ‘cross pilot’, where the v ehicle tra v els in a
cross-wise manner to the corners of the surv ey area at the start of adaptiv e sampling. In Chapter 8
w e explore the design of in tegrated pilot surv eys, i.e. what mo v emen ts are b est used for starting
adaptiv e sampling, to collect represen tativ e data for correct estimation of the h yp erparameters.
Finally in Chapter 9 w e use the softmax-based pilot from Chapter 8.
W e use log-Gaussian Pro cesses (`GPs), similar to (Lo w et al., 2009c), whic h are used when
the data b etter ts a log-normal distribution, as is often the case for biological data (Cro w and
Shimizu, 1988). F ormally , let Y
x
denote an `GP , mo deling the sensor v alue y
x
at lo cation xPX ,
whereX R
2
, i.e. w e sample in the plane. Let Z
x
log
e
Y
x
, denote a GP . Then w e can create
the `GP using GP regression b y utilizing the fact that z
x
log
e
y
x
. The GP’s p osterior mean and
v ariance,
Zx|d
i
and
2
Zx|d
i
(for sampled data d
i
), can then b e used to calculate the p osterior mean
and v ariance for the `GP (Lo w et al., 2009c):

Yx|d
i
expt
Zx|d
i

2
Zx|d
i
{2u (3.4)

2
Yx|d
i

2
Yx|d
i
pexpt
2
Zx|d
i
u1q (3.5)
This p osterior mean and v ariance represen t the mo del’s estimation of the data v alue, and the
uncertain t y in this estimate. These v alues can then b e used, in tegrated in to information-theoretic
metrics, to let the v ehicle decide where to sample.
36 CHAPTER 3. AN INTR ODUCTION TO INF ORMA TIVE AD APTIVE
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A daptiv e Sampling with A UV s Stephanie Kemna
3.3 Path planning
The goal of the v ehicle’s actions is to reduce the uncertain t y in the mo del. As our information-
theoretic metric, w e use p osterior en trop y , and w e use the maxim um p osterior en trop y criterion on
our created`GP to nd the next w a yp oin t. As deriv ed in (Lo w et al., 2009c), this can b e expressed
in terms of the GP p osterior mean
Z
and v ariance
2
Z
as:
H

Y
x
i1
|d
i

log
b
2e
2
Z
x
i1
|d
i

Z
x
i1
|d
i
(3.6)
where d
i
is the already sampled data.
F or path planning, w e tak e a globally greedy approac h to nding future sampling lo cations,
similar to (Krause et al., 2008, Singh et al., 2007), based on the `GP mo del. A set of lo cations for
p oten tial w a yp oin ts is generated at the start of a mission from a 10m spaced grid o v er the area.
T o decide where a v ehicle should sample, it calculates the GP’s predictiv e mean and v ariance for
previously un visited lo cations. It then calculates the `GP’s p osterior en trop y , and sets a w a yp oin t at
the lo cation with highest en trop y . The single b est lo cation, whic h has not b een visited y et, an ywhere
in the surv ey area, is c hosen as the next w a yp oin t. F or the `GP , as follo ws from Equation (3.6),
this means lo cations with high p osterior v ariance (to reduce it) and high exp ected sensor v alues
(in teresting areas). Th us the A UV optimizes b oth for mo del uncertain t y as w ell as high exp ected
means, p oten tial algal blo oms. This approac h w as tak en b ecause it is simple, y et at the same time
non-m y opic, i.e. it a v oids the problem of lo cal minima.
3.4 Related work in informative (adaptive) sampling
There are man y recen t w orks that build on the seminal w orks of Guestrin, Krause, Singh and Lo w.
These can b e dieren tiated in man y w a ys. W e w ould lik e to p oin t out some of the dierences
in applications, approac hes tak en, and researc h fo ci. There are a couple of main dierences in
approac hes, related to foreseen applications, e.g.:
eld estimation vs. target searc h vs. mapping (of structured en vironmen ts)
m y opic vs. non-m y opic sensors
o-line vs. on-line
single vs. m ulti-rob ot
W e fo cus our researc h and related w orks discussion on approac hes that deal with eld estimation
using m y opic sensors.
T able 3.1 and T able 3.2 pro vide a listing of related w orks in informativ e sampling for eld
estimation with m y opic sensors. T able 3.1 sho ws the dieren t mo deling approac hes, metrics,
and path planning approac hes. T able 3.2 divides the pap ers b y oine and online approac hes,
decen tralized and cen tralized planning, and p oin ts out the researc h fo cus of eac h pap er. More
details ab out m ulti-rob ot w ork will b e discussed in Chapter 7.
As is clear from T able 3.2, most related w orks ha v e fo cused on path planning. Appro ximately
a quarter ha v e fo cused on m ulti-rob ot applications. In this w ork w e are particularly in terested
CHAPTER 3. AN INTR ODUCTION TO INF ORMA TIVE AD APTIVE
SAMPLNG
37
Stephanie Kemna A daptiv e Sampling with A UV s
in further exploring m ulti-rob ot co ordination for adaptiv e informativ e sampling. Chapter 7 will
further discuss related w orks in m ulti-rob ot informativ e sampling. The most recen t related w orks
are discussed in Chapter 5 and Chapter 9.
1
RIG, Rapidly exploring Information Gathering, com bines ideas from RR T, RR G (Rapidly exploring Random
Graph) and PRM (Hollinger and Sukhatme, 2014).
38 CHAPTER 3. AN INTR ODUCTION TO INF ORMA TIVE AD APTIVE
SAMPLNG
A daptiv e Sampling with A UV s Stephanie Kemna
pap er mo del metric path planning approac h
Guestrin et al.
(2005)
GP m utual information greedy selection
Krause et al. (2005),
Singh et al. (2009b)
GP m utual information pSPIEL (greedy selection
within decomp osition space)
Krause and Guestrin
(2007), Krause et al.
(2008)
GP
(non-stationary)
m utual information appro ximation algorithm
(greedy)
Singh et al. (2007,
2009a)
GP
(non-stationary)
m utual information eMIP (recursiv e greedy) &
sequen tial allo cation (m ulti-
rob ot)
Lo w et al. (2008,
2009a,b,c)
GP , `GP sum of p osterior
v ariances &
p osterior
map en trop y
dynamic programming
Binney et al. (2013,
2010)
GP a v erage reduction in
v ariance
recursiv e greedy (generalized)
Sc h w ager et al.
(2011, 2014)
linear com bina-
tion of m static
basis functions
function appro xima-
tion error
TSP tour & cen troidal
V oronoi con troller
Thompson et al.
(2011)
GP en trop y recursiv e greedy , lo cal horizon
Soltero et al. (2012,
2014)
linear com b o of
a set of kno wn
basis functions
mass-momen t
appro ximation
adaptiv e con troller (on
w a yp oin ts)
Cao et al. (2013) GP en trop y &
m utual information
dynamic programming
P atten et al. (2013) GP m utual information greedy subset selection & TSP
tour, decen tralized v oronoi
F rolo v et al. (2014) b est linear
un biased
estimator
mean squared
p osterior error
la wnmo w er, A* & genetic
algorithm
Garg and A y anian
(2014)
GP en trop y TSP tour
Hitz et al. (2014) GP m utual information dynamic programming (lev el
set estimation)
Hollinger and
Sukhatme (2014)
GP unsp e cie d RIG
1
-{tree, graph,
roadmap}
Ouy ang et al. (2014) DPM-GP p osterior join t
en trop y
greedy + co ordination graph
Ma et al. (2016a,b) GP m utual information hierarc hical planner & TSP
solv er & MDP for curren ts
T able 3.1: Literature review comparison based on mo deling and path planning approac hes. Sorted
b y y ear of publication, then alphab etical. TSP: T ra v eling Salesp erson Problem
CHAPTER 3. AN INTR ODUCTION TO INF ORMA TIVE AD APTIVE
SAMPLNG
39
Stephanie Kemna A daptiv e Sampling with A UV s
pap er on-/oine de-/cen tralized researc h fo cus
Guestrin et al. (2005) oine cen tralized mac hine learning
Krause et al. (2005) oine cen tralized path planning
Krause and Guestrin
(2007), Krause et al.
(2008)
oine cen tralized theory , ev aluation
Singh et al. (2007,
2009a)
oine cen tralized m ulti-rob ot path planning
Binney et al. (2013,
2010)
oine cen tralized
(1 ASV)
path planning
P atten et al. (2013) oine decen tralized m ulti-rob ot path planning
F rolo v et al. (2014) oine cen tralized path planning
Hollinger and
Sukhatme (2014)
oine cen tralized
(1 ASV)
path planning
Lo w et al. (2008,
2009a,b,c, 2012)
online (de)cen tralized adaptivit y , path planning,
m ulti-rob ot
Singh et al. (2009b) online cen tralized adaptivit y , path planning
Sc h w ager et al. (2011,
2014)
online decen tralized analysis & con trol design
Thompson et al. (2011) online cen tralized
(1 A GV)
eld ops, ‘science on the y’
Soltero et al. (2012,
2014)
online decen tralized con trol la ws (path planning),
m ulti-rob ot
Cao et al. (2013) online cen tralized metrics
Garg and A y anian
(2014)
online decen tralized b elief distribution o v er
h yp erparameters
Hitz et al. (2014) online cen tralized
(1 ASV)
lev el set estimation
Ouy ang et al. (2014) online decen tralized learning, decen tralization,
m ulti-rob ot
Ma et al. (2016a,b) online cen tralized path planning, m ulti-rob ot
planning
T able 3.2: Literature review comparison based on planning c haracteristics and researc h fo cus. Sorted
b y on-/oine, then y ear.
40 CHAPTER 3. AN INTR ODUCTION TO INF ORMA TIVE AD APTIVE
SAMPLNG
4 | Single-Robot Adaptive Informative Sampling
The previous c hapter, 3, explained the basic premise of adaptiv e informativ e sampling. In this
c hapter, w e explain the basic sim ulation set-up, and v erify single v ehicle adaptiv e informativ e
sampling p erformance. Our adaptiv e informativ e sampling approac h consists of the follo wing
comp onen ts: On eac h v ehicle, w e rst use GP regression to create an `GP mo del of the en vironmen t,
from measuremen ts tak en b y the v ehicle (as explained in Section 3.2). Then w e use a greedy metho d
for selecting w a yp oin ts, based on the p osterior map en trop y of the mo del that is b eing built, to
decide where the v ehicle should sample next (as explained in Section 3.3). F or all exp erimen ts, w e
ev aluate mo deling p erformance based on a v erage p erformance across sim ulations.
4.1 Simulation set-up & Implementation
W e sim ulate up to t w o underw ater v ehicles, whic h run at 1.5 m/s, and at v e meters depth while
sampling. The v ehicles are sim ulated using the MOOS-IvP middlew are (Benjamin et al., 2010),
whic h includes a simple sim ulation of v ehicle dynamics and PID con trol. MOOS-IvP enables
b eha vior-based autonom y , and w e use the follo wing standard b eha viors for our mission; w a yp oin t,
loiter, constan t depth, and (in ter-v ehicle) collision a v oidance (Benjamin et al., 2010). Eac h v ehicle
indep enden tly samples data, creates an `GP mo del, and runs nds next w a yp oin ts based on `GP
predictions and uncertain t y , to decide where to go next. Thereb y w e k eep the adaptiv e sampling
approac h completely decen tralized.
In order to sim ulate the biological data, w e create a 3-D grid of data (400x200x15m, see
Figure 4.1) that incorp orates t w o 3-D Gaussians and additiv e Gaussian noise, to sim ulate (an
area in) a lak e with algal blo oms. W e sample in the horizon tal plane, at a certain depth, and mak e
a 2-D GP mo del. The grid space is o v er a pre-sp ecied area of in terest, with 10 m spacing for the
longitude and latitude axes, and 0.5 m spacing for the depth axis. The noise amplitude on the
sim ulated data is 20 p ercen t of the data v alue amplitude. This data v alue amplitude is set to 40, as
a pro xy for high Chloroph yll g/L v alues. Note that the data v alue distribution for this eld will
follo w a log-normal distribution. W e run our sim ulations on this one sim ulated eld only , suc h that
w e can directly compare mo dels and their p erformance b et w een the dieren t set-ups.
Figure 4.2 sho ws an example horizon tal slice from the sim ulated data, at v e meters depth. T o
sim ulate a sensor, the A UV retriev es the closest (Euclidean distance) data p oin t from the sim ulated
grid, and w e add Gaussian noise ( 1:5) to mo del sensor noise. Data is sampled at a frequency
This c hapter is mostly a subset of A daptiv e Informativ e Sampling with Autonomous Underw ater V ehicles:
A coustic v ersus Surface Comm unications (Kemna et al., 2016).
41
Stephanie Kemna A daptiv e Sampling with A UV s
Figure 4.1: Example surv ey area (y ello w
rectangle) in a lak e, grid size 100m.
Figure 4.2: Example grid sim ulated data at
5m depth, for the 400x200m surv ey area
sho wn in Figure 4.1.
of 1 Hz.
T o estimate the h yp erparameters for the `GP , w e run a pilot surv ey on the A UV b efore ev ery
exp erimen t. This surv ey is a coarse la wnmo w er (100m trac k spacing), run horizon tal and v ertical
o v er the surv ey area. When run b y t w o v ehicles, the area is split v ertically , and eac h v ehicle
runs the pilot surv ey o v er one half (200x200m). F or m ulti-v ehicle parallel and timed data sharing
approac hes, the data measuremen ts are shared after the pilot, for acomms approac hes measuremen ts
are shared con tin uously during the pilot surv ey .
4.2 Results
W e compare the mo deling p erformance b et w een dieren t t yp es of mission set-ups using Ro ot-Mean
Squared Error (RMSE) and negativ e log-lik eliho o d (NLL). The RMSE compares the predictiv e
means from the`GP , created on eac h v ehicle, to the sim ulated data mo del from whic h measuremen ts
are tak en (with sim ulated sensor noise). The NLL tak es in to accoun t not only the predictiv e mean,
but also the predictiv e v ariance, while comparing to the sim ulated data mo del. Ov erall, w e see
increases in NLL b ecause the incoming data measuremen ts mak e the mo del deviate from it’s initial
estimate, i.e. the state of the initial h yp erparameter optimization. T ypically , w e do see a drop
in NLL after the nal h yp erparameter optimization ( t 12 for single A UV, t 7 for t w o A UV
exp erimen ts). F or all p erformances, w e a v erage o v er ten sim ulation runs. Giv en our decen tralized
set-up, eac h v ehicle has their o wn GP , and th us w e rep ort the a v erage p erformances p er v ehicle.
T o b e able to compare the RMSE and NLL as eac h surv ey progresses, w e store the GP’s p osterior
mean and v ariance for the sample grid ev ery 600 seconds. The GP p erformance is rst ev aluated
after the rst h yp erparameter optimization ( t 1), and from then on w ards ev ery 600 seconds.
F or all Figures, the last time step is the time step after the nal h yp erparameter optimization
(t 12 for single A UV, t 7 for t w o A UV exp erimen ts). As men tioned in Section 6.3.2, w e end the
adaptiv e sampling after the same amoun t of time has passed as it tak es to do the high resolution
la wnmo w er surv ey . Giv en that the last time step is after the nal h yp erparameter optimization,
it t ypically sho ws a bigger c hange compared to the time steps b efore. Note that, t ypically , for a
la wnmo w er surv ey one w ould not need to run a separate pilot for h yp erparameter optimization, if
one can w ait un til the end of the surv ey for the mo del. Ho w ev er, considering in termediate access to
42 CHAPTER 4. SINGLE-R OBOT AD APTIVE INF ORMA TIVE SAMPLING
A daptiv e Sampling with A UV s Stephanie Kemna
(a) Ro ot-Mean Squared Error (RMSE) (b) Negativ e Log-Lik eliho o d (NLL)
Figure 4.3: RMSE and NLL a v erages of ten sim ulations for 1 A UV running la wnmo w er and adaptiv e
surv eys.
the mo del, robustness to v ehicle failures, and to b e able to do this time-based comparison, w e run
the same pilot surv ey b efore the la wnmo w er surv eys with h yp erparameter optimization.
4.2.1 Single AUV results; lawnmo wer vs. adaptive
Figure 4.3 sho ws the single A UV results, where w e compare the `GP qualit y for ten sim ulations
of la wnmo w er and adaptiv e surv eys. Figure 4.3a sho ws the ro ot mean squared error (RMSE)
b et w een the sim ulated data mo del and the v ehicle’s `GP mo del. On the righ t, Figure 4.3b sho ws
the negativ e log-lik eliho o d (NLL) of the created `GP mo del. The NLL also incorp orates p osterior
v ariances, whilst RMSE only ev aluates p osterior means.
W e can see that running adaptiv e sampling instead of a standard la wnmo w er surv ey consisten tly
decreases the RMSE more quic kly , and the negativ e log lik eliho o d gro ws more slo wly and is lo w er
at an y time. This conrms the result found in related w ork (Lo w et al., 2009c, Singh et al., 2007),
whic h sho w ed the b enets of adaptiv e sampling o v er running standard la wnmo w er surv eys. The
quic k reduction of RMSE for adaptiv e sampling suggests that the adaptiv e sampling surv ey could
p oten tially nish earlier than the la wnmo w er surv ey .
4.3 Discussion & F uture work
Ov erall, w e ha v e sho wn the b enets of adaptiv e informativ e sampling o v er running standard la wn-
mo w er surv eys. Sim ulation exp erimen ts sho w ed clear impro v emen ts in mo del error, as w ell as an
o v erall impro v emen t in mo del uncertain t y . F or future w ork, it w ould b e in teresting to in v estigate
the p erformance when c hanging curren t greedy metho d of w a yp oin t selection to a full path planning
approac h. F urthermore, it w ould b e in teresting to see whether the adaptiv e sampling can p erform
as w ell when w e do not run a pilot surv ey in adv ance. Finally , it w ould b e in teresting to ev aluate
p erformance for running missions with m ultiple v ehicles.
CHAPTER 4. SINGLE-R OBOT AD APTIVE INF ORMA TIVE SAMPLING 43
5 | Field T esting of Single-Robot Adaptive In-
formative Sampling
In the previous c hapter w e conrmed the b enets of adaptiv e informativ e sampling o v er running
standard la wnmo w er surv eys for en vironmen tal monitoring. In order to c hec k the feasibilit y of these
approac hes for eld exp erimen ts, the single rob ot adaptiv e informativ e sampling co de w as tested
with our EcoMapp er A UV. This c hapter pro vides information on the trials and the results for eld
testing of the A UV during the spring and summer of 2017.
5.1 Introduction
The use of autonomous underw ater v ehicles (A UV s) is b ecoming more common for sampling lak es
and o ceans. A UV s can mak e measuremen ts of ph ysical prop erties of the w ater or biology , suc h as
w ater temp erature, o xygen saturation, or Chloroph yll abundance for algal blo oms. One tec hnique
for enabling A UV s to gather useful data is through informative sampling , also kno wn as informative
p ath planning . In informativ e sampling, a mo del is created of the en vironmen t and information-
theoretic metrics are used on the mo del to collect informativ e data. When this is done on-line, while
the mo del is b eing created, this is called adaptive informative sampling (AIS).
Previous w orks, e.g. Lo w et al. (2009c), Singh et al. (2007) ha v e demonstrated the b enets of AIS
o v er running standard co v erage metho ds, suc h as la wnmo w er surv eys. W e are particularly in terested
in using AIS to create spatial mo dels. T o this end, w e ran eld trials to assess the feasibilit y of
running AIS on b oard a commercial-o-the-shelf A UV. Our con tributions are that w e:
demonstrate the feasibilit y of creating a Gaussian Pro cess mo del on b oard an A UV, and using
it for adaptiv e sampling,
prop ose an approac h for quan titativ e analysis of adaptiv e sampling in the eld,
sho w that reasonable mo dels of the en vironmen t can b e created in half the time it tak es to
run a full co v erage surv ey o v er the area.
This c hapter is largely a preprin t of: On-b oard A daptiv e Informativ e Sampling for A UV s: a F easibilit y Study
(Kemna et al., 2018a).
44
A daptiv e Sampling with A UV s Stephanie Kemna
5.2 Modeling Approach
F or mo deling algal blo oms, an A UV needs to create a 2D mo del of a spatial phenomena. In
informativ e sampling, there are t ypically three steps:
1. construct a mo del of the en vironmen t,
2. c ho ose an information-theoretic metric, and ev aluate the mo del,
3. based on this ev aluation, c ho ose lo cations for sensor deplo ymen t or rob ot path planning.
A common metho d for spatial mo deling is Gaussian Pro cess (GP) regression (Rasm ussen and
Williams, 2006). In GP regression a signal is mo deled b y estimating its mean and v ariance based on
measuremen ts , using a pre-sp ecied k ernel, or co v ariance function. F ollo wing Lo w et al. (2009c), w e
use a log Gaussian Pro cess (`GP) to mo del the eld: the v ehicle tak es the log of the measuremen ts
b efore incorp orating them in to the GP . This approac h considers that biological data from elds with
‘hotsp ots’ tend to follo w a log-normal distribution, due to large areas with lo w v alues and small
areas with high v alues (Cro w and Shimizu, 1988).
W e follo w the notation and c hoices previously in tro duced in Kemna et al. (2016), Lo w et al.
(2009c)
1
: F ormally , let Y
x
denote an `GP , mo deling the sensor v alue y at lo cation x P R
2
, i.e.
w e sample in the plane. Let Z
x
log
e
Y
x
, denote a GP . Then w e can create the `GP using GP
regression b y utilizing the fact that z
x
log
e
y
x
. The GP’s predictiv e mean and v ariance,
Zx
and

2
Zx
(dened in Rasm ussen and Williams (2006)), can then b e used to calculate the predictiv e mean
and v ariance for the `GP (Lo w et al., 2009c):

Yx
expt
Zx

2
Zx
{2u (5.1)

2
Yx

2
Yx
pexpt
2
Zx
u1q (5.2)
F or the GP’s k ernel, or co v ariance function, w e use a com bination of the isotropic squared
exp onen tial k ernel (Rasm ussen and Williams, 2006) and a white noise co v ariance function. The SE
co v ariance function is giv en b y (Rasm ussen and Williams, 2006):
kpx;x
1
q
2
f
expt
1
2l
2
|xx
1
|
2
u (5.3)
where x and x
1
are t w o training sample lo cations, xPR
2
,
2
f
is the signal v ariance (or amplitude),
and l is the k ernel’s length scale.
2
f
and l are h yp erparameters. W e com bine the SE k ernel
with a white noise k ernel, to b etter mo del the exp ected noise in the data. This k ernel has one
h yp erparameter
2
n
, the noise v ariance.
The GP computes for an y lo cation the exp ected v alue (predictiv e mean) and mo del uncertain t y
(predictiv e v ariance). These v alues can b e used with information-theoretic metrics. W e t ypically
1
In this c hapter, for ease of reading w e ha v e left out an explicit men tion of dep endence on sampled data di , e.g.

2
Zx
means
2
Zx|d
i
. All calculations are done while there is some data in the GP , using all data collected so far, in an
on-line fashion.
CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
SAMPLING
45
Stephanie Kemna A daptiv e Sampling with A UV s
use an`GP and its p osterior map en trop y: As deriv ed in Lo w et al. (2009c), the `GP’s en trop y can
b e expressed in terms of the GP’s predictiv e mean
Zx
and v ariance
2
Zx
as:
HrY
x
s log
b
2e
2
Zx

Zx
(5.4)
F or deciding where the A UV should sample, the A UV selects w a yp oin ts. While the GP is
con tin uous, predictions from the GP need to b e calculated for a sp ecic input, in our case for
longitude, latitude lo cations. W e generate a set of lo cations from a 10m spaced grid o v er the area.
F or the subset of un visited p oten tial w a yp oin t lo cations, the A UV calculates the p osterior map
en trop y . The lo cation with the highest en trop y is c hosen as the next w a yp oin t. Giv en Equation (5.4)
this means that the A UV go es to lo cations with high mo del uncertain t y and/or high exp ected means,
i.e. p oten tial algal blo oms.
F or one eld run, w e used a standard Gaussian Pro cess, rather than the `GP . The en trop y for
the regular GP is:
HrZ
x
s log
b
2e
2
Zx
(5.5)
whic h is dep enden t only on the predictiv e v ariance. In terms of optimization, w e com bine the GP’s
en trop y with the predictiv e mean. The predictiv e mean is m ultiplied b y a w eigh t factor of 0:25 and
added to the GP’s p osterior en trop y .
5.3 Related W ork
Most related w orks in informativ e sampling use sim ulated data or real datasets, e.g. Krause et al.
(2008), Lo w et al. (2012), Ouy ang et al. (2014), and/or run calculations o-line, e.g. Binney et al.
(2013), Hollinger and Sukhatme (2014), Krause and Guestrin (2007). W e briey discuss related
w orks that ran adaptiv e informativ e sampling in the eld. T o the b est of our kno wledge, there
are no prior w orks running a GP mo del on b oard of an A UV, including running h yp erparameter
optimization and GP prediction calculations. There are sev eral w orks where AIS w as run on b oard
an autonomous surface v essel (ASV) (Hitz et al., 2014, 2017, Ma et al., 2018), and a couple where
AIS runs on b oard an autonomous ground v ehicle (A GV) (Sc h w ager et al., 2014, Thompson et al.,
2011).
Thompson et al. (2011) describ ed the use of AIS for a planetary exploration rob ot, surv eying
a part of Am b o y crater in California, USA. They test an AIS approac h that uses GP regression,
maximizing for en trop y and using recursiv e-greedy path planning tec hniques, and compare this
against other metho ds, suc h as co v erage and transects. Man ually lab eled o v erigh t images w ere used
for the ground truth. The sp ecs of their on-b oard computer are not listed. Sc h w ager et al. (2014)
dev elop ed a distributed con trol algorithm for adaptiv e sensor co v erage of an en vironmen t. Instead
of using Gaussian Pro cess regression, they appro ximated the eld using a linear com bination of
Gaussian basis functions. They fo cused on con trolling all rob ots for optimal co v erage. Exp erimen ts
w ere run indo ors, mo deling a ligh t in tensit y eld using a team of iRob ot Creates with Asus Eee PC
1015PX.
In terms of recen t w orks using ASV s for en vironmen tal mo deling, Hitz et al. (2014) sho w ed an
ASV that adaptiv ely sampled along a transect, where the mo del w as created in 2D o v er the v ertical
space. They ran 3 eld exp erimen ts. T o ha v e a ground truth for comparison, they sampled along
46 CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
SAMPLING
A daptiv e Sampling with A UV s Stephanie Kemna
a uniform grid b efore and after the adaptiv e mission. Hitz et al. (2017) extended their prior w ork,
b y creating an adaptiv e sampling system that can reason o v er con tin uous spaces, sampling in 3D
b y ha ving the ASV tra v el in 2D while using a sensor on a winc h. They ran 3 eld exp erimen ts,
in dieren t mon ths of the y ear. No ground truth w as used for the eld testing, b ecause of the
temp oral v ariabilit y of the cy anobacteria presence. Ma et al. (2018) recen tly describ ed an approac h
for mo deling en vironmen tal phenomena that can handle spatio-temp oral v ariabilit y , utilizing sparse
GP tec hniques for reducing computational complexit y . They mostly ev aluated p erformance in
sim ulations, but also tested the ASV AIS p erformance against lak e bath ymetry during a single
eld trial, using an earlier v ersion of the in terp olated lak e bath ymetry data that w e use in this
w ork. The ASV used has a Mac mini with a quad core In tel pro cessor and 16 GB RAM, whic h is
more p o w erful than our A UV’s computer, as detailed in the next section.
5.4 Field T esting Set-up
In order to c hec k the feasibilit y of running AIS on b oard an A UV, w e tested single rob ot adaptiv e
informativ e sampling co de with our EcoMapp er A UV. Section 4.1 describ ed ho w sim ulations are
run using the MOOS-IvP rob ot middlew are (Benjamin et al., 2010). This middlew are mak es it easy
for us to run the same pro cesses in the eld as in sim ulation, switc hing out the v ehicle sim ulator for
the fron tseat computer in terface. W e use the libgp op en source library (Blum, 2016) for creating a
Gaussian Pro cess mo del.
5.4.1 The autonomous underwater vehicle
Figure 5.1: USC’s EcoMapp er A UV. Photographer: Luk e Fisher
The EcoMapp er A UV, sho wn in Figure 5.1, is a 5:8" diameter A UV. It is an OceanServ er Iv er2
v ehicle, whic h has b een extended b y YSI with a sensor head (YSI Incorp orated and OceanServ er,
2008). Our sp ecic v ehicle is appro ximately 67" or 170cm long, with an in-air w eigh t of ap-
pro ximately 53 lbs or 24 kg. Our curren t sensor suite includes sensors to measure: temp erature,
salinit y , pressure or depth, pH, Chloroph yll via uorescence, Blue-Green Algae or Cy anobacteria
via uorescence, and dissolv ed o xygen. F urthermore it has a D VL (Doppler V elo cit y Log), whic h
also functions as an altimeter to measure the v ehicle’s altitude, whic h is equal to the lak e depth
when the v ehicle is run on the surface. The sensors sample at a rate of 1Hz , and w e skip erroneous
sensor data, i.e. negativ e v alues for Chloroph yll. The EcoMapp er A UV has t w o on-b oard computers,
whic h b oth ha v e an A TOM CPU with a single core pro cessor at 1:6 GHz, and 1 GB RAM. The
main v ehicle computer runs Windo ws XP Em b edded, for YSI’s and OceanServ er’s soft w are. The
pa yload computer runs Ubun tu 16.04. All soft w are dev elop ed for our researc h is run on the pa yload
computer. In comparison to standard w orkstations, it is therefore computationally limited.
CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
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Stephanie Kemna A daptiv e Sampling with A UV s
Figure 5.2: A UV eld exp erimen ts mission area, 300200m (left, y ello w rectangle), and the initial
cross tra jectory (righ t, white). Grid spacing is 50m. The A UV is sho wn at the deplo ymen t p oin t,
not to scale.
All eld tests w ere run at a w ater reserv oir in San Dimas. Figure 5.2 sho ws exp erimen tal set-up.
The A UV w as ask ed to create a 2D mo del of sensor measuremen ts for a 300 200m area, the
y ello w rectangle in Figure 5.2. The v ehicle started ev ery adaptiv e sampling run b y making a cross
tra jectory o v er the area, the righ t image in Figure 5.2. This tra jectory w as run to attempt collecting
represen tativ e data to correctly estimate the GP’s h yp erparameters. Chapter 8 further explores the
design of suc h ‘pilot surv eys’ used at the start of adaptiv e sampling. The GP mo del w as initialized
with h yp erparameters that w ere estimated based on rough estimates of the exp ected length scale,
signal and noise v ariance. The log of the h yp erparameters w as set to: 12:4292;0:4055;1:8971 for
length scale, signal and noise standard deviations resp ectiv ely . F or the length scale, an error w as
made in the calculation, as this w as mean t to b e set to 8:5 corresp onding to appro ximate 20m
but it w as set instead to 12:4292 corresp onding to appro ximately 0:4m. The h yp erparameters
are re-estimated ev ery 500 seconds using a conjugate gradien t metho d with 100 iterations, on a
subsampled v ersion of the GP , where the data is subsampled b y a factor of 4.
5.4.2 Lo cation and exp erimen tal set-up
All eld tests w ere run at the Puddingstone w ater reserv oir in San Dimas, California, USA. Figure 5.2
sho ws the exp erimen tal set-up. The A UV w as ask ed to create a 2D mo del of sensor measuremen ts
for a 300 200m area, the y ello w rectangle in Figure 5.2. The v ehicle started ev ery adaptiv e
sampling run b y making a cross tra jectory o v er the area, the white cross in the righ t image in
Figure 5.2. This tra jectory w as run to attempt collecting represen tativ e data to correctly estimate
the GP’s h yp erparameters from sampled data b efore adaptiv ely c ho osing w a yp oin ts. Kemna et al.
(2018b) further explored the design of suc h ‘pilot surv eys’ used at the start of adaptiv e sampling, if
no prior data is a v ailable.
W e ran t w o t yp es of missions; full and half duration. The full length w as based on ho w long
it tak es to run t w o la wnmo w ers o v er the area, one v ertical and one horizon tal (i.e. a grid) with
20m trac k spacing, whic h tak es appro ximately 90 min utes. In prior w orks w e claimed that adaptiv e
sampling can pro duce a go o d mo del more quic kly (Kemna et al., 2016). Therefore w e also ran eld
tests at half the mission duration, for appro ximately 45 min utes of adaptiv e sampling.
48 CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
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A daptiv e Sampling with A UV s Stephanie Kemna
Figure 5.3: Bath ymetry ground truth: in terp olated data from (unrelated) A UV missions run
b et w een August 2012 and Marc h 2017. Mission area outline sho wn in white.
5.4.3 Ground truth & analysis
Previously , w e ev aluated adaptiv e informativ e sampling p erformance using the ro ot-mean squared
error (RMSE) b et w een a sim ulated ground truth and the mo del created b y the sim ulated v ehicle. F or
these eld tests, w e ha v e no ground truth for biological sensor measuremen ts suc h as Chloroph yll.
It is hard to obtain a ground truth for m ulti-da y eld testing, b ecause phenomena suc h as algal
blo oms uctuate with time. One fairly static measuremen t in an y lak e or o cean is the bath ymetry
(bath y). W e comp osed a ground truth mo del from bath y measuremen ts, in terp olating o v er data
from unrelated A UV missions b et w een August 2012 and Marc h 2017, sho wn in Figure 5.3. This
bath ymetric mo del is used as the ground truth suc h that w e can ev aluate p erformance in terms of
RMSE across m ulti-da y eld tests.
The results in the next section are from missions run across 8 eld trips, whic h include: 3 full
90-min bath y runs, 7 short 45-min bath y runs, and 4 short 45-min runs for Chloroph yll (Chl). One
of the short bath y runs used the GP mo del, rather than the `GP mo del. F or all bath y runs, the
A UV is run on the surface of the lak e (depth = 0m), using its altitude measuremen ts to estimate
the lak e depth (bath ymetry). F or the Chl runs, the sampling depth w as determined eac h da y from
a pre-executed y o y o mo v emen t through the w ater column to estimate the depth of an algal blo om.
F or the four Chl sampling missions the v ehicle w as run at 2m, 8m, 8m and 7m depth.
5.5 Field T esting Results
In this section, w e list a couple examples of the created on-b oard mo dels, and sho w all mo dels
in the App endix. F or eac h created mo del, w e sho w the nal predictiv e mean
Yx
and predictiv e
v ariance
2
Yx
sampled along a grid across the area with 10m trac k spacing. Figure 5.4 sho ws a
mo del for a full bath ymetry run: for a full duration run the v ehicle gets a visually go o d estimate
CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
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Stephanie Kemna A daptiv e Sampling with A UV s
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 1
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 1
0.1
0.2
0.3
0.4
0.5
Pred. variance
Figure 5.4: Example full run bath y , `GP: predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 1
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 1
2
4
6
8
10
12
Pred. variance
Figure 5.5: Example half run bath y , `GP: predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 3
5
10
15
20
25
30
Chl ( g/L)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 3
1
2
3
4
5
6
Pred. variance
Figure 5.6: Example half run Chloroph yll, `GP: predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
on the bath ymetry , as compared to the ground truth in Figure 5.3. Figure 5.5 sho ws a mo del for a
short bath ymetry run, demonstrating that a half duration run creates a go o d mo del as w ell, whic h
still iden ties the main features. These results are quan tied in the next paragraph. Figure 5.6
sho ws a mo del created for a short Chloroph yll run. The Chloroph yll mo dels w ere created to assess
the appro ximate structure and h yp erparameters for these t yp es of elds, whic h is ev aluated in the
next subsection regarding estimated h yp erparameters.
W e ev aluate the p erformance for all bath y runs in terms of the RMSE b et w een the ground truth
mo del, sho wn in Figure 5.3, and the on-b oard mo dels. Figure 5.7 sho ws the RMSE curv es, where
the RMSE w as calculated ev ery 600s. All runs ha v e appro ximately similar RMSE curv es. F or the
half duration runs the A UV nishes sampling at 4:5 time steps, where p erformance is similar to full
run p erformance at t 4:5: half run bath y nal RMSE is 1:32:7m, where full run mo dels ha v e
an RMSE of 1:51:9m. F ull runs ev en tually obtain an RMSE of 0:880:90m. The sixth short
50 CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
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0 1 2 3 4 5 6 7 8 9
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
RMSE
full lGP run 1
full lGP run 2
full lGP run 3
short lGP run 1
short lGP run 2
short lGP run 3
short lGP run 4
short lGP run 5
short GP run 6
short lGP run 7
Figure 5.7: RMSE curv es for all bath y runs, predictions at ev ery 600s.
run (orange line) is the run with a GP mo del instead of the `GP mo del. The initial p erformance
is b etter and suggests that bath ymetry ma y b e b etter mo deled using a GP instead of an `GP .
Ho w ev er, this could b e a luc ky run, comparable to the second short `GP run (cy an line).
GP hyp erparameter ev aluation
T able 5.1 sho ws the log h yp erparameters that w ere estimated on b oard the v ehicle at the end of ev ery
adaptiv e sampling run. All bath y and Chl measuremen ts are put in to the GP using their longitude
and latitude lo cation. Therefore the (log) length scale op erates on those scales. W e calculated the
appro ximate length scale in meters to giv e a more in tuitiv e description: W e tak e the appro ximate
con v ersion rates of longitude and latitude for our deplo ymen t lo cation, where one degree longitude is
appro ximately 110924 meters, and one degree latitude is appro ximately 92287 meters
2
. The a v erage
b et w een these is 101605, whic h is used as the m ultiplication rate: r
ll
101605. Th us w e calculate
the length scale in meters:
lpmqr
ll
exp
lnl
(5.6)
2
Num b ers obtained via h ttp://www.csgnet w ork.com/degreelenlla v calc.h tml at an appro ximate latitude of 34:09
N.
CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
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Stephanie Kemna A daptiv e Sampling with A UV s
Run log length scale lnl l (m) log signal log noise
Bath y full 1 -7.691 46 0.583 -2.697
Bath y full 2 -7.755 44 0.604 -3.065
Bath y full 3 -7.718 45 0.537 -2.538
Bath y short 1 -7.897 38 0.542 -2.998
Bath y short 2 -7.947 36 0.454 -2.965
Bath y short 3 -7.711 45 0.677 -3.029
Bath y short 4 -8.036 33 0.486 -3.113
Bath y short 5 -7.721 45 0.559 -3.000
Bath y short 6 (GP) -7.838 40 2.237 -0.540
Bath y short 7 -7.810 41 0.561 -2.836
Chl 1 -5.289 513 0.503 -0.562
Chl 2 -7.253 72 0.787 -1.048
Chl 3 -7.236 73 0.744 -1.258
Chl 4 -7.457 59 1.018 -1.201
T able 5.1: Final log-h yp erparameters estimated on b oard the v ehicle at the end of ev ery adaptiv e
sampling run: log length scale l, and the log of signal and noise standard deviations.
The second column of T able 5.1 sho ws the length scale in meters. F or most runs, the length scale
is b et w een appro ximately 35 and 70 meters.
As can b e seen from T able 5.1, the h yp erparameters for the Chloroph yll runs 2 4 giv e an
appro ximate length scale of 5973m. Based on these results and con v ersations with Biology Prof.
Da vid A. Caron (see F o otnote 3 in Section 1.2: In tro duction to algal blo oms, page 17), w e think the
length scale h yp erparameter for the rst Chloroph yll run w as mis-estimated. Length scales of tens
of meters are more lik ely in small lak es, suc h as the Puddingstone w ater reserv oir in San Dimas,
where these measuremen ts w ere made (F o otnote 3). Note also that the surv ey area w as 300200m,
in a part of the lak e where the appro ximate lak e heigh t is 300450m. A length scale of 513m
is therefore v ery unlik ely . The h yp erparameters for Chloroph yll runs 24 are of a similar range
to the h yp erparameters of the bath ymetry , making bath ymetry a go o d pro xy for ev aluating AIS
p erformance.
5.6 Field T esting Discussion, Conclusion & F uture W ork
In this c hapter w e sho w ed the results of running adaptiv e informativ e sampling on b oard the
EcoMapp er A UV. W e sho w ed that it is feasible to create a GP mo del on b oard of the A UV and
to run calculations on it for adaptiv e sampling. W e prop osed a metho d of ev aluating against
lak e bath ymetry to ev aluate p erformance. F or b oth full and half duration runs, the A UV created
reasonable mo dels of the lak e bath ymetry .
As can b e seen in T able 5.1, the length scale for the measured Chl elds is similar to the length
scales estimated for the lak e’s bath y . Bath ymetry th us pro vides a go o d and easy w a y to compare
m ultiple adaptiv e sampling metho ds, as a stable ground truth. In order to understand whether
bath y can alw a ys b e used as a pro xy , it w ould b e useful to run a study to estimate ho w far the
eld c haracteristics impact the trial results. F or prosp ectiv e elds, one can do a quic k exploratory
52 CHAPTER 5. FIELD TESTING OF SINGLE-R OBOT AD APTIVE INF ORMA TIVE
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A daptiv e Sampling with A UV s Stephanie Kemna
run, if no prior kno wledge ab out an area’s bath y is a v ailable, to ev aluate similarit y to the elds to
b e mo deled. Note that this is not necessary for science missions, but only for rob otic tests where
quan titativ e ev aluation is desired.
F or the RMSE graph, Figure 5.7, w e sa w that the p erformance is initially getting w orse b efore
it impro v es. This could b e due to the fact that the h yp erparameters w ere initialized to incorrect
v alues. It w ould b e in teresting to see whether the same eect con tin ues if the h yp erparameters are
initialized to v alues closer to what they ended up b eing at the end of eld trials. The nal bath y
h yp erparameters w e estimated in the eld are used for initializing the GP mo del for all sim ulations
run in Chapter 9, as w ell as the sim ulated mo dels generated from GPs in Chapter 9.
F or the eld run with the GP mo del, w e com bined the p osterior en trop y with the predictiv e
mean, using a w eigh t factor. This w eigh t factor w as empirically determined based on a small set of
sim ulations. It could b e ne-tuned further based on more sim ulations and/or eld trials. It w ould
b e in teresting to explore whether this can impro v e mo deling p erformance further. There is also the
p ossibilit y of adding more ob jectiv es in to the equation, suc h as considering the distance b et w een
w a yp oin ts.
F or all runs, w e initialized the GP mo del with a zero mean prior. This is a reasonable v alue when
sampling for algal blo oms, if it is not clear whether an y blo om is presen t. F or bath ymetry it w ould
mak e sense to use a prior that is equal to the a v erage bath ymetric depth, and/or non-uniform. W e
recommend this for future w ork on bath ymetric mapping using Gaussian Pro cesses, assuming some
estimate on lak e or o cean depth is a v ailable or can b e made.
One of the main concerns in this study w as whether or not the A UV could p erform all calculations
necessary for adaptiv e sampling, giv en the limited computational capacit y . The same co de w as used
b et w een sim ulations as eld trials, and this w as sho wn to run successfully . T o k eep computation time
reasonable, w e subsampled our GP for running h yp erparameter optimization. The computational
load could b e further decreased b y optimizing the co de for run time eciency and b y using sparse
GP tec hniques (Csat and Opp er, 2002).
Ov erall, w e ha v e demonstrated the feasibilit y of running adaptiv e informativ e sampling on b oard
an A UV with limited computing p o w er. W e prop osed a metho d of ev aluating p erformance using
lak e bath ymetry , sho wing RMSE curv es b et w een on-b oard mo dels and the created ground truth.
W e ha v e sho wn that the A UV can create go o d mo dels of lak e bath ymetry in short amoun ts of time.
F urthermore, it constructed mo dels of Chloroph yll elds where the k ernel length scale w as similar
to exp ected c haracteristics. These kinds of mo dels can b e useful for biologists or o ceanographers to
b etter understand p oten tially harmful algal blo oms.
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6 | Multi-Robot Adaptive Informative Sampling:
Data Sharing
In the previous c hapter w e sho w ed that a single v ehicle running adaptiv e sampling can outp erform
a single v ehicle running la wnmo w er surv eys in terms of mo deling a eld. In this c hapter, w e lo ok
at extending this approac h to m ultiple v ehicles. W e run la wnmo w er surv eys, while splitting the
surv ey area in equal parts, and run adaptiv e sampling in parallel. More in teresting is what w e can
ac hiev e b y ha ving the v ehicles activ ely co ordinate their sampling eorts. T o that end, this c hapter
in v estigates the ‘step zero’ of m ulti-rob ot co ordination; data sharing.
6.1 Related work
In this section w e briey discuss related w ork in m ulti-rob ot adaptiv e informativ e sampling, to giv e
con text to the data sharing approac h. F or general related w ork in adaptiv e informativ e sampling,
w e refer bac k to Section 3.4. F or an extensiv e ev aluation of related w orks in m ulti-rob ot adaptiv e
informativ e sampling, see Section 7.2.
Multi-rob ot approac hes for adaptiv e informativ e sampling ha v e b een explored to some exten t.
Examples include: planning paths for v ehicles sequen tially (Singh et al., 2007), running v ehicles in
geographically separate regions (Marino et al., 2015, P atten et al., 2013, Soltero et al., 2014), or
running v ehicles in parallel or one after another (Lo w et al., 2009c). In some cases, path planning and
m ulti-rob ot co ordination are all done oine, e.g. (Ma et al., 2016b, Singh et al., 2007). Do wnsides of
oine cen tralized planning include ha ving a single p oin t of failure. F or online cen tralized planning
there can also b e a comm unication o v erhead due to sharing of measuremen ts and plans, and another
do wnside could b e the duration and computational complexit y of cen tralized planning. Recen t w orks
b y Lo w et al. and Ouy ang et al. (Lo w et al., 2012, Ouy ang et al., 2014) explored decen tralized
adaptiv e sampling with lo cal planning. In their case, planning is decen tralized, and eac h v ehicle
mak es their o wn sampling plan. T o this end, all v ehicles broadcast their measuremen ts, as w ell as the
c hosen sampling lo cation or the adjacency information. Similarly , Soltero et al. (2014) assume that
v ehicles can share estimates within a connected net w ork of rob ots. In this c hapter, w e ev aluate the
p erformance of m ulti-rob ot adaptiv e informativ e sampling for rob ots simply sharing data, without
further co ordination, and w e explore the trade-o b et w een using surface (Wi-Fi) and underw ater
(acoustic) comm unications for A UV s.
This c hapter is largely based on A daptiv e Informativ e Sampling with Autonomous Underw ater V ehicles:
A coustic v ersus Surface Comm unications (Kemna et al., 2016).
54
A daptiv e Sampling with A UV s Stephanie Kemna
6.2 Approach
W e are in terested in dev eloping informativ e sampling approac hes for m ulti-A UV systems, with
fully decen tralized planning and co ordination. Our system is designed to allo w v ehicles to plan
indep enden tly o v er the whole surv ey area. W e in v estigate ho w increased co ordination through data
sharing can increase mo deling p erformance.
F or this w ork, our main fo cus is comparing the en vironmen tal mo deling p erformance for m ulti-
A UV adaptiv e informativ e sampling, while sharing data through t w o metho ds of comm unication:
1) the A UV s in terrupt their at-depth surv ey to come to the surface and share all measuremen ts
tak en so far (Wi-Fi),
2) the A UV s attempt to share measuremen ts (semi-) con tin uously during at-depth surv eys, using
underw ater acoustic comm unications (acomms).
The A UV s will b e able to share few er measuremen ts when using acomms, but will not ha v e to sp end
an y time on surfacing actions. Giv en that acomms are often lossy (W alls et al., 2015), w e also lo ok
at the scenario where throughput is reduced, e.g. only 70% or 50% of the messages get through.
In these cases of deteriorated comm unications, w e see that although the mo del’s predictiv e mean
p erformance reduces only sligh tly , the mo del uncertain t y can gro w signican tly .
6.3 Experimental set-up
6.3.1 Simulated communications
As men tioned in the previous section, eac h v ehicle indep enden tly mo dels the en vironmen t with
an `GP and runs greedy w a yp oin t selection. There are no cen tral comp onen ts to the system.
F or m ulti-v ehicle co ordination, w e consider at this p oin t only data sharing approac hes. W e are
in terested in comparing m ulti-v ehicle p erformance b et w een when the v ehicles ha v e limited, but
(semi-) con tin uous, underw ater comm unication, v ersus when the v ehicles can comm unicate fully ,
but need to surface.
T o sim ulate underw ater acoustic comm unications, w e use the Goby acomms suite (Sc hneider,
2014), with a TDMA (Time Division Multiple A ccess) sc heme. The TDMA sc heme is set up suc h
that eac h v ehicle has a three second time slot in whic h it can send 32-b yte messages. Giv en the
sim ulated acoustic mo dem pro cesses and acomms proto cols, this means that eac h v ehicle can send
1-2 messages p er time slot. The underw ater comm unication range is limited to 500m. The acomms
is alw a ys used b y the v ehicles to exc hange v ehicle p ositions for collision a v oidance. F or initial
exp erimen ts, w e assume that no messages are lost, i.e. obtain a throughput of appro ximately 100%.
F or the nal t w o exp erimen ts, w e probabilistically drop 30% and 50% of the messages, i.e. obtain
a throughput of appro ximately 70% and 50% resp ectiv ely .
When on the surface, w e assume wireless comm unications for data sharing. This allo ws for m uc h
greater bandwidth and frequency of messaging compared to acomms. When v ehicles surface, they
can share data only after completing a successful handshak e, to guaran tee that b oth v ehicles are on
the surface and ready to share data.
CHAPTER 6. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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Stephanie Kemna A daptiv e Sampling with A UV s
F or data sharing through acomms, the v ehicles are unable to exc hange all measuremen ts, due
to the limited bandwidth of acomms. Giv en the TDMA sc heme, eac h v ehicle can send on a v erage
t w o 32-b yte messages ev ery six seconds. T o minimize the amoun t of messages, w e merge data
measuremen ts in to v ehicle status messages, whic h are already sen t for collision a v oidance. Eac h
message th us con tains v ehicle ID, p osition (x, y , depth, altitude), orien tation (heading, pitc h, roll),
sp eed, and t w o data p oin ts (x, y , depth, data v alue). The data p oin ts con tain their lo cation, b ecause
the measuremen ts ma y b e older than the curren t v ehicle p osition.
6.3.2 Simulation experiments
In total, w e ha v e run sim ulations for adaptiv e sampling with t w o A UV s for six dieren t scenarios:
la wnmo w er surv ey ,
adaptiv e, parallel,
adaptiv e, timed data sharing (TDS) on surface,
adaptiv e, con tin uous data sharing through acomms,
adaptiv e, con tin uous data sharing through deteriorated acomms, at 70% throughput,
as the previous item, at 50% throughput.
In order to determine the mo deling p erformance of our m ulti-rob ot approac h, w e rst compare a
standard la wnmo w er surv ey with running adaptiv e sampling in parallel, and with running adaptiv e
sampling with timed data sharing on the surface. The la wnmo w er surv ey is a high resolution (20m
trac k spacing) la wnmo w er, run b oth horizon tally and v ertically o v er the surv ey area. F or the t w o
v ehicle scenario, the area is split v ertically , with one v ehicle co v ering the w est, and the other v ehicle
co v ering the east part. The duration of running the la wnmo w er surv ey is used as the mission
duration for the adaptiv e surv eys.
In the adaptiv e sampling scenario, v ehicles c ho ose w a yp oin ts in the resolution of the data grid
(10m spacing), using Equation (3.6) (page 37). F or the parallel adaptiv e sampling case, b oth
v ehicles run adaptiv e sampling, without sharing data or co ordinating their actions. F or the timed
data sharing, the v ehicles surface ev ery 10 min utes, to exc hange data. In b oth cases, the v ehicles
also share data after the pilot surv ey , and at the end of the whole surv ey , suc h that b oth v ehicles
should ha v e all measuremen ts at the end, for the b est mo del.
Finally , w e compare the timed data sharing approac h, to acomms-based data sharing. The
adv an tage of acomms is that the v ehicles do not ha v e to surface to b e able to share their data.
Ho w ev er, the comm unication c hannel is m uc h more restricted, and therefore they cannot exp ect to
b e able to share all measuremen ts. W e test three dieren t acomms scenarios: 100%, 70% and 50%
throughput.
56 CHAPTER 6. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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A daptiv e Sampling with A UV s Stephanie Kemna
(a) Ro ot-Mean Squared Error (RMSE) (b) Negativ e Log-Lik eliho o d (NLL)
Figure 6.1: RMSE and NLL a v erages of ten sim ulations for 2 A UV s running la wnmo w er and adaptiv e
sampling surv eys. A daptiv e surv eys are parallel, and timed data sharing. Error bars are omitted
for readabilit y .
6.4 Results
6.4.1 Multiple AUV s; lawnmower vs. adaptive parallel vs. adaptive timed data
sharing
F or sim ulations with t w o A UV s, Figure 6.1 compares the sim ulation results of standard la wnmo w er
surv eys to t w o adaptiv e informativ e sampling approac hes. RMSE and NLL of the `GP are plotted
against time. As in the single-v ehicle exp erimen ts, w e use time steps of 600 seconds, where the
rst result ( t 1) is after initial h yp erparameter optimization, and the last result (t 7) is after
the nal h yp erparameter optimization. Considering the time steps for predictions made during the
surv ey , i.e. t 1 to 11 for single A UV and t 1 to 6 for dual-A UV, it is clear that the whole surv ey
tak es only ab out half the time when running with t w o A UV s.
The results sho w that the mo del’s RMSE decreases more quic kly when running either of the
adaptiv e sampling approac hes, and the NLL is con tin uously b etter. Note that, for the la wnmo w er
surv ey , one of the A UV s (‘auv1’) p erforms signican tly w orse on RMSE, up un til the nal timestep
where all data is shared. This is due to the fact that the surv ey area is split for t w o A UV s. Only
one half con tains the sim ulated blo om, and therefore, without gathering more data in that area,
the second A UV can not impro v e the mo del as m uc h as the other. F or adaptiv e sampling, w e sho w
sim ulation results of running t w o A UV s in parallel, and using timed data sharing (on the surface).
The results clearly sho w the impro v emen ts of adaptiv e sampling o v er standard la wnmo w er surv eys.
The addition of timed data sharing further impro v es the mo deling p erformance, i.e. b oth RMSE
and NLL ha v e decreased.
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Stephanie Kemna A daptiv e Sampling with A UV s
(a) Ro ot-Mean Squared Error (RMSE) (b) Negativ e Log-Lik eliho o d (NLL)
Figure 6.2: RMSE and NLL a v erages of ten sim ulations for 2 A UV s running adaptiv e sampling with
either timed data sharing or acoustic comm unications. Error bars are omitted for readabilit y .
6.4.2 Multiple AUV s; timed data sharing vs. acoustic comm unications
Figure 6.2 compares the sim ulation results of t w o A UV s using timed data sharing (TDS) on the
surface, with t w o A UV s con tin uously sharing data through acomms. As has b een explained in
Section 4.1, the v ehicles run their surv ey at 5 meters depth. Hence, this is also the v ertical distance
the TDS A UV s need to transit to the surface to b e able to share data. As Figure 6.2a sho ws, the
mo deling p erformance giv en the RMSE is similar for the t w o approac hes. Figure 6.2b sho ws that
the mo deling p erformance is b etter in terms of negativ e log-lik eliho o d for the acomms approac h.
The go o d p erformance of acomms is most lik ely due to spatial correlation b et w een measuremen ts,
suc h that subsampling the measuremen ts still giv es go o d results. F urthermore, b ecause the A UV s
do not ha v e to in terrupt the surv ey , they can sp end more time impro ving the mo del.
6.4.3 Multiple AUV s; deteriorating acoustic communications
As explained in Section 6.3.2, w e ran ten sim ulations for acomms with reduced message throughput,
resp. 70 and 50%. T able 6.1 sho ws the a v erage n um b er of messages exc hanged b et w een the v ehicles
through acomms, for eac h throughput setting, as w ell as the empirical throughput.
Throughput setting A vg msgs receiv ed Empirical p ercen tage
100 2681 100
70 1883 70.2%
50 1336 49.8%
T able 6.1: A v erage n um b er of messages receiv ed on eac h v ehicle p er sim ulation, and empirical
p ercen tage of messages receiv ed v ersus the full 100% throughput.
58 CHAPTER 6. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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(a) Ro ot-Mean Squared Error (RMSE) (b) Negativ e Log-Lik eliho o d (NLL)
Figure 6.3: RMSE and NLL a v erages of ten sim ulations for 2 A UV s running adaptiv e sampling with
dieren t throughput (100, 70, 50 %) acoustic comm unications. Error bars are omitted for readabilit y .
Figure 6.3 sho ws the RMSE and NLL for all acomms sim ulations. F or the RMSE, w e can see
that p erformance, on a v erage, decreases sligh tly with decreased throughput. F or the NLL, w e can
see that most p erform similarly , but for one of the A UV s the degradation increases a lot more with
decreased throughput. W e further discuss this result in the next section, 6.5.
6.5 Discussion
In this w ork w e explored ho w exc hanging data b et w een the sampling rob ots b enets en vironmen tal
mo deling with (log-)Gaussian Pro cesses. W e see that increased sharing of measuremen ts impro v es
individual mo deling p erformance, when running sim ulations with m ultiple v ehicles. When v ehicles
share measuremen ts through timed data sharing, they p erform b etter than when running adaptiv e
sampling in parallel, without sharing measuremen ts.
W e further explore the p erformance for timed data sharing on the surface, v ersus underw ater
acoustic comm unications (acomms). The b enets of surfacing are increased throughput and band-
width, but there is a cost in terms of time sp en t on surfacing, data sharing, etc. Section 6.4.2
compared the mo deling p erformance b et w een timed data sharing and acoustic comm unication.
While the mo deling p erformance is similar in terms of RMSE, w e see that the mo deling p erformance
in terms of negativ e log-lik eliho o d is not as go o d for the timed data sharing. W e h yp othesize that this
has t w o causes: F or one, the timed surfacing for data sharing reduces the o v erall time a v ailable for
sampling. In the end, the v ehicles will ha v e tak en few er measuremen ts, and therefore there remains
greater uncertain t y in the created mo del. The second reason that timed data sharing is p erforming
w orse for NLL, ma y come from the fact that there is no co ordination of v ehicle actions. Ev ery
time the v ehicles surface and share their data, they end up with appro ximately the same mo del.
Without co ordinating actions, they will th us try to go to the same areas for further sampling, un til
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small dierences in route and sensor noise in tro duce enough v ariation to lead to dieren t sampling
lo cations. This is somewhat mitigated in the acomms case b ecause, ev en with 100% throughput,
not all measuremen ts can b e shared, and therefore the mo dels are at all times sligh tly dieren t. A t
the same time, with acomms, the A UV s do not sync hronize their actions at an y time, and therefore
there will b e more div ersit y in paths and sampling lo cations.
Finally , w e compare the p erformance for acomms with dieren t throughput lev els; 100%, 70%
and 50%. Section 6.4.3 sho w ed that mo deling p erformance deteriorates with decreased acomms
throughput. Figure 6.3 sho w ed furthermore that p erformance decreases more for one of the v ehicles
than the other. This dierence is lik ely due to the dierence in measuremen ts tak en during the
pilot surv ey . Curren tly , the area is split v ertically for the pilot surv ey; one A UV runs the w est half,
while the other runs the east half. A t the same time, the sim ulated algal blo om is in the w est area.
F or the acomms sim ulations, data is shared only through acomms and not through surfacing ev en ts.
Therefore, with loss of throughput, one of the A UV s will initially get few er measuremen ts inside
the ‘hot sp ot’. The pilot data is k ept after the pilot, and therefore the A UV s start out with sligh tly
dieren t mo dels. Due to ha ving dieren t mo dels, they will also sample in dieren t lo cations, and
one of the A UV s is th us running adaptiv e sampling on a mo del that is not as go o d.
6.6 F uture work
T o impro v e timed data sharing on the surface, it w ould b e useful to co ordinate actions b et w een
the v ehicles. When sharing measuremen ts through lossy acomms, w e sa w that one of the A UV s
ma y ha v e a less accurate mo del than the other. T o a v oid this, w e can consider t w o approac hes;
either w e can remo v e the pilot data from the GP , i.e. merely use the data for h yp erparameter
estimation, and start adaptiv e sampling from a blank slate. This ho w ev er, seems lik e a w aste of
data. Another approac h w ould b e to ha v e one surfaced data sharing ev en t after the pilot, to mak e
sure b oth v ehicles ha v e the same initial dataset. This is also in the in terest of robustness, b ecause
w e w ould lik e b oth v ehicles to ha v e as go o d a mo del as p ossible at all times, in case one of the
v ehicles w ould ha v e problems.
6.7 Conclusion
Ov erall, w e ha v e demonstrated the b enets of data sharing b et w een m ultiple v ehicles that run
decen tralized adaptiv e sampling. Our sim ulations sho w that when using acoustic comm unications,
mo deling p erformance is sup erior to timed data sharing, when there is 100% throughput. Ho w ev er,
it is also clear that the p erformance, esp ecially in terms of mo del uncertain t y , deteriorates with
reduced throughput. F or future w ork, it w ould b e in teresting to in v estigate the eects of increased
co ordination on v ehicle actions.
60 CHAPTER 6. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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7 | Multi-Robot Adaptive Informative Sampling:
Coordination
The previous c hapter in v estigated t w o comm unication approac hes for data sharing in m ulti-rob ot
adaptiv e informativ e sampling. In this c hapter w e in v estigate a co ordination approac h, based on
dynamic, rep eated, V oronoi partitioning.
7.1 Introduction
W e in v estigate a m ulti-rob ot co ordination approac h for decen tralized, informativ e, adaptiv e sam-
pling with autonomous underw ater v ehicles. W e w an t a decen tralized approac h for robustness of
the system, suc h that there is no single p oin t of failure, and to allo w for an ytime prediction; an y
rob ot at an y p oin t in time should ha v e a reasonable mo del of the whole en vironmen t. F urthermore
w e w an t an approac h that k eeps the required amoun t of comm unication to a minim um. Esp ecially
in underw ater en vironmen ts, comm unication is sev erely limited, and w e cannot assume con tin uous
access to a reliable comm unication c hannel.
T o k eep the approac h decen tralized, eac h rob ot main tains their o wn mo del of the en vironmen t.
A t certain p oin ts in time, rob ots can share measuremen ts with eac h other, and add these to their
o wn mo dels. Eac h rob ot uses its o wn mo del, together with the mo del’s en trop y , to decide whic h
lo cations to sample next. W e com bine this with dynamic V oronoi partitioning, to decrease o v erlap
in actions and decisions b et w een v ehicles, eectiv ely co ordinating actions b et w een the v ehicles,
with minimal comm unication o v erhead. The v oronoi partitioning is re-calculated after ev ery data
sharing ev en t, suc h that the partitioning c hanges with the uncertain t y in the mo del, i.e. where the
v ehicles need to sample. In suc h, w e create a decen tralized, m ulti-rob ot co ordination approac h for
informativ e, adaptiv e sampling of unkno wn en vironmen ts.
7.2 Related W ork
F or related w ork in single-rob ot adaptiv e sampling, w e refer bac k to Section 3.4.
F or an in tro to related w ork in m ulti-rob ot adaptiv e informativ e sampling, w e refer bac k to Sec-
tion 6.1. In this section, w e discuss m ulti-rob ot co ordination approac hes for adaptiv e informativ e
sampling, as w ell as general approac hes to m ulti-rob ot co ordination.
This c hapter is largely based on Multi-Rob ot Co ordination through Dynamic V oronoi P artitioning for
Informativ e A daptiv e Sampling in Comm unication-Constrained En vironmen ts (Kemna et al., 2017)
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Stephanie Kemna A daptiv e Sampling with A UV s
In the realm of adaptiv e informativ e sampling, Singh et al. (2007) used an oine and cen tralized
approac h to m ulti-rob ot co ordination, namely sequen tial allo cation. In sequen tial allo cation a
cen tralized path planner plans paths for eac h rob ot in sequence, and all rob ots subsequen tly run
their informativ e sampling paths in parallel. Lo w et al. (2012) and Ouy ang et al. (2014) used activ e
co ordination in a decen tralized approac h. V ehicles w ould co ordinate their actions, but only when
there w ere other v ehicles within the planning neigh b orho o d of the o wn v ehicle.
T ypical m ulti-rob ot co ordination approac hes used in other domains, e.g. exploration and map-
ping with ground v ehicles, include auction-based metho ds (Sheng and Xi, 2004, Simmons et al.,
2000, Zlot et al., 2002) and spatial segregation, t ypically through V oronoi partitioning (Marino et al.,
2015, P atten et al., 2013, Soltero et al., 2012). Nieto-Granda et al. (2014) used three heuristics for
m ulti-rob ot co ordination; 1) additional rob ots w ait un til they are explicitly needed, 2) rob ots tra v el
in groups and split when appropriate, 3) rob ots tra v el in teams of t w o and split when needed. The
results indicated that a divide & conquer strategy is more eectiv e than k eeping rob ots as w aiting.
The m ulti-rob ot strategies used in adaptiv e sampling are mostly considering only lo cal collab-
oration or requiring a cen tral planner. W e do not w an t to use an y cen tral comp onen ts in our
system, to a v oid ha ving a single p oin t of failure. F urthermore, w e w ould prefer strategies that
consider the global space, in order to b e less susceptible to lo cal minima, and to accoun t for the
exploration-exploitation trade-o. Some commonly used metho ds of co ordination, suc h as auction-
based metho ds, require a fair amoun t of comm unication b et w een the v ehicles. W e w an t to k eep
comm unication b et w een v ehicles to an absolute minim um, giv en the constrain ts of the acoustic
comm unication c hannel, and to limit time sp en t on comm unication, v ersus sampling.
Previously , w e ha v e in v estigated the impro v emen ts that can b e obtained from adaptiv e infor-
mativ e sampling with m ultiple rob ots sharing data through timed surfacing ev en ts or acoustic
comm unications (Chapter 6 and (Kemna et al., 2016)). In this w ork, w e sho w that the mo deling
p erformance for the m ulti-rob ot approac h can further b e impro v ed through co ordinating actions
b et w een v ehicles. This prev en ts the scenario where v ehicles c ho ose the same w a yp oin ts, based on
similar mo dels of the w orld. W e use an approac h that com bines dynamic V oronoi partitioning with
a comm unication strategy for data sharing b et w een v ehicles, to ac hiev e a decen tralized m ulti-rob ot
co ordination approac h.
Previous approac hes using V oronoi partitioning include the w orks of P atten, Sc h w ager and
Soltero r10;13;14s. P atten et al. (2013) and Sc h w ager et al. (2014) used a single initial V oronoi
partitioning is used to divide the sample space across the rob ots. P atten et al. (2013) then had eac h
rob ot run a TSP tour o v er sampling lo cations. These sampling lo cations ha v e b een greedily selected
based on m utual information from within the V oronoi region. Sc h w ager et al. (2014), Soltero et al.
(2014) discussed co v erage con trol approac hes. In b oth cases, the densit y function to b e estimated
is mo deled using a linear com bination of a set of basis functions. Sc h w ager et al. (2014) had eac h
rob ot also run a TSP tour inside their partition, but o v er all sampling lo cations, to create the mo del.
The estimated densit y function is then used to calculate the (w eigh ted) V oronoi cen troids, to whic h
rob ots are deplo y ed for sensor co v erage. In Soltero et al. (2014), rob ots either already ha v e the
densit y function, or run a la wnmo w er surv ey to obtain it. Rob ots then run paths whose w a yp oin ts
are V oronoi generators. The w a yp oin ts mo v e based on a con trol la w, that tak es in to accoun t the
densit y function, to w ards the (w eigh ted) cen troid of the area. The paths th us c hange shap e to
monitor the in teresting regions of the surv ey area only . Both of these approac hes run t w o stages:
mo del estimation, follo w ed b y static sensor deplo ymen t or p ersisten t monitoring. Note that in this
62 CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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w ork, w e fo cus only on the eld estimation part, i.e. creating an informativ e mo del. W e do not
assume to kno w the densit y function b eforehand, and are in terested in using online and adaptiv e
approac hes for mo deling it.
7.3 Approach
In this w ork, w e dev elop a dynamic V oronoi partitioning approac h for decen tralized adaptiv e
sampling. The v ehicles create a mo del of the en vironmen t using Gaussian Pro cess regression, and
running adaptiv e sampling utilizing the p osterior map en trop y of the mo del. T o dieren tiate v ehicle
actions, eac h v ehicle runs V oronoi partitioning o v er p ossible sampling lo cations. The p osterior map
en trop y is used here as a densit y function for shifting the cen troids of the V oronoi partitions to w ards
in teresting regions. While the v ehicles are sampling, at depth, they can not share data with eac h
other. Ho w ev er, they can request data sharing ev en ts, at whic h time data is shared, and the V oronoi
partitions are re-calculated. This section will briey explain eac h of these subparts of our dynamic
V oronoi partitioning for v ehicle co ordination in adaptiv e informativ e sampling.
7.3.1 Dynamic V oronoi partitioning
F or action co ordination b et w een v ehicles, w e use dynamic V oronoi partitioning. This allo ws us
to co ordinate v ehicle mo v emen ts without the need for constan t comm unication. The v ehicles
indep enden tly estimate V oronoi regions, to limit their prosp ectiv e sampling lo cations. Note that this
is not used as a con trol la w for v ehicle mo v emen t. Assuming all v ehicles ha v e a fairly recen t estimate
of eac h other’s p ositions, they can eac h calculate the V oronoi partitioning for the surv ey area: Eac h
v ehicle considers all (un visited) sampling lo cations, and creates a subset with only those lo cations
closest to itself. Note that if the v ehicles w ould not kno w the p ositions of all other v ehicles, then
one could use decen tralized V oronoi partitioning, e.g. (CortØs et al., 2002). F or these initial V oronoi
partitions, w e then consider the densit y function, in our case the p osterior map en trop y on the
`GP , giv en b y Equation (3.6) (page 37), and calculate the w eigh ted cen troid for eac h partition. The
w eigh ted cen troids are used as the V oronoi generators for a second round of V oronoi partitioning.
The resulting partitions are then used in the path planning algorithm (Section 3.3).
7.3.2 Data sharing
Due to the limited bandwidth and p ossible reduced throughput of underw ater acoustic comm unica-
tions, it is not practicable to ha v e all v ehicles broadcast their measuremen ts. W e assume ho w ev er,
that the underw ater comm unication c hannel is stable enough to get some messages through, e.g.
for in ter-v ehicle collision a v oidance, and for requesting surfacing ev en ts.
Eac h v ehicle, at an y time, can request a surfacing ev en t. It broadcasts a message to the other
v ehicle(s) to request surfacing, and in the mean time con tin ues sampling. V ehicles receiving suc h
a request send an ac kno wledgmen t and start surfacing. Up on receipt of all ac kno wledgmen ts, the
initiating v ehicle will also surface. Once on the surface, the v ehicles initiate a handshak e proto col,
to mak e sure all other v ehicles are also at the surface and ready to start sharing data. After the
handshak e, all v ehicles broadcast their measuremen ts, through the Wi-Fi comm unications. The
receiv ed measuremen ts from other v ehicles are added to the v ehicle’s lo cal `GP . A t this p oin t, eac h
CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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Figure 7.1: Scenario 1: single blo om Figure 7.2: Scenario 2: dual blo om
v ehicle will recalculate the V oronoi partitioning (as p er Section 7.3.1), and then re-commence with
(at-depth) adaptiv e sampling.
There are man y p ossible w a ys of determining when a surfacing ev en t is required, e.g. the
criterion could b e time-based, or information-based. In this w ork, w e tak e the approac h of requesting
surfacing ev en ts when the v ehicles detect that they are sampling close to the b order of their V oronoi
region. In suc h case the in teresting areas are near the b order of their region, and th us it is considered
a go o d time to reconsider the partitioning. Note that v ehicles can not request a surfacing ev en t
within v e min utes of a previous surfacing ev en t.
7.4 Implementation
W e ran sim ulation exp erimen ts with t w o autonomous underw ater v ehicles, using the MOOS-IvP
middlew are (Benjamin et al., 2010). The middlew are includes a simple sim ulation of v ehicle dynam-
ics and PID con trol, as w ell as b eha vior-based autonom y . W e use the follo wing standard b eha viors
for our sim ulations; loiter, w a yp oin t, constan t depth, and (in ter-v ehicle) collision a v oidance. W e
use a constan t sp eed of 1:5m{s and constan t depth of 5m. Our path planning approac h up dates
the w a yp oin t b eha vior.
T o sim ulate algal blo oms in a lak e, w e generated a 2-D grid space (400x200m, 10m spacing)
with a 2-D Gaussian to represen t a blo om, and additiv e Gaussian noise. F or the data, w e use a data
v alue amplitude of 40, as a pro xy for high Chloroph yll g{L v alues, with a noise amplitude of 10-20
p ercen t. Within the MOOS-IvP sim ulation, eac h v ehicle samples from this sim ulated data, and w e
add Gaussian noise ( 1:5) to mo del sensor noise (Kemna et al., 2016). W e sim ulate t w o dieren t
scenarios for the grid space; a single blo om with lo w noise, and t w o (dieren tly sized) blo oms in
opp osite corners with higher noise, as sho wn in Figure 7.1 and Figure 7.2.
T o sim ulate comm unications b et w een the v ehicles, w e use t w o forms of sim ulated comm uni-
cations: acoustic and Wi-Fi. F or acoustic comm unications (acomms), the Goby acomms suite
enables us to sim ulate the whole acomms stac k; mo dem driv er, medium access con trol, priorit y-
based message queuing, and enco ding and deco ding of messages (Sc hneider, 2014). W e use a TDMA
(Time Division Multiple A ccess) sc heme for sharing the data c hannel b et w een the v ehicles. Eac h
v ehicle has a pre-assigned 3-second time slot, in whic h it can send one to t w o 32-b yte messages.
W e limit the acomms range to 500m, and are able to reduce the throughput of the c hannel to
probabilistically drop messages, e.g. to drop 30% of the messages. F or Wi-Fi comm unications,
64 CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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A daptiv e Sampling with A UV s Stephanie Kemna
v ehicles use UDP comm unications, without restrictions on throughput or range (giv en that the
curren t exp erimen tal area is smaller than Wi-Fi range restrictions).
Exp erimen ts
In our previous w ork (Kemna et al., 2016), w e sho w ed the impro v emen ts in mo deling p erformance
when adding data sharing b et w een v ehicles. V ehicles sharing data p erformed b etter than those
v ehicles that did not share data and ran standard la wnmo w er surv eys
1
or adaptiv e sampling in
parallel.
In this w ork, w e compare the dynamic V oronoi partitioning approac h for adaptiv e informativ e
sampling with the data sharing approac h, and run the follo wing exp erimen ts:
2 A UV s, timed data sharing, no co ordination,
2 A UV s, dynamic V oronoi partitioning,
3 A UV s, timed data sharing, no co ordination,
3 A UV s, dynamic V oronoi partitioning.
In the timed data sharing approac h, the A UV s surface ev ery ten min utes
2
, to b e able to share
data. When all v ehicles are on the surface, they share data after executing the handshak e proto col
(Section 7.3.2).
F or ev ery 2 A UV and 3 A UV exp erimen ts, w e ran 10 and 15 sim ulations resp ectiv ely , and w e
a v eraged o v er all results. F urthermore, w e ran all these sim ulations o v er b oth scenarios (Figure 7.1
and Figure 7.2). The duration of eac h exp erimen t w as limited to the duration of sim ulations
with the v ehicles running la wnmo w er surv eys. F or example, to surv ey the area with three v ehicles
running high resolution, 20m trac k spacing, la wnmo w er surv eys tak es on a v erage appro ximately
3500 seconds. Therefore, after the v ehicles ha v e run adaptiv e sampling for 3500 seconds, they are
requested to return to the start lo cation, for the nal data sharing and h yp erparameter optimization.
7.5 Results
The results from all exp erimen ts are ev aluated using ro ot mean squared error (RMSE) b et w een the
p osterior mean from the `GP and the generated data, and using the negativ e log-lik eliho o d (NLL).
The RMSE captures the predictiv e mean p erformance of the `GP , and the NLL incorp orates also the
predictiv e v ariances. W e store the mo del predictions throughout the mission, at 10 min ute in terv als
(600s), for ev aluation. W e run a rst h yp erparameter optimization at the rst surfacing ev en t. F or
the timed data sharing, this is at around 600 seconds in to the mission. F or the V oronoi mission,
this is on a v erage at 400-450 seconds in to the mission. A second h yp erparameter optimization is
run at the end of the surv ey .
1
A la wnmo w er surv ey is a t ypical co v erage b eha vior where a v ehicle tra v els bac k and forth across the surv ey area.
2
Note, this assumes that the v ehicles ha v e sync hronized clo c ks, whic h is a giv en in our sim ulations, but should
b e paid atten tion to at eld trials.
CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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65
Stephanie Kemna A daptiv e Sampling with A UV s
Figure 7.3: Scenario 1 (s1), one blo om: A v er-
age RMSE and one standard deviation error
bars, a v eraged o v er all A UV s in the 2-A UV
mission, for b oth timed data sharing (tds)
and dynamic V oronoi partitioning (v or).
Figure 7.4: Scenario 1 (s1), one blo om: A v-
erage NLL and one standard deviation error
bars, a v eraged o v er all A UV s in the 2-A UV
mission, for b oth timed data sharing (tds)
and dynamic V oronoi partitioning (v or).
7.5.1 T w o AUV s
W e ran sim ulation with t w o A UV s, running either timed data sharing or dynamic V oronoi partition-
ing. Results are a v eraged o v er all v ehicles, for 10 sim ulations p er exp erimen t and scenario. Figure 7.3
- Figure 7.6 sho w the results, in terms of RMSE and NLL, for t w o A UV s running adaptiv e sampling
with only data sharing, v ersus co ordination through dynamic V oronoi partitioning. Note that the
nal time step is after the nal h yp erparameter optimization, when the surv ey is nished, and can
hence lead to a bigger reduction of RMSE or NLL. The v ehicles running timed data sharing surfaced
5 times during the mission. The n um b er of surfacing ev en ts for the dynamic V oronoi approac h w as
7-9 times.
Figure 7.3 and Figure 7.4 sho w the RMSE and NLL for the rst scenario, running with t w o
A UV s. As can b e seen, the p erformance for the t w o approac hes is on a v erage the same.
Figure 7.5 and Figure 7.6 sho w the RMSE and NLL for the second scenario, running with t w o
A UV s. As can b e seen, the RMSE initially drops more quic kly for the dynamic V oronoi partitioning,
sho wing impro v ed p erformance. Both metho ds reac h similar v alues at the end of the mission. The
p erformance is ab out the same in terms of NLL, but the dynamic V oronoi approac h is in general
more consisten t in p erformance. Ov erall, for the exp erimen ts with 2 A UV s, w e see that the mo deling
p erformance b et w een the t w o metho ds is the same for the rst scenario, but b etter with dynamic
V oronoi partitioning in the second scenario.
7.5.2 Three AUV s
W e also ran sim ulation with three A UV s, running timed data sharing and dynamic V oronoi par-
titioning. Results are a v eraged o v er all v ehicles, for 15 sim ulations p er exp erimen t and scenario.
66 CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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A daptiv e Sampling with A UV s Stephanie Kemna
Figure 7.5: Scenario 2 (s2), t w o blo oms:
A v erage RMSE and one standard deviation
error bars, a v eraged o v er all A UV s in the
2-A UV mission, for b oth timed data shar-
ing (tds) and dynamic V oronoi partitioning
(v or).
Figure 7.6: Scenario 2 (s2), t w o blo oms: A v-
erage NLL and one standard deviation error
bars, a v eraged o v er all A UV s in the 2-A UV
mission, for b oth timed data sharing (tds)
and dynamic V oronoi partitioning (v or).
Figure 7.7 - Figure 7.10 sho w the a v eraged results for the sim ulations with three A UV s. Note that
the nal time step is after the nal h yp erparameter optimization, when the surv ey is nished, and
can hence lead to a bigger reduction of RMSE or NLL. The v ehicles running timed data sharing
surfaced 4 times during the mission. The a v erage n um b er of surfacing ev en ts for the dynamic
V oronoi approac h w as 6-7 times.
Figure 7.7 and Figure 7.8 sho w the RMSE and NLL for the rst scenario with a single blo om. The
gures sho w that with the co ordination through V oronoi partitioning, the mo deling p erformance
impro v es b oth in terms of RMSE and NLL, in particular o v er the rst 3-4 time steps (1800-2400
seconds) of adaptiv e sampling.
Figure 7.9 and Figure 7.10 sho w the RMSE and NLL for the second scenario with t w o blo oms.
Note that, due to the higher noise in the dual blo om scenario (see Figure 7.2), the RMSE and NLL
are higher than for the single blo om scenario. Again w e see that the p erformance is b etter when
using co ordination through V oronoi partitioning, instead of only data sharing. Ov erall, w e see for
the exp erimen ts with 3 A UV s that the use of dynamic V oronoi partitioning for v ehicle co ordination
results in higher qualit y mo dels, in particular for the second scenario with t w o blo oms.
7.6 Discussion
The results sho w that the mo deling p erformance impro v es with the addition of a co ordination
approac h, in m ulti-rob ot adaptiv e informativ e sampling. F or the 2-A UV exp erimen ts, w e note
that the p erformance is the same for the exp erimen ts on the rst scenario. Also for the 3-A UV
exp erimen ts, the p erformance impro v emen t is not as w ell dened for this scenario. This is lik ely
CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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Stephanie Kemna A daptiv e Sampling with A UV s
Figure 7.7: Scenario 1 (s1), one blo om: A v er-
age RMSE and one standard deviation error
bars, a v eraged o v er all A UV s in the 3-A UV
mission, for b oth timed data sharing (tds)
and dynamic V oronoi partitioning (v or).
Figure 7.8: Scenario 1 (s1), one blo om: A v-
erage NLL and one standard deviation error
bars, a v eraged o v er all A UV s in the 3-A UV
mission, for b oth timed data sharing (tds)
and dynamic V oronoi partitioning (v or).
Figure 7.9: Scenario 2 (s2), t w o blo oms:
A v erage RMSE and one standard deviation
error bars, a v eraged o v er all A UV s in the
3-A UV mission, for b oth timed data shar-
ing (tds) and dynamic V oronoi partitioning
(v or).
Figure 7.10: Scenario 2 (s2), t w o blo oms: A v-
erage NLL and one standard deviation error
bars, a v eraged o v er all A UV s in the 3-A UV
mission, for b oth timed data sharing (tds)
and dynamic V oronoi partitioning (v or).
68 CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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A daptiv e Sampling with A UV s Stephanie Kemna
b ecause the single blo om scenario, with lo w noise, is a simple scenario, where the addition of v ehicles,
or co ordination in the m ulti-rob ot approac h, do es not pa y o.
F or the second scenario, the p erformance impro v emen t is more pronounced. W e see that in
particular the RMSE impro v emen t is bigger at the start of the mission, and o v erall the NLL
p erformance is more consisten t. The impro v emen t is bigger at the b eginning, b ecause this is where
the biggest impro v emen t can b e obtained. After ca. 3-4 time steps (1800-2400 seconds) of sampling,
the p erformance starts to lev el o for all metho ds. This indicates that the mo del after this time
span is ab out as go o d as it gets, and reac hing the limit in p ossible p erformance giv en mo del and
sensor noise. The addition of another h yp erparameter optimization step at this time ma y aid in
impro ving mo deling p erformance. Ho w ev er, it is also an indicator that the mission could b e ended
earlier for all these adaptiv e sampling approac hes.
7.7 F uture work
In the future, w e in tend to explore dieren t co ordination approac hes, as w ell as the eect on
p erformance of the use of dieren t path planning algorithms, and the application to more div erse and
larger areas. F urthermore, eorts are ongoing to demonstrate the adaptiv e sampling p erformance
through eld trials. Th us w e also aim to create new scenarios for future sim ulations based on eld
data.
7.8 Conclusion
Ov erall, w e ha v e sho wn that adaptiv e informativ e sampling with m ultiple rob ots b enets from
the addition of action co ordination b et w een v ehicles. While previous w ork ha v e fo cused mostly
on co ordinating within close range, or planning sequen tially , w e dev elop ed an approac h where the
v ehicles co ordinate, while considering the global space in path planning. F urthermore, our approac h
is completely decen tralized, and creates a robust m ulti-rob ot system for adaptiv e sampling. In
com bination with the comm unications strategy , this mak es the approac h applicable for deplo ymen ts
in hazardous or comm unication-constrained en vironmen ts. Our dynamic V oronoi partitioning tec h-
nique for m ulti-rob ot co ordination is th us an eectiv e metho d in running decen tralized, adaptiv e
informativ e sampling with m ultiple rob ots, in unkno wn en vironmen ts.
CHAPTER 7. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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69
8 | Pilot Surveys for Adaptive Informative Sam-
pling
So far w e ha v e lo ok ed at metho ds for adaptiv e informativ e sampling with single and m ultiple
autonomous underw ater v ehicles. In this c hapter, w e lo ok at the problem of deciding ho w to start
an y adaptiv e sampling routine when no data has b een collected y et and y ou do not kno w where to
collect the most represen tativ e data to start o y our GP mo del.
8.1 Introduction
Informativ e sampling w as pioneered b y Krause and Guestrin (2007), Krause et al. (2008), Singh
et al. (2007). Lo w et al. (2008) and Singh et al. (2009b) extended these informativ e sampling
metho ds in to adaptiv e informativ e sampling approac hes. In all these pap ers, and man y thereafter,
Gaussian Pro cess (GP) regression is used for mo deling the spatial elds. The GP is fully sp ecied
b y its prior mean and co v ariance function (Rasm ussen and Williams, 2006). A common c hoice for
the mean function is zero mean, and a common c hoice of co v ariance function is the isotropic squared
exp onen tial (SE) function, i.e. the Gaussian k ernel. The k ernel sp ecies the smo othness assumption
b et w een data p oin ts. While the GP mo del has no direct parameters, it do es ha v e h yp erparameters:
the k ernel’s parameters, as further explained in Section 8.2. These h yp erparameters can b e estimated
from data using, for example, maxim um lik eliho o d estimation (Rasm ussen and Williams, 2006).
F or o-line metho ds, e.g. (Binney et al., 2013, Hollinger and Sukhatme, 2014, Krause et al., 2008,
P atten et al., 2013, Singh et al., 2007), the h yp erparameters can b e estimated after all of the data
has b een collected. F or example, the w orks in (Hollinger and Sukhatme, 2014, Krause et al., 2008,
Singh et al., 2007) use a subset of all collected data for h yp erparameter optimization. F or on-line
estimation of the mo del, i.e. in activ e learning and for adaptiv e sampling, the h yp erparameters
should b e estimated b efore or during execution.
Some previous w orks estimate the h yp erparameters b efore running their adaptiv e sampling path
planning: Hitz et al. (2014) estimated h yp erparameters based on prior data for the sampling region.
Binney et al. (2013) estimated h yp erparameters b y using data from an initial run, what w e call a
pilot surv ey , whic h w as executed prior to running an y other sampling routines. Ho w ev er, their pap er
do es not sp ecify the shap e or length of the pilot surv ey (Binney et al., 2013). Other w orks estimate
the h yp erparameters during the sampling: Thompson et al. (2011) estimated the h yp erparameters
initially b y starting ev ery adaptiv e mission with a 1020s straigh t line driv e, and then p erio dically
This c hapter is mostly a reprin t of Pilot Surv eys for A daptiv e Informativ e Sampling (Kemna et al., 2018b).
70
A daptiv e Sampling with A UV s Stephanie Kemna
re-estimated the h yp erparameters during adaptiv e sampling. Their approac h assumes that the data
collected within this straigh t line driv e is represen tativ e for the whole eld and leads to reasonable
h yp erparameters. F or some of the scenarios w e are considering, this assumption do es not hold, see
for example Figure 8.3. Garg and A y anian (2014) estimated the h yp erparameters during execution
b y k eeping a b elief distribution o v er the h yp erparameters, initialized randomly , and using particle
ltering for determining the h yp erparameters at an y time. This approac h also allo w ed them to
accoun t for spatio-temp orally v arying elds. Ho w ev er, the random initialization could still lead to
problems with mo del learning. T o the b est of our kno wledge, there are no other w orks that explicitly
use pilot surv eys and/or in v estigate ho w b est to design a pilot surv ey for mo del initialization.
W e are in terested in dev eloping approac hes that assume no prior data is a v ailable. This means
that w e cannot estimate the h yp erparameters o-line, prior to running our sampling routines. If
p ossible, the h yp erparameters should b e set to reasonable v alues based on exp ert kno wledge, or
kno wledge ab out the area size or phenomena. An initial guess can decrease c hances of estimating
the h yp erparameters incorrectly , e.g. b y a v oiding lo cal maxima. W e recommend the follo wing steps
for estimating the h yp erparameters during an adaptiv e sampling surv ey:
1. Start adaptiv e sampling with an in tegrated pilot surv ey , to estimate the h yp erparameters and
initialize the mo del.
2. Re-estimate the h yp erparameters ev ery X min utes, to up date the mo del based on new data.
W e mak e the case for using an in tegrated pilot, where the pilot is an in tegral part of the
adaptiv e sampling routine. This is recommended b ecause adaptiv e sampling metho ds will not w ork
w ell without a go o d estimation of the h yp erparameters. The pilot should b e in tegrated in to the
mission and subtracted from the o v erall mission time, rather than b eing a separate mission, when
comparing to approac hes that do not need a pilot surv ey , e.g. la wnmo w er surv eys. The data from
the pilot is k ept in the mo del and used for the subsequen t adaptiv e selection of w a yp oin ts for further
sampling.
In this section w e ev aluate four in tegrated pilots created using the softmax function, with a
‘temp erature’ parameter , whic h is set to t1;6;30;100u. This roughly corresp onds to a cross
tra jectory o v er the sampling area, t w o in termediary solutions, and one pilot of randomly dra wn
w a yp oin ts, resp ectiv ely . Sim ulation results sho w that the pilots with lo w er v alues of , whic h
spread out the w a yp oin ts more, are on a v erage more successful in obtaining a go o d estimate on the
h yp erparameters of the mo del.
8.2 Theory
In this section, w e discuss the theory b ehind our adaptiv e informativ e sampling approac h, and
the c hoice of pilots. This theory follo ws explanations in prior w orks, e.g. (Kemna et al., 2017,
Lo w et al., 2009c): The rob ot in ternally constructs a mo del of en vironmen tal phenomena, e.g.
Chloroph yll abundance, using Gaussian Pro cess regression. This mo del is used to pic k w a yp oin ts
with maxim um en trop y for further sampling. The con tributions in this section lie in the dev elopmen t
of the pilot surv eys and metho ds of handling h yp erparameter estimation.
CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING 71
Stephanie Kemna A daptiv e Sampling with A UV s
8.2.1 Gaussian Process Regression for Model Creation
Gaussian Pro cess (GP) regression is a standard metho d for spatial eld mo deling (Rasm ussen and
Williams, 2006). The GP is sp ecied b y its prior mean and co v ariance function. W e use a zero
mean prior and for the co v ariance function a com bination of an isotropic squared exp onen tial (SE)
k ernel, and white noise co v ariance function. The SE co v ariance function is giv en b y (Rasm ussen
and Williams, 2006):
kpx;x
1
q
2
f
expt
1
2l
2
|xx
1
|
2
u (8.1)
where x and x
1
are t w o training sample lo cations, x PX ,X R
2
,
2
f
is the signal v ariance (or
amplitude), and l is the k ernel’s length scale.
2
f
and l are h yp erparameters. W e com bine the SE
k ernel with a white noise k ernel, to b etter mo del the exp ected noise in the data. This k ernel has
one h yp erparameter
2
n
, noise v ariance. F ollo wing Lo w et al. (2009c), w e use a log Gaussian Pro cess
(`GP) to mo del the eld: the v ehicle tak es the log of the measuremen ts b efore incorp orating them
in to the GP . This approac h considers that biological data from elds with ‘hotsp ots’ tend to follo w
a log-normal distribution, due to large areas with lo w v alues and small areas with high v alues (Cro w
and Shimizu, 1988).
W e follo w previously in tro duced notation for the `GP mo del (Kemna et al., 2017, Lo w et al.,
2009c): Let Y
x
denote an `GP , whic h is used to mo del the sensor v alue y
x
at lo cation xPX . Let
Z
x
lnY
x
, denote a GP . Then w e can create the `GP using GP regression b y utilizing the fact that
z
x
lny
x
. The GP’s p osterior mean and v ariance,
Zx|d
i
and
2
Zx|d
i
for sampled data d
i
, are used
to calculate the p osterior mean and v ariance of the `GP (Lo w et al., 2009c) as:

Yx|d
i
expt
Zx|d
i

2
Zx|d
i
{2u (8.2)

2
Yx|d
i

2
Yx|d
i
pexpt
2
Zx|d
i
u1q (8.3)
The v ehicle th us creates an `GP mo del on b oard, while it is sampling the en vironmen t.
The h yp erparameters of the`GP are estimated ev ery 500s. T o reduce computational complexit y
for h yp erparameter optimization, w e do wnsample the data b y a factor of four, k eeping ev ery fourth
sample, for the optimization only . The mo del created on the v ehicle con tains all measuremen ts. W e
test four pilot surv eys that gather data for initial h yp erparameter estimation, as further explained
in Section 8.2.3. W e use the lib gp library (Blum, 2016) and the conjugate gradien t metho d for
h yp erparameter optimization, with 100 iterations.
8.2.2 P ath Planning
The v ehicle uses the `GP mo del to decide where to sample next. W e tak e a state-indep enden t
approac h to path planning: based on the measuremen ts made so far, w e nd the most informativ e
sampling lo cation across the whole space, whic h is then c hosen as the next w a yp oin t. The v ehicle
mak es straigh t line mo v emen ts b et w een these w a yp oin ts via a standard w a yp oin t b eha vior. W e
measure informativ eness using the p osterior en trop y on the mo del, as deriv ed b y Lo w et al. (2009c):
H

Y
x
i1
|d
i

log
b
2e
2
Z
x
i1
|d
i

Z
x
i1
|d
i
(8.4)
72 CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING
A daptiv e Sampling with A UV s Stephanie Kemna
The next w a yp oin t is th us an (un visited) lo cation with the highest p osterior map en trop y , an ywhere
in the sampling space, regardless of the distance from the curren t lo cation. F or the log-GP this
sampling approac h means that w e maximize b oth for lo cations with high p osterior v ariance, as w ell
as lo cations with high exp ected sensor v alues. F or example, if w e are sampling for algae abundance,
then high sensor v alues are measured in areas where algal blo oms exist. These areas are lik ely to
b e most in teresting to the data customer, e.g. biologists or o ceanographers.
8.2.3 In tegrated Pilot Surveys
T o estimate the initial h yp erparameters of the `GP mo del, w e use an in tegrated pilot surv ey . W e
w an t to collect data that is represen tativ e of the eld, i.e. including the full sp ectrum of data v alues,
but w e ha v e to c ho ose sampling lo cations without ha ving prior data from the eld. T o optimize for
co v erage and spread o v er the area, one can use the area’s corners as w a yp oin ts. Ho w ev er, this ma y
lea v e large gaps b et w een sampling lo cations, whic h could mean missing out on small hotsp ot areas.
Alternativ ely , one can visit random lo cations in the area. Ho w ev er, the risk then is that only part
of the eld ma y b e co v ered, and features in other parts of the eld will b e missed. Therefore, w e
w an t to balance b et w een random sampling and maximizing the spread of w a yp oin ts.
T o obtain a pilot with p oin ts spread across the area, w e ev aluate a utilit y function D . This
function D is the minim um distance b et w een w a yp oin ts and previously visited paths, whic h w e
w an t to maximize:
Dpx
i
q minpdpx
i
;s
j
qq ; @s
j
PS (8.5)
wherex
i
is the lo cation of a w a yp oin t candidate, d is the distance function for the Euclidean distance
b et w een p ossible w a yp oin ts and previous line segmen ts, and s
j
is a line segmen t from the set S of
line segmen ts b et w een previously c hosen w a yp oin ts.
T o c ho ose w a yp oin ts, w e ev aluate the probabilit y of c ho osing a p ossible w a yp oin t lo cation using
a softmax equation (Sutton and Barto, 1998) on the utilit y function:
ppx
i
q
e
Dpx
i
q{
°
j
e
Dpx
j
q{
(8.6)
where is the ‘temp erature’ factor (Sutton and Barto, 1998). If is high, all actions b ecome nearly
equally probable and w e ha v e a uniform random sampling approac h. F or 1, it maximizes the
minim um distance b et w een p oten tial w a yp oin ts and sampled paths, c ho osing w a yp oin ts at corners
of the area. P aths are generated using a maxim um length equal to the path length for 1. The
n um b er of w a yp oin ts is unconstrained.
Cho osing P arameter
In order to use Equation (8.6), w e need to c ho ose a v alue for the ‘temp erature’, . Therefore w e
ev aluated dieren t metrics for the v alue function for the eld. Remem b er that the v alue function
considers the minim um distance b et w een p ossible w a yp oin ts and previously sampled lo cations.
Because the softmax sampling is probabilistic, w e ran 500 trials for ev ery v alue of . F or ev ery
run, w e calculated the minim um distance of all grid p oin ts to the c hosen pilot path. Based on this,
w e calculated the exp ected minim um distance for eac h grid p oin t lo cation (exp ected min distances)
CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING 73
Stephanie Kemna A daptiv e Sampling with A UV s
o v er all runs, and w e calculated the maxim um minim um distance for eac h eld (maxim um of min
distances). The metrics are, for eac h , the maxim um (max) and a v erage (a vg) o v er the exp ected
minim um distances, and the a v erage of all maxima, as sho wn in Figure 8.1. Figure 8.1 also sho ws
the a v erage n um b er of w a yp oin ts, whic h is not used for deciding . Ho w ev er, it sho ws a general
trend of increasing n um b er of w a yp oin ts with increasing v alues of . This means that w a yp oin ts
often end up b eing closer together, and more w a yp oin ts can b e c hosen within the same path length
budget.
W e w an t to c ho ose a v alue for that b oth reduces the c hance of lea ving large areas systematically
un visited for 1, or not co v ering the whole area for Ñ inf . Based on Figure 8.1 w e c hose 6,
whic h corresp onds to a minim um in the graphs for a v erage o v er exp ected minim um distances (blac k
dash-dot) and a v erage o v er maxima (magen ta dashed). W e also c hose 30, whic h corresp onds to
one of the minima in the graph for maxim um o v er exp ected minim um distances (green solid). By
c ho osing these v alues, w e aim to balance b et w een spreading out w a yp oin t lo cations and randomizing
sampling lo cations. A v alue of 6 is a conserv ativ e minima, and corresp onds to pilots that are
still v ery similar to the cross pilot. A v alue of 30 is closer to uniform random sampling, but
w ould still try and spread out the w a yp oin ts to some exten t. Figure 8.2 sho ws an example of
Figure 8.1: Determining : The maxim um (green solid) and a v erage (blac k dash-dot) o v er the
exp ected minim um distances, the a v erage o v er all maxima (magen ta dashed), and the a v erage
n um b er of w a yp oin ts (blue dotted), for 500 runs p er c hoice of . Y axis as p er lab els: (scaled)
distance or (scaled) n um b er w a yp oin ts. Best view ed in color.
74 CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING
A daptiv e Sampling with A UV s Stephanie Kemna
w a yp oin ts and paths c hosen b y the v ehicle for the dieren t pilot surv ey cases; 1 (cross), 6;30;
and 100 (random).
Figure 8.2: Example tra jectories for 1 (top left), 6 (top righ t), 30 (b ottom left) and
100 (b ottom righ t).
8.3 Experimental set-up
F or our ev aluation of the in tegrated pilots, w e ran sim ulation studies. W e briey explain the
implemen tation and set-up details, for eac h t yp e of exp erimen t, in this section.
W e sim ulate algae abundance for six scenarios, as sho wn in Figure 8.3. The rst t w o scenarios
w ere used in prior w ork (Kemna et al., 2016, 2017). The other four scenarios w ere added to test
p erformance in case there w ould b e less pronounced blo oms, or non-Gaussian shap es. W ork is
underw a y to create scenarios from data obtained in the eld. All scenarios assume a rectangular
sampling region, i.e. a 2-D grid space, of 400x200m. Data are sim ulated at 10m grid spacing with
output v alues ranging from 040g{L, as a pro xy for high Chloroph yll v alues. Random Gaussian
noise is added, with a noise amplitude up to 1020% of the data range. The sim ulated v ehicle tak es
samples with added Gaussian noise (signal v ariance 1:5). The v ehicle is not giv en information
ab out the sensor noise.
W e ran sim ulations for v e dieren t surv eys:
la wnmo w er surv ey (non-adaptiv e)
adaptiv e surv ey , 1, ‘cross pilot’
CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING 75
Stephanie Kemna A daptiv e Sampling with A UV s
a) b) c)
d) e) f )
Figure 8.3: Six scenarios with generated data. Theoretically the data can represen t an ything, in
this w ork the ‘data v alue’ represen ts Chloroph yll, g{L.
adaptiv e surv ey , 6
adaptiv e surv ey , 30
adaptiv e surv ey , 100, ‘random w a yp oin ts pilot’
The la wnmo w er surv ey is a comp osite of b oth a v ertical and horizon tal la wnmo w er o v er the surv ey
area, with 20m trac k spacing, implemen ted via a w a yp oin t b eha vior. The other pilot surv eys use
Equation (8.5) and Equation (8.6) for w a yp oin t selection.
F or ev ery sim ulation run, the v ehicle starts in the b ottom left corner of the eld. V ariabilit y in
scenarios appro ximately co v ers for p oten tial dieren t starting lo cations, though future studies could
in v estigate the eects of v ehicle starting p ositions. F or a real w orld scenario, the starting lo cation
ma y also b e restricted b y p ossible deplo ymen t lo cations.
W e ran 30 sim ulations for eac h surv ey t yp e for eac h scenario. Eac h sim ulation w as time-limited
to the duration of the la wnmo w er surv ey . Our fo cus is on impro ving initial sampling p erformance
to pro vide an an ytime prediction capabilit y . During ev ery sim ulation, w e recorded the latest mo del
created on the v ehicle ev ery 10 min utes (600s).
F or our implemen tation w e used the MOOS-IvP middelw are (Benjamin et al., 2010), whic h
incorp orates a b eha vior-based autonom y . W e use standard b eha viors suc h as; w a yp oin t, loiter, and
constan t depth. F or the sim ulations, w e use a simple v ehicle dynamics mo del with PID con trol to
sim ulate an autonomous underw ater v ehicle (A UV), and the biological data (Chloroph yll) sim ulator
describ ed at the start of this section.
76 CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING
A daptiv e Sampling with A UV s Stephanie Kemna
8.4 Results
W e ev aluate p erformance in terms of Ro ot Mean Squared Error (RMSE) b et w een the mo del and
the ground truth, and in terms of the estimated h yp erparameters v ersus their ground truth v alues.
8.4.1 Ro ot Mean Squared Error
W e ran 30 sim ulations for eac h surv ey t yp e for eac h scenario. Figure 8.4 sho ws the sim ulation results
in terms of the RMSE b et w een the v ehicle’s mo del and the generated data, i.e. the ground truth
(Figure 8.3). Eac h subgure sho ws the results for a single scenario, for all v e surv eys. RMSE is
plotted against time steps of 600s, where time step t 1 corresp onds to the start of the surv ey .
W e sho w b o xplots, rather than a v erages with standard deviations, to b etter visualize outliers and
general trends. In general, outliers corresp ond to the runs when no go o d mo del w as created, and
for scenario e) the runs that did not create a go o d mo del created a bimo dal RMSE p erformance
graph. Our main fo cus in the ev aluation is on the early stages of mo del creation, to ev aluate the
pilot surv eys, and not the other path planning metho d.
Figure 8.4 sho ws that for most scenarios, the RMSE quic kly drops for adaptiv e sampling.
Scenarios b) and f ) see a more gradual decline for all metho ds. F or most scenarios, dierences
b et w een the pilot surv eys’ p erformances are not statistically signican t, giv en that all b o xplots
o v erlap. W e briey note: F or scenarios a) - d) and f ), all adaptiv e sampling surv eys get a signican tly
b etter mo del more quic kly than the la wnmo w er surv ey . The la wnmo w er p erformance in most cases
drastically impro v es after 5 time steps at t 6, whic h appro ximately corresp onds to when the
v ehicle is executing the second la wnmo w er pattern (horizon tal) and revisits areas. In terms of pilot
surv ey p erformance, w e see: F or scenario b), 1 and 6 do b etter than the softmax surv eys
with high v alues of . F or scenario c), there is a wide spread on the initial estimate. V alues of
t1;6u do a little b etter initially . F or scenario e), softmax surv ey 1 clearly outp erforms high
v alues from timestep t 35.
RMSE outlier analysis: F rom Figure 8.4 it is clear that: F or scenario a), the softmax surv eys
with high v alues of ha v e more outliers. F or scenario d), t1;100u initially ha v e more outliers.
F or scenario e), high surv eys ha v e more outliers. T able 8.1 sho ws the a v erage n um b er of outliers,
for eac h surv ey t yp e, a v eraged o v er all scenarios, for four time steps: 2;3;4 and the nal, 12. Time
step t 2 corresp onds to the predictions that are sa v ed after the rst h yp erparameter estimation,
and time step t 12 corresp onds to predictions sa v ed after the nal h yp erparameter estimation.
The n um b er of outliers is initially highest for 100 and lo w est for 1. F rom t 2 to t 3
the n um b er of outliers drops the most for 6, whic h also ends with the few est outliers. This
indicates more consisten t p erformance across sim ulations and across scenarios.
8.4.2 Hyp erparameters
W e further in v estigate p erformance in terms of the estimation of the h yp erparameters, whic h mainly
determine the qualit y of the mo del, in particular the k ernel’s length scale. As previously men tioned,
when the h yp erparameters are misestimated, the adaptiv e sampling approac h will not w ork as w ell.
Therefore, w e w an t to mak e sure that w e c ho ose a go o d initial sampling approac h to start the
adaptiv e sampling surv ey o with. Data that are collected initially should b e represen tativ e for the
CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING 77
Stephanie Kemna A daptiv e Sampling with A UV s
Figure 8.4: Bo xplots (median, 25th and 75th p ercen tiles) on RMSE for scenario a) - f ), 30
sim ulations p er surv ey . Crosses are outliers. Ev aluations are done based on mo dels that w ere
sa v ed ev ery 10 min utes (600s).
78 CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING
A daptiv e Sampling with A UV s Stephanie Kemna
Figure 8.5: Bo xplots (median, 25th and 75th p ercen tiles) on estimated length scale h yp erparameter
(HP), for scenarios a-f, 30 sim ulations p er approac h. Crosses are outliers. Ev aluations are done
based on mo dels that w ere sa v ed ev ery 500 seconds.
CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING 79
Stephanie Kemna A daptiv e Sampling with A UV s
Surv ey t yp e t2 t3 t4 t12
la wnmo w er 0.67 1.17 0.33 0.33
1 1.67 2 2.67 2
6 2 0.67 1.83 0.67
30 2 2.17 1.67 1.83
100 2.83 2.33 2.5 1.17
T able 8.1: A v erage n um b er of RMSE outliers p er time step, a v eraged o v er all scenarios, for ev ery
t yp e of surv ey .
eld, and lead to go o d estimation of h yp erparameters.
Figure 8.5 sho ws the estimated log length scale o v er time, stored after ev ery h yp erparameter
optimization (ev ery 500 seconds). As previously men tioned, t 1 corresp onds to the start of the
mission. Note that all v alues are distances in longitude-latitude degrees and therefore quite small.
The ground truth v alues of the h yp erparameters are calculated from all data in the sim ulated data
les, using the GPML Matlab libraries (Rasm ussen, 2017). These are indicated as dashed grey lines.
The dash-dot ligh t-grey lines are error b ounds. These error b ounds are determined b y a v eraging the
nal error across all sim ulations and all scenarios, and taking the a v erage error plus one standard
deviation. If the log length scale v alue of a single sim ulation is more (or less) than the true length
scale plus (or min us) the error b ound, then w e consider it a misestimation of the h yp erparameters.
The results sho w that the p o or p erformance for scenario e) corresp onds to badly estimated
length scales. F or scenario a), where 30 has one bad run, with a corresp onding outlier in
the log length scale plot. F or the la wnmo w er surv eys, the initial p o or estimations are also due to
incorrect estimation of the length scale, whic h do es not c hange from its initial v alue un til t 7.
The p erformance b et w een the dieren t pilot surv eys is quite similar. The h yp erparameters start to
settle do wn after the second h yp erparameter estimation, at timestep t 3. F or scenario b) and e),
w e see that with t30;100u, it tak es longer for the log length scale to get close to the correct
v alue. F or scenario c), w e see that for all surv eys the log length scale is sligh tly underestimated,
whic h corresp onds to a length scale that is appro ximately 20-40 meters shorter than the actual
v alue.
L ength sc ale outlier analysis: F rom Figure 8.5 it is clear that: F or scenario a), there is one
outlier for 30. F or scenario e), there are man y outliers. While there are some outliers for
t1;6u, these are few er than for t30;100u, meaning that o v erall they w ere more successful.
F or scenario d), t1;100u ha v e more outliers at the end. F or scenario f ), 30 initially has more
outliers. T able 8.2 sho ws the a v erage n um b er of outliers for the length scale log-h yp erparameter
(lHP) b o xplots, for eac h surv ey t yp e, a v eraged o v er all scenarios, for four time steps: 2;3;4 and
the nal, 14. Note that, in comparison to the RMSE plots, b ecause h yp erparameter optimization
happ ens ev ery 500 seconds rather than ev ery 600, there are 2 more time steps. Time step t 2
corresp onds to the rst h yp erparameter estimation, and time step t 14 corresp onds to the nal
h yp erparameter estimation. Note that while there are no outliers for the la wnmo w er p erformance
during t 2 to t 4, the length scale is consisten tly misestimated during this time. W e see that
after the rst h yp erparameter estimation, t 2, the n um b er of outliers reduces on a v erage for
t6;30u. This do wn w ards trend con tin ues for 6.
80 CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING
A daptiv e Sampling with A UV s Stephanie Kemna
Surv ey t yp e t2 t3 t4 t14
la wnmo w er 0 0 0 1.17
1 1.33 3 2.33 0.83
6 3.17 2.67 1.83 0.67
30 2.83 2.17 1.33 2.33
100 4 1.5 2.33 2
T able 8.2: A v erage n um b er of lHP outliers p er time step, a v eraged o v er all scenarios, for ev ery t yp e
of surv ey .
8.5 Discussion & F uture work
The sim ulation results conrmed that adaptiv e sampling can impro v e mo deling p erformance during
the early stages of mo del creation. W e in v estigated four pilot surv eys for obtaining represen tativ e
data for mo del initialization. Results conrmed that an initial p o or estimation of the h yp erparam-
eters can b e detrimen tal to the o v erall mo deling p erformance. W e found that for lo w er v alues of ,
w e obtained b etter estimated h yp erparameters on a v erage and lo w er mo del error early on, than for
higher v alues. This suggests that spreading out w a yp oin ts is to b e preferred o v er randomly pic king
w a yp oin ts. W e recommend using the softmax-based w a yp oin t selection metho d for pilots, using
6, whic h on a v erage pro vided the b est and most stable p erformance.
F or the la wnmo w er surv eys, w e sa w the RMSE greatly reduce after 6 time steps. This appro xi-
mately corresp onded to the second pass o v er the area, leading to more samples through the blo oms.
F rom Figure 8.5 w e concluded that the initial bad p erformance w as due to bad estimates of the
k ernel length scale. This highligh ts the need for quic kly collecting represen tativ e samples when the
actual h yp erparameters are not kno wn. F urthermore, if an ytime prediction capabilit y is desired for
an o-line surv ey approac h, it ma y b e necessary to also run a pilot surv ey b efore the main surv ey .
F or future w ork, there are man y p ossible a v en ues for further in v estigations. F or one, w e did not
nd theoretical pro ofs y et to guaran tee an initial go o d mo del creation, when no prior information is
a v ailable. F or the softmax approac h, it is imp ossible to set the temp erature based on the scenario, if
the scenario is not kno wn. Ho w ev er, if one allo ws, for example, for some exp ert kno wledge to guide
sampling, this ma y b ecome feasible. Therefore w e recommend in v estigating approac hes for b est
incorp orating exp ert kno wledge. F urthermore, w e ha v e c hosen a utilit y function that maximizes
minim um distance b et w een sampled p oin ts, optimizing for co v erage. Again, this is based on the
fact that no prior data is a v ailable. It w ould b e in teresting to explore other utilit y functions. Finally ,
in our ev aluation of pilots w e ha v e c hosen to use a set length for the pilot, equal to the distance
of a cross tra jectory o v er the area. It w ould b e in teresting to ev aluate whether represen tativ e data
could b e obtained in a shorter amoun t of time, i.e. a shorter path.
8.6 Conclusions
In this section w e ev aluated four pilot surv eys for adaptiv e informativ e sampling. These pilots are
essen tial at the start of an y adaptiv e mission where no prior data is a v ailable, to collect represen tativ e
CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING 81
Stephanie Kemna A daptiv e Sampling with A UV s
data for h yp erparameter estimation. An initial bad estimate on h yp erparameters can lead a v ehicle
to construct a bad mo del and th us collect non-informativ e samples. One metho d of running a pilot
is to tra v el b et w een all corner lo cations of a sampling area. W e explored whether adding a degree
of randomness to this approac h impro v es its p erformance. W e ev aluated a softmax function for
w a yp oin t selection, whic h balances b et w een spreading out w a yp oin ts and uniform random sampling.
W e sho w ed that, for the giv en v alue function, lo w v alues of , e.g. 6 with spread out w a yp oin ts,
lead to the most stable p erformance in terms of initial h yp erparameter estimation.
82 CHAPTER 8. PILOT SUR VEYS F OR AD APTIVE INF ORMA TIVE SAMPLING
9 | Multi-Robot Adaptive Informative Sampling:
Asynchronous Surfacing Strategies
In Chapter 7 w e discussed a co ordination approac h for m ulti-rob ot adaptiv e informativ e sampling.
The approac h relied on v ehicles sending eac h other a surfacing request, and then surfacing at the
same time. A little handshak e routine at the surface w ould mak e sure the v ehicles w ould b e ready
to share data, b efore sharing data, and then calculating the V oronoi partitions. Because time can
b e lost in the o v erhead of sync hronized surfacing ev en ts, e.g. the time it tak es to request surfacing
ev en ts and for all v ehicles to surface, and b ecause ha ving and main taining sync hronized clo c ks
can complicated eld trials, w e lo ok at async hronous surfacing strategies in this c hapter. F or this
purp ose, w e place a system on the surface as a data h ub. The follo wing sections explain our approac h
and results.
9.1 Introduction
The use of autonomous underw ater v ehicles (A UV s) is b ecoming more common for sampling lak es
and o ceans. One tec hnique for setting up A UV s to gather data that is most useful for the end user is
informativ e sampling, or informativ e path planning, where the A UV creates an on-b oard mo del and
uses information-theoretic metrics to decide where to collect data measuremen ts. An op en researc h
question is ho w m ultiple A UV s can b est collab orate for quic kly creating a mo del of, for example,
temp erature or algae distributions. In previous w ork, w e ev aluated a tec hnique for co ordinating
rob ot mo v emen ts through V oronoi partitioning, with data sharing through sync hronized surfacing
ev en ts (Kemna et al., 2017). In this w ork, w e compare the former metho d to a new metho d that uses
a surface-based data h ub, allo wing async hronous surfacing of v ehicles. Our con tributions include
t w o new metho ds for deciding when b est to surface: an altruistic surfacing metho d based on the
estimated v alue of the A UV’s o wn samples, and a gain-based surfacing metho d based on estimating
the amoun t of samples that can b e collected at the surface.
9.1.1 Related work
In terms of related w orks, there are man y cases where p eople ha v e lo ok ed at data sharing b et w een
sampling systems via data m uling, e.g. Bhadauria et al. (2011), Dun babin et al. (2006), T ekdas et al.
(2009), Zhang et al. (2004). In most of these cases a single data m ule is used to collect and transfer
This c hapter is mostly a preprin t of Surfacing strategies for m ulti-rob ot adaptiv e informativ e sampling with a
surface-based data h ub (Kemna and Sukhatme, 2018).
83
Stephanie Kemna A daptiv e Sampling with A UV s
data from and b et w een static sensing no des. This turns the problem in to solving the tra v eling
salesp erson problem (TSP), either for single (Dun babin et al., 2006) or m ultiple (Bhadauria et al.,
2011, T ekdas et al., 2009) autonomous v ehicles.
There are sev eral w orks that fo cus more sp ecically on data sharing strategies (Hollinger and
Singh, 2010, Pngsthorn et al., 2010, Y ordano v a and Griths, 2016, Y ordano v a et al., 2017).
Hollinger and Singh (2010) in tro duced a metho d to utilize p erio dic connectivit y b et w een rob ots
in m ulti-rob ot co ordination for information gathering tasks. The in terv al of disconnection w as
assumed to b e dictated b y applications or c hosen b y the user. The rob ots did not try to optimize
the time of data sharing based on their gathered data, as w e address in this w ork. Pngsthorn et al.
(2010) in v estigated a m ulti-rob ot map up date strategy for p ose graph sim ultaneous lo calization and
mapping. The w ork fo cused on what data to transmit, giv en the limited underw ater comm unications
bandwidth. In prior w ork (Kemna et al., 2016), w e explored the trade-o b et w een underw ater and
surface-based comm unications. Giv en the p oten tial unreliabilit y of the underw ater comm unication
c hannel, w e fo cus here on surface-based comm unications.
Y ordano v a and Griths (2016), Y ordano v a et al. (2017) fo cused on dev eloping strategies for
rendezv ous planning in m ulti-rob ot m ulti-target searc h. In their scenario the underw ater rob ots
need to meet at certain rendezv ous p oin ts to share data. Initially , the rendezv ous p oin ts are sp ecied
based on pre-dened in terv als using rule-based logic, though the later w ork adapts the pre-dened
in terv als based on what the rob ots are sensing and predicted target distributions. This is more
similar to our former w ork where all v ehicles sync hronously surfaced to share data (Kemna et al.,
2017), though they did not ha v e to rendezv ous in terms of lo cation. In this w ork w e remo v e the
sync hronization constrain t, suc h that the v ehicles lose less time in data sharing, and w e use a
surface-based data h ub for async hronous data sharing. A w ork that similarly uses async hronous
comm unications is b y Garg and A y anian (2014). They use a cen tral serv er to k eep a b elief adaptation
for h yp erparameters of the mo del they create. Rob ots can comm unicate to the serv er p erio dically
and async hronously , though their pap er do es not explore the strategies used for deciding when to
comm unicate.
9.1.2 Contributions
The main question w e address in this c hapter is when to surface for data sharing, for a decen tralized
system with a surface-based data h ub. A trade-o exists in minimizing surfacing ev en ts in order to
a v oid time that is w asted on surfacing, v ersus maximizing surfacing ev en ts in order to obtain data
from other v ehicles. Eac h underw ater v ehicle do es not kno w when the other underw ater v ehicles
surface to o-load and obtain data. W e dev elop ed t w o dieren t metho ds for deciding when to
surface:
1. altruistic surfacing: estimate the v alue of y our o wn samples, and calculate y our desire to share,
2. gain-based surfacing: estimate the p oten tial gain that y ou can obtain from collecting samples
on the surface.
Our approac h is distinct from rendezv ous metho ds where all rob ots are required to come together,
or to the surface, to share data. W e compare our approac h to t w o formerly published approac hes,
84 CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
ASYNCHR ONOUS SURF A CING STRA TEGIES
A daptiv e Sampling with A UV s Stephanie Kemna
where the rob ots (a) p erio dically surface, assuming sync hronized clo c ks, and (b) sync hronize sur-
facing ev en ts b y using surfacing requests via acoustic comm unication with V oronoi-based v ehicle
co ordination (Kemna et al., 2017).
9.2 Method
In this section w e briey recap some c hoices for our mo deling approac h, whic h uses Gaussian Pro cess
regression. Then w e discuss more elab orately the t w o prop osed metho ds that the v ehicles can use
for deciding when to surface.
9.2.1 Mo deling Approach
The v ehicles are task ed to create a 2-D mo del of a spatial phenomena, for example an algal blo om. A
common metho d for spatial mo deling is Gaussian Pro cess (GP) regression (Rasm ussen and Williams,
2006). W e refer to Chapter 3 and Chapter 5 for the theory and equations regarding GP regression.
W e initialize the h yp erparameters as log h yp erparameters to 7:5, appro ximately 55m, for
log length scale, 1:38 for log signal and 0:92 for log noise standard deviations, based on prior
exp erimen ts and exp ert kno wledge (Kemna et al., 2018a). In this w ork the h yp erparameters are re-
estimated after ev ery surfacing and data sharing ev en t, using a conjugate gradien t metho d with 50
iterations. The h yp erparameters are only up dated if the newly estimated h yp erparameters deviate
no more than 25% from the old h yp erparameters, to a v oid erroneous estimation due to lo cal optima.
9.2.2 Asynchronous Surfacing Methods
W e use a set-up with t w o sampling rob ots and one surface-based system. The surface-based system
serv es as a data h ub and could b e a v ehicle, for ease of deplo ymen t, or a buo y , to minimize cost.
W e explore t w o metho ds for deciding when to surface:
1. altruistic surfacing: the A UV s estimate the v alue of their o wn samples, and calculate their
desire to share,
2. gain-based surfacing: the A UV s estimate the p oten tial gain they can obtain from collecting
samples on the surface.
Altruistic surfacing
In order to determine when to surface for altruistic surfacing, the A UV needs to estimate the v alue
of the samples it has gathered so far, and transform this in to a ‘desire to share’. W e appro ximate
the v alue of gathered samples b y ev aluating the c hange in the sum of predictiv e v ariances in the
mo del. The v ehicle calculates the predictiv e mean and v ariance estimates whenev er it reac hes a
w a yp oin t and needs to decide where to go next. As men tioned in Section 9.2.1, the A UV calculates
the predictiv e v ariance for all as of y et un visited lo cations from a 10m spaced grid o v er the mission
area. A t this p oin t w e can ev aluate the decrease in the sum of predictiv e v ariances v ersus the last
sum of predictiv e v ariances, to estimate the informativ eness of collected samples that ha v e not y et
b een shared.
CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
ASYNCHR ONOUS SURF A CING STRA TEGIES
85
Stephanie Kemna A daptiv e Sampling with A UV s
The curren t algorithm considers the c hange b et w een the last and the curren t sum of predictiv e
v ariances. If the curren t sum of v ariances
2
i
deviates more than a set p ercen tage from the previous
sum of v ariances
2
i1
, calculated at the last surfacing ev en t, then the v ehicle decides to surface:
¸

2
i
{
¸

2
i1
1 (9.1)
The v ariable is a parameter, whic h w as empirically set to 0.4 in the curren t sim ulations.
Gain-based surfacing
In order to determine when to surface for gain-based surfacing, w e consider ho w m uc h information
can b e collected at the surface. W e assume that the amoun t of information can b e appro ximated b y
the n um b er of samples that w ere collected. There are sev eral factors that inuence when a v ehicle
should w an t to surface, including: a) when the v ehicle last surfaced, b) ho w m uc h time is lost in
surfacing, whic h can b e appro ximated in n um b er of missed samples, c) whether the other v ehicles
ha v e surfaced and o-loaded data to the surface h ub, and d) the v alue of samples with time. The
v alue of samples decreases o v er time, b ecause of the prop ert y of submo dularit y , whic h applies to
informativ e sampling problems (Guestrin et al., 2005).
In the follo wing exp erimen ts eac h v ehicle decides to surface when the n um b er of samples the other
v ehicles ma y ha v e collected since the last surfacing ev en t (considering a) exceeds t wice the n um b er
of samples the A UV loses out on while surfacing (considering b), increased o v er time (considering
d). W e use t wice the amoun t of samples ‘lost’ to accoun t for the fact that other v ehicles ma y
also surface within this time span (considering c), in whic h case few er samples will b e a v ailable at
the surface, and to allo w enough time to increase the lik eliho o d that other v ehicles ha v e surfaced
(considering c). W e ev aluate whether or not to surface con tin uously .
F ormally , w e surface when:
d
i1
f
s
pn
auvs
1q ¡ 2p1pt
i
{t
e
qqf
s
d
os
(9.2)
where d
i1
is the duration since the last surfacing ev en t, f
s
is the sampling frequency , n
auvs
is the
total n um b er of A UV s, t
i
is the curren t time, t
e
is time of mission end, and d
os
is the total duration
of surfacing and b eing on the surface:
d
os
2d
s
d
b
d
e
d
c
(9.3)
where d
s
is the duration of the actual surfacing, i.e. ascending to the surface and descending bac k
to sampling depth, d
b
is a buer duration during whic h w e mak e sure the v ehicle is consisten tly at
the surface, d
e
is the duration of data exc hange, whic h t ypically is ¤ 1s, and d
c
is the duration of
running calculations to nd the next sampling lo cation. The duration of surfacing, d
s
, is:
d
s
h{v (9.4)
hz{sinpq (9.5)
where h is the h yp oten use, whic h is the distance along the surfacing tra jectory , v is v ehicle sp eed,
z is v ehicle depth, and is the diving/surfacing pitc h angle in radians. F or simplicit y w e assume
the v ehicle is w ell trimmed and con trolled, suc h that the pitc h angle is the same and appro ximately
86 CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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0 2000 4000 6000 8000 10000
GP size
0
200
400
600
800
1000
1200
Calculation duration (s)
AUV A
AUV B
polynomial fit
Figure 9.1: P olynomical function t for duration (s) of w a yp oin t calculations giv en the size of the
GP (n um b er of samples).
constan t for diving and surfacing. In this w ork w e set a pitc h angle of 15 degrees, based on our
lab’s A UV’s maxim um pitc h angle of 20 degrees.
W e appro ximate d
c
using a p olynomial function:
d
c
310
9
n
3
gp
10 (9.6)
where n
gp
are the n um b er of p oin ts in the GP’s sample set. The function t of d
c
is empirically
determined from the output durations of w a yp oin t calculations during sev eral exploratory sim u-
lations. Figure 9.1 sho ws an example from a sim ulation with t w o A UV s, where the size of the
GP is on the x-axis, and duration of calculations on the y-axis. The calculation times for b oth
sim ulated A UV s are sho wn through the green dashed and magen ta dash-dot lines, and the tted
function is the dotted blac k line. In a t ypical sim ulation the do wnsampled GP on whic h w e run
h yp erparameter optimization will con tain appro ximately 9000 sample p oin ts b y the end of the run,
sho wn in Section 9.4. Note that w e do wnsample b y a factor of 6 for h yp erparameter optimization
in this c hapter. F unction t could b e dieren t dep ending on the computer used for sim ulations,
computational p o w er a v ailable, and the implemen tation of the GP library . The main tak ea w a y here
is that it is of sup erlinear gro wth.
T o giv e an example:
If the A UV samples at 5m depth at a sp eed of 1:0m{s, then the duration of a surfacing ev en t is at
CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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Stephanie Kemna A daptiv e Sampling with A UV s
least 45 seconds:
h 5:0{sinp15:0q 19:32 (9.7)
d
s
19:32{1:0 19:32 (9.8)
d
os
2d
s
d
b
d
e
d
c
(9.9)
38:6451d
c
(9.10)
44:64d
c
(9.11)
In previous w ork (Kemna et al., 2017), w e lo ok ed at activ e co ordination of the v ehicles through
decen tralized V oronoi partitioning, whic h w as run dynamically as the mission progressed. In
that case the v ehicles surfaced sync hronously and therefore could obtain appro ximately similar
partitioning b y indep enden tly calculating V oronoi partitions. With async hronous surfacing, when
V oronoi partitions are calculated at dieren t times, decen tralized V oronoi calculations will not result
in the same partitioning across A UV s. The main reason w e added co ordination w as to mak e sure
that the v ehicles w ould not go to the same lo cation after data sharing, at whic h p oin t they had
appro ximately the same mo del. By making the surfacing times async hronous, it is unlik ely that
the v ehicles will ha v e the same mo del after data sharing, suc h that there is less of a need for activ e
co ordination. In this c hapter w e pro ceed without an activ e co ordination algorithm and compare
the async hronous surfacing strategies to our prior dev elop ed approac hes.
9.3 Experimental Set-up
T o test the dieren t surfacing strategies, w e run sim ulation studies o v er sev eral sim ulated elds.
These elds w ere generated using t w o metho ds: (1) creating a Gaussian Mixture Mo del (GMM)
from a random n um b er (110) of Gaussians of random size at random lo cations in the sampling
area, with random normal distributed noise added, and (2) randomly sampling a Gaussian Pro cess
mo del, initialized with h yp erparameters that w ere based on those estimated during eld exp erimen t.
F or the second case, w e set the length scale to 7:805, appro ximately 40m, and the a v erage signal
v ariance to 1:675, and randomly sample from the GP to create the sim ulation scenarios. Figure 9.2
sho ws the six scenarios, the top ro w sho ws the GMM elds a) - c), and the b ottom ro w sho ws the
GP sampled elds d) - f ).
W e compare p erformance for v e dieren t approac hes:
timed surfacing without the surface h ub, as in Kemna et al. (2017),
A UV-triggered surfacing with V oronoi partitioning, as in Kemna et al. (2017),
timed surfacing, with a surface h ub,
altruistic surfacing, with a surface h ub, and
gain-based surfacing, with a surface h ub.
88 CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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Figure 9.2: Scatterplots of the six sim ulated elds, left three are scenarios a) - c) created as a GMM
from random Gaussians, righ t three are scenarios d) - f ) created from sampling a Gaussian Pro cess
mo del. Eac h eld is for a 500600m area. Y ello w represen ts high concen trations of algae, and
dark blue is no algae.
Sim ulations are run using the MOOS-IvP middlew are (Benjamin et al., 2010) for sim ulating
the A UV s, their v ehicle dynamics, and con trol b eha viors, the gob y pro ject (Sc hneider, 2014) for
sim ulating acoustic comm unications, and the libGP library (Blum, 2016) for Gaussian Pro cess
regression. Because the GP calculations tak e longer as the size of the GP gro ws, and these
calculations cannot b e run faster than real time, w e limit the sim ulation sp eed to 3 times clo c k
sp eed. This is to mak e sure that the relativ e duration of calculations do es not negativ ely impact
mo deling p erformance o v er time to o m uc h. F or eac h sim ulation, adaptiv e sampling w as run for the
duration that it w ould tak e to run t w o la wnmo w er surv eys, one horizon tal and one v ertical, o v er
the surv ey area of 500600m, with 40m trac k spacing. This equals appro ximately 200 min utes,
or 67 min utes when w arp ed b y a factor of 3. A t this time the v ehicles w ere task ed to return to their
start lo cation while running a nal h yp erparameter optimization and mo del sa v e, lengthening eac h
sim ulation up to a total length of appro ximately 78 min utes. F or all scenarios w e run 30 sim ulations
for all v e tested approac hes. Ev ery adaptiv e sampling routine starts with a pilot surv ey as designed
in Kemna et al. (2018b), whic h is a quic k route o v er the area to collect data to initialize the GP
mo del b efore optimizing on it.
9.4 Results
Due to space constrain ts, w e list only results for A UV 2 here. In this section w e sho w example
results from our sim ulation runs. All plots are giv en in the app endix, Section 14.2.
Figure 9.3-Figure 9.7 sho w the median RMSE, RMSE b o xplots and cum ulativ e v ariance b o xplots
for scenario a) for A UV 2 (Bernard). As can b e v eried in the app endix, Section 14.2, these are
represen tativ e for scenarios a) - c). If w e judge p erformance purely on the median RMSE v alues,
Figure 9.3, w e see that all metho ds p erform appro ximately equal. Only the V oronoi approac h seems
to do a little w orse at the start.
Figure 9.5 sho ws the b o xplots, where the horizon tal line is the median, and the b ottom and top
edge are the 25th and 75th p ercen tile, resp ectiv ely . F or the V oronoi approac h, w e see that not all
runs at timestep 3 are bad, as compared to Figure 9.3. W e note that for scenarios a) and c) for
A UV 1, altruistic surfacing also has more v ariable p erformance in the early stages.
W e also ev aluate the p erformance in terms of the cum ulativ e v ariance in the mo del, i.e. the sum
of all the predictiv e v ariances, o v er all p ossible lo cations from the 10m spaced grid o v er the area.
CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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Stephanie Kemna A daptiv e Sampling with A UV s
Again w e see more v ariable p erformance for the V oronoi approac h at the start. All other approac hes
ha v e appro ximately equal p erformance.
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 9.3: Median RMSE for scenario a) for
A UV 2
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 9.4: Median RMSE for scenario e) for
A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
RMSE
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 9.5: RMSE b o xplots for scenario a) for
A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
1
10
2
10
3
RMSE
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 9.6: RMSE b o xplots for scenario e) for
A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
cumulative pred. variance
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 9.7: Cum ulativ e v ariance b o xplots for
scenario a) for A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
cumulative pred. variance
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 9.8: Cum ulativ e v ariance b o xplots for
scenario e) for A UV 2
Figure 9.4- 9.8 sho w the median RMSE, RMSE b o xplots, and cum ulativ e v ariance b o xplots for
scenario e). This scenario is represen tativ e for GP sampled scenarios e) - f ) (see Section 14.2).
90 CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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no h ub, timed no h ub, v or with h ub, timed with h ub, altruistic with h ub, gain-based
20.0 0.06 14.7 1.1 20.6 2.9 6.4 0.9 18.7 1.1
T able 9.1: A v erage n um b er of surfacing ev en ts, with one standard deviation, a v eraged o v er all
scenarios, o v er b oth v ehicles, o v er all 30 sim ulation runs.
no h ub, timed no h ub, v or with h ub, timed with h ub, altruistic with h ub, gain-based
9478 189 8979 409 9337 293 10135 366 9347 298
T able 9.2: A v erage n um b er of samples in nal GP for h yp erparameter optimization, with one
standard deviation, a v eraged o v er all scenarios, o v er b oth v ehicles, o v er all 30 sim ulation runs.
no h ub, timed no h ub, v or with h ub, timed with h ub, altruistic with h ub, gain-based
1309.9 23.2 2101.3 228.6 1269.3 24.3 1268.8 17.0 1278.8 30.1
T able 9.3: A v erage time of rst surfacing ev en t with standard deviation, a v eraged o v er all scenarios,
o v er b oth v ehicles, o v er all 30 sim ulation runs.
W e again see similar p erformance across all approac hes. Ho w ev er, ev en though the initial V oronoi
p erformance is more v ariable (timestep 3), it outp erforms the alternativ e approac hes during the
later stages of the run.
In terms of the n um b er of surfacing ev en ts, T able 9.1 sho ws the a v erage n um b er of surfacing
ev en ts, a v eraged o v er b oth v ehicles and all scenarios. The a v erage n um b ers p er v ehicle for ev ery
scenario are sho wn in Section 14.2.4. As can b e seen from T able 9.1, the altruistic approac h has b y
far the smallest n um b er of surfacing ev en ts. This is determined b y the threshold on the v ariance
reduction, and could b e ne-tuned, if more data sharing ev en ts w ere desired. The lo w n um b er of
surfacing ev en ts could explain the early high v ariance in p erformance for some scenarios for A UV 1,
for example if there is more time in b et w een the rst t w o surfacing ev en ts. W e sho w that for all the
adaptiv e surfacing approac hes (V oronoi, altruistic, gain-based), few er surfacing ev en ts are required
than with the timed approac hes. This is useful b ecause less time is lost in surfacing, whic h allo ws
more time for sampling. And as w e ha v e sho wn in the previous gures, the p erformance do es not
decrease under a decrease of surfacing ev en ts.
T able 9.2 sho ws the n um b er of samples in the do wnsampled GP that is used for h yp erparameter
optimization, at the time of the nal h yp erparameter optimization. A v erages p er v ehicle for ev ery
scenario are giv en in Section 14.2.5. As can b e seen from T able 9.2, the most samples are gathered
under the altruistic approac h, whic h has the few est surfacing ev en ts.
F or the surfacing ev en ts, the sp ecic approac h used aects the initial surfacing time. T able 9.3
sho ws the a v erage time of the rst surfacing ev en t, a v eraged o v er all scenarios o v er b oth v ehicles. The
a v erage rst surfacing time p er v ehicle for ev ery scenario is giv en in Section 14.2.6. App endix 14.2.6
on page 136 sho ws the a v erage rst surfacing time p er v ehicle for ev ery scenario. T able 9.3 sho ws
that for the V oronoi-based approac h the rst surfacing ev en t is on a v erage around 2100 seconds, for
the altruistic around 1269 seconds, and for the gain-based around 1279 seconds. Because the rst
surfacing ev en t for the V oronoi-based approac h is on a v erage a lot later in to the mission, whic h is
also when the rst h yp erparameter optimization ev en t tak es place, the initial p erformance can b e
w orse.
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Stephanie Kemna A daptiv e Sampling with A UV s
9.5 Discussion & F uture work
The sim ulation results sho w ed that p erformance is appro ximately equal across the tested surfacing
strategies for m ulti-rob ot adaptiv e informativ e sampling. The previously published V oronoi-based
co ordination approac h (Kemna et al., 2017) had wider v ariance on p erformance at/b efore timestep
3 (appro ximately 1800s), whic h is of particular imp ortance if y ou quic kly w an t to obtain a go o d
mo del. This corresp onded to a dela y ed rst surfacing ev en t, meaning that the rst h yp erparameter
optimization w as also dela y ed. W e h yp othesize that this is due to the curren tly used triggering
mec hanism for requesting surfacing ev en ts. The trigger used w as that a v ehicle w ould request a
surfacing ev en t when its approac hes the b order of its V oronoi region. The though t b ehind this
w as that if the in teresting sampling regions are near the b order, it ma y b e time to re-estimate
the V oronoi partitions. The scenarios w e tested the approac h on previously w ere smaller areas at
400200m than the curren tly tested scenarios at 500600m. Therefore it can tak e longer in
these bigger areas b efore the v ehicles rst request a surfacing ev en t. Esp ecially giv en the go o d
p erformance of the V oronoi-based approac h from the middle to end of sampling for scenarios e) - f ),
w e think it w ould b e w orth while to replace the curren t trigger mec hanism. P oten tially the V oronoi
co ordination could b e used with the triggers dev elop ed here, suc h as the gain-based trigger.
Another metho d to impro v e p erformance across the initial stages of mo deling could b e to run
h yp erparameters optimization earlier. Curren tly , the rst h yp erparameter optimization runs at the
rst surfacing ev en t. Instead it could b e run in the bac kground at a regular in terv al, p oten tially
with extra h yp erparameter optimization runs triggered when large amoun ts of data are receiv ed.
This could help in particular at the start of sampling, when more c hange can b e exp ected regarding
the h yp erparameters. By doing so y ou could impro v e y our mo del through the data y ou ha v e already
collected, irresp ectiv e of when a surfacing ev en t is.
F or future w ork, it w ould also b e in teresting to further in v estigate activ e co ordination ap-
proac hes. Out of the approac hes tested in this c hapter, only the approac h that dynamically
estimated V oronoi partitions is activ ely co ordinating b et w een the rob ots. F or scenarios e) - f )
this seems to pa y o. In the case of async hronous surfacing ev en ts, the co ordination b ecomes more
complex b ecause the v ehicles need to receiv e or calculate directions at dieren t times, when they
do not kno w what the other v ehicle is up to. If V oronoi partitions w ould b e estimated at dieren t
times, the resulting partitions w ould b e dieren t across v ehicles. One alternativ e approac h is to giv e
the data h ub more p o w er and mak e it a cen tral ‘con troller’. It could k eep trac k of v ehicle in ten tions
and direct v ehicles to certain regions of the surv ey area.
Curren tly , the gain-based surfacing approac h uses an empirically determined form ula for estimat-
ing calculation time to consider the time needed on the surface. The calculation time is dep enden t
on the system used, b ecause more cores can sp eed up computation. The approac h could p oten tially
b e adapted with a more generic estimation of the computational time. A t the same time, dev eloping
and utilizing metho ds to decrease the computation time, esp ecially as the size of the GP gro ws,
w ould b e useful to in v estigate and incorp orate, suc h as sparse GP tec hniques.
Finally , w e w an t to note that although the timed surfacing ev en ts p erform w ell, they rely on
ha ving sync hronized computer clo c ks. F or elded systems, an y drift in the clo c ks is not lik ely to
signican tly impact the p erformance rep orted here for short duration sampling runs. Ho w ev er, for
p ersisten t monitoring or long range missions, this could b e a concern. In those cases the altruistic,
gain-based, or V oronoi-trigger approac hes are more reliable.
92 CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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9.6 Conclusions
In this c hapter, w e ha v e discussed surfacing strategies for autonomous underw ater v ehicles that run
adaptiv e informativ e sampling with a surface-based data h ub. W e prop osed t w o surfacing strategies;
altruistic and gain-based. In the altruistic approac h the v ehicles estimate ho w m uc h information
they ha v e to share, and in the gain-based approac h the v ehicles estimate the amoun t of data
a v ailable at the surface. W e compared these metho ds to timed surfacing with a surface h ub, and
t w o metho ds without a data h ub; sync hronized timed surfacing, and v ehicle-triggered sync hronized
surfacing with V oronoi partitioning. Our sim ulation studies sho w ed that all approac hes p erform
appro ximately equal in terms of the RMSE b et w een the created mo dels and the ground truth.
There is no explicit gain from adding a data h ub to allo w for async hronous surfacing, o v er the
sync hronized surfacing strategies, in terms of mo deling p erformance. The V oronoi co ordination
approac h has a wider v ariance on p erformance in the early stages of sampling, but this could b e
impro v ed b y c hanging the surfacing trigger. A t the same time, the V oronoi co ordination approac h
obtains b etter mo deling p erformance for the scenarios that w ere sampled from a GP mo del. F or
the async hronous strategies the b est result is ac hiev ed b y the altruistic surfacing strategy , where
similar p erformance is obtained with far few er surfacing ev en ts. This could b e particularly useful
for missions at greater depths, where the cost of surfacing increases.
CHAPTER 9. MUL TI-R OBOT AD APTIVE INF ORMA TIVE SAMPLING:
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10 | Discussion
This dissertation has discussed sev eral metho ds for adaptiv e sampling with autonomous underw ater
v ehicles. Chapter 2 discussed an approac h for adaptiv e, robust, and decen tralized formation con trol
for a team of A UV s that are follo wing a surface v ehicle to sample a lak e. While the approac h
seemed to w ork w ell, w e b eliev e that it w as not addressing the righ t questions. In our rob otic
designs, w e should alw a ys b e considering the end goal and end pro duct. In this case, w e are
trying to get a go o d mo del of certain en vironmen tal phenomena for biologists and o ceanographers.
Therefore, w e should w ork on path or motion planning approac hes that determine future v ehicle
mo v emen ts based on mo del qualit y and not based on arbitrary other criteria. Chapter 3-Chapter 7
th us discuss sampling approac hes that are using information-theoretic metrics to adapt v ehicle
mo v emen ts, to w ards creating more informativ e mo dels of en vironmen tal phenomena.
Chapter 3 pro vides an in tro duction to adaptiv e informativ e sampling, and Chapter 4 sho ws
p erformance for a single v ehicle, in comparison to running standard la wnmo w er surv eys. In Chap-
ter 5 w e follo w this up with results from eld testing, to assess the feasibilit y of running adaptiv e
informativ e sampling on an actual A UV. W e sho w ed that it is p ossible to run the adaptiv e sampling
on b oard a commercial-o-the-shelf A UV. F urthermore w e prop osed a metho d of comparing eld
p erformance, b y using bath ymetry as a pro xy for Chloroph yll elds.
Chapter 6 is the rst step to w ards m ulti-rob ot collab oration for adaptiv e informativ e sampling,
whic h lo oks in to adding data sharing for decen tralized m ulti-rob ot systems. The comparison
b et w een indep enden t la wnmo w ers, indep enden t adaptiv e sampling, and adaptiv e sampling with
data sharing sho w ed that p erformance is sup erior when the v ehicles can share data with eac h
other. F urthermore w e explored the trade-o b et w een acoustic comm unications and surface-based
comm unications. This exploration sho w ed that without message corruption or loss, subsampled data
sharing through acoustic comm unications can p erform b etter than surfaced data sharing. Ho w ev er,
one can not exp ect to ha v e 100% throughput underw ater, and p erformance deteriorates with reduced
throughput. Therefore, surfaced data sharing migh t b e a more reliable comm unication strategy for
shallo w underw ater sampling missions.
Chapter 7 discussed a rst co ordination approac h for m ulti-rob ot adaptiv e informativ e sampling.
The idea b ehind adding a co ordination approac h w as to a v oid scenarios where the rob ots go to the
same sampling lo cations and are, p oten tially , sampling the same areas. The dynamic V oronoi
approac h to co ordination sho w ed impro v emen ts in the early stages of mo del creation.
W e then to ok a brief detour in Chapter 8 to discuss pilot surv eys for adaptiv e informativ e
sampling. W e presen ted one approac h for determining pilot surv ey w a yp oin t lo cations for collecting
represen tativ e data at the start of adaptiv e sampling. The approac h p erforms a trade-o b et w een
spreading w a yp oin ts for co v erage and randomizing w a yp oin ts, using a softmax equation. W e sho w ed
94
A daptiv e Sampling with A UV s Stephanie Kemna
that with this metho d and a lo w ‘temp erature’ parameter for the softmax equation, w e could
obtain the most stable p erformance. This metho d w as then used in our nal m ulti-rob ot sim ulation
exp erimen ts.
In Chapter 9 w e ev aluated the p erformance of dieren t surfacing strategies for adaptiv e in-
formativ e sampling with a surface-based data h ub, while trying to minimize time sp en t in data
sharing. W e dev elop ed t w o new strategies; altruistic and gain-based surfacing, and compared these
to our dynamic V oronoi approac h, as w ell as to timed surfacing metho ds. Ov erall, the approac hes
p erformed similar, though the V oronoi approac h had bigger v ariabilit y at the start of the sampling
mission, due to a late rst surfacing and therefore late rst h yp erparameter optimization ev en t. W e
also sho w ed that the altruistic approac h can obtain similar p erformance with far few er surfacing
ev en ts. This is esp ecially in teresting for deep er sampling missions, where the cost of surfacing
increases.
In the next section, w e will discuss some ideas for future researc h, whic h w e think are promising
and necessary a v en ues. In this thesis, w e ha v e dev elop ed adaptiv e sampling metho ds for A UV s
while fo cusing on k eeping realistic assumptions ab out the systems, dev eloping robust metho ds, and
creating decen tralized m ulti-rob ot systems where p ossible. W e explored what w e migh t gain in
giving up complete decen tralization b y including a data h ub, whic h do es not seem to result in
signican t gains in mo deling p erformance o v er our decen tralized metho ds, though it can decrease
the n um b er of required surfacing ev en ts. Ov erall, w e ha v e sho wn that the addition of data sharing
and co ordination strategies to m ulti-rob ot adaptiv e sampling can impro v e sampling p erformance
and p oten tially reduce o v erall mission time b y creating a go o d mo del, minimizing mo del error,
faster.
CHAPTER 10. DISCUSSION 95
11 | Potential F uture Research Directions
In this w ork w e ha v e discussed dieren t metho ds for adaptiv e sampling in aquatic, in particular lak e,
en vironmen ts with A UV s. W e w an t to briey touc h on some a v en ues of further in v estigation whic h
w e delib erately side-stepp ed, and/or that are natural directions follo wing the curren t researc h. F or
ease of nding and iden tifying topics, this is presen ted as a bulleted list:
Spatio-temp oral v ariabilit y and external disturbances : In this w ork, w e ha v e delib er-
ately ignored the asp ect of spatio-temp oral v ariabilit y . P art of the reason wh y w e could, to
some exten t, safely ignore it, is that w e made the assumption early on to op erate in small lak e
en vironmen ts with small systems of rob ots. Our mission areas can b e completely surv ey ed in
less than one to t w o hours. In man y lak es, the (in ternal) o w of the w ater and mo v emen ts
of algae are slo w enough that w e can assume to obtain a reasonable mo del within that time
span. When deplo ying A UV s in the o cean, one often do es not ha v e this luxury though, ev en
when op erating in small en vironmen ts, b ecause there are stronger curren ts and (in ternal)
w a v es. These external disturbances should b e considered b oth in creating mo dels that can
deal with spatio-temp orally v arying elds, and in dev eloping path planning metho ds that
consider disturbances suc h as curren ts. There ha v e b een other authors who are lo oking at
these cases, b oth for rob ot con trol and general Ba y esian optimization, e.g. Liu and Sukhatme
(2018), Lo w et al. (2015), Ma et al. (2016a), Senana y ak e et al. (2016a,b). Incorp orating their
tec hniques is going to b e crucial for elding adaptiv e sampling systems in the w orld’s o ceans.
Lo calization uncertain t y : Underw ater v ehicles, and in particular small-scale v ehicles with-
out D VL and/or exp ensiv e INS systems, accum ulate large amoun ts of lo calization uncertain t y
when tra v eling underw ater. In this thesis, w e ha v e assumed that the lo calization is go o d
enough for our purp oses: the lo calization error ma y gro w to a couple of meters during the
duration of the sampling mission, whic h, considering the smo othness of the eld w e measure,
do es not signican tly aect the created mo del. Ho w ev er, it w ould b e b etter to consider the
lo calization uncertain t y in the mo deling approac h, and in the path planning. Dos San tos
de Oliv eira et al. (2018) ha v e recen tly started to address this b y dev eloping a Ba y esian
optimization metho d whic h can tak e probabilit y distribution, i.e. regarding v ehicle lo cation,
as input to the Gaussian Pro cess mo del.
Sparse GP tec hniques : As b ecame clear in Chapter 5 and Chapter 9, the computational
complexit y of an y (Ba y esian) optimization approac h is imp ortan t to consider for computationally-
limited systems suc h as most A UV s. T o k eep computation time reasonable, w e subsampled our
GP for running h yp erparameter optimization. It w ould b e useful to see if smarter tec hniques
96
A daptiv e Sampling with A UV s Stephanie Kemna
can b e used to reduce computational time, for example through sparse GP tec hniques, e.g.
Csat and Opp er (2002).
Exp ert kno wledge : In this thesis, w e briey men tioned the p ossibilit y of initializing a GP’s
h yp erparameters based on exp ert kno wledge. If no prior data is a v ailable, this is the b est w a y
to get reasonable h yp erparameters. There are man y more w a ys in whic h exp ert kno wledge
could b e incorp orated in autonomous v ehicle path planning. F or example: in early design
c hoices e.g. mo deling approac h or k ernel, for initializing parameters, for dev eloping system
strategies (i.e. ship, A UV, buo y or UA V co ordination metho ds), or through h uman-in-the-lo op
advice. Figuring out the b est w a ys to ac hiev e this, is a ric h area for future researc h.
Multi-rob ot path planning : W e ha v e discussed data sharing and co ordination strategies
for m ulti-rob ot systems in adaptiv e informativ e sampling. Ho w ev er, in this w ork, w e did not
lo ok in to connecting our w ork with m ulti-rob ot or m ulti-agen t path planning metho ds. Ev en
for the single rob ot case, w e go for a single globally optimal lo cation, rather than planning a
full path. P art of our reason for this w as to a v oid an y more computation. In researc h with
undergraduate and master studen ts at USC, w e lo ok ed at whether the use of more sophisticated
path planning metho ds can impro v e up on the curren t w a yp oin t selection metho d, for single
A UV adaptiv e sampling. This researc h is ongoing and so far results are inconclusiv e and
unpublished. It w ould b e in teresting to see if m ulti-rob ot path planning tec hniques could
b e used, and in ho w far they can impro v e up on the approac hes tested within this thesis. It
ma y b e useful for co ordinating v ehicles, ev en if considering the information collected along a
path do es not lead to great gains. F urthermore, for dev eloping a more accurate ‘gain-based
surfacing’ approac h, it w ould b e useful to kno w future actions of the A UV s to estimate where
they will sample and ho w m uc h information they migh t collect. Multi-step m ulti-rob ot path
planning metho ds could allo w for doing these calculations.
Multi-rob ot eld testing : W e ran eld tests for the single-A UV adaptiv e informativ e
sampling. All m ulti-rob ot approac hes ha v e b een tested in sim ulation, partly b ecause our
lab only had one A UV, and partly to a v oid the o v erhead of eld testing, and to b e able to
compare m ulti-rob ot approac hes o v er man y trials/sim ulations. It w ould still b e in teresting
to v alidate the sim ulation results in the eld. W e ha v e tried to adhere to constrain ts of
elded systems, for example in the use of acoustic comm unication range and throughput, to
pro vide condence that these systems can b e put to use in the eld without needing ma jor
mo dications.
Design c hoices : Finally , it w ould b e useful to run a study that in v estigates the impact of
design c hoices on the (elded) system. F or example; the c hoice of mo deling tec hnique, the
c hoice of k ernel, the size of op erating areas, n um b er of v ehicles used, the op erating/sampling
depth, etc. F or example: In recen t w ork w e ha v e ev aluated the use of dieren t t yp es of
k ernels for mo deling elds that con tain non-smo oth transitions (Denniston et al., 2018). The
k ernel imp oses assumptions ab out the eld to b e mo deled, whic h should b e considered when
trying to realistically mo del the en vironmen t. The c hoice of k ernel could b e based on exp ert
kno wledge ab out the eld’s c haracteristics. Smo oth k ernels, suc h as the squared exp onen tial
k ernel, are considered ne for mo deling algal blo oms, b ecause these phenomena lik ely do not
CHAPTER 11. POTENTIAL FUTURE RESEAR CH DIRECTIONS 97
Stephanie Kemna A daptiv e Sampling with A UV s
exhibit sharp b orders or discon tin uities. F or the studies rep orted in this dissertation, w e ha v e
not ev aluated the impact on mo deling p erformance of the c hoice of k ernel.
98 CHAPTER 11. POTENTIAL FUTURE RESEAR CH DIRECTIONS
12 | Acknowledgements
This w ork w as supp orted in part b y the Oce of Na v al Researc h (ONR, N000141410536), and the
Arm y Researc h Lab oratory (ARL).
First and foremost, thanks to m y advisor, Prof. Gaura v Sukhatme, for guiding this researc h!
Thanks to Prof. Da vid Caron for pro viding the biological p ersp ectiv e to our rob otic sampling eorts,
for pro viding his input to w ards m y researc h eorts, for b eing in b oth the dissertation prop osal
committee and the dissertation committee, and for alw a ys b eing op en to discussing p oten tial
pro jects.
Thanks to Prof. Nora A y anian for early feedbac k on the Oceans’15 w ork through the class she
taugh t, and for b eing a mem b er of b oth the dissertation prop osal committee and the dissertation
committee.
Thanks to Prof. Jernej Barbi c and Prof. Ramesh Go vindan for b eing mem b ers of the dissertation
prop osal committee.
Thanks to all mem b ers of the Rob otic Em b edded Systems Lab oratory at the Univ ersit y of Southern
California for their constructiv e feedbac k on (parts of ) this w ork, and for pro viding a great w ork
en vironmen t o v er the last 6 y ears.
Thanks in general to ev ery one who has listened to me, v en tured in to discussions with me, or help ed
me when I w as stuc k on certain problems. Thanks to all m y friends, all around the w orld, who ha v e
supp orted me, help ed me cop e with the lo w p oin ts, and who ha v e celebrated m y successes with me.
Sp ecic thanks go to:
Alyssa Gellene and A v ery T atters for b eing in terested and in v olv ed in rob otic biological data
gathering. Thanks to Alyssa for all the help with sensor calibration!
Prof. Karla Heidelb erg and Prof. Da v e Caron for in viting me on the Septem b er 2016 Lak e
Arro whead, thanks to all who attended the trip for the pleasurable compan y , and thanks to all
who help ed retriev e the EcoMapp er when it decided to v en ture in to the wild w orld!
Sha wn Sneddon at YSI, Kevin Ludlam and Mik e F erreira at OceanServ er, for all their help with
EcoMapp er problems.
Oleksiy Kebk al for help with our Ev oLogics mo dems.
Mik e Benjamin and T ob y Sc hneider, who ha v e help ed me inn umerable times with MOOS-IvP and
Gob y-A Comms bugs and supp ort.
Cindy Bedell, for kic king o the ARL-W oce, facilitating join t researc h, and also pro viding me
with a w estside w orkplace and a standing desk solution when I needed it most. Thanks to all
ARL-W emplo y ees for b eing suc h friendly cubicle/oce neigh b ors.
99
Stephanie Kemna A daptiv e Sampling with A UV s
A tlas Elektronik and Amazon Rob otics for pro viding me with in teresting summer in ternships.
And to:
All undergraduate and graduate studen ts who ha v e help ed with the researc h rep orted in here and
n umerous tangen tial or class pro jects: James Collins, Chris Denniston, Kevin Geeting, Cliord
Lee, Prashan t Mulge, Prac hi Na w athe, Amey Ruik ar, Supreeth Subbara y a, Divy a Sw aminathan,
Yingyu Sun, Jaimin Upadh y a y , and t w o w onderful high sc ho ol studen ts: Jessica Gonzalez and Sara
Kangaslah ti.
Hrur Heiarsson for man y lak e trips, go o d con v ersations on the ride there and bac k, and help
with prett y m uc h an y cyb er infrastructure and troubles.
Carl Ob erg for help with the b oats and EcoMapp er, and creating the EcoMapp er acoustic mo dem
moun ting rig.
Oliv er Kro emer for helping explain topics that w ere confusing m y mind, for writing explanatory
Matlab scripts, and probing in to p oten tial researc h questions.
Alisha Deshpande for b eing a presen tation practice buddy :)
Mic hael So o-Ho o for handling all our lab’s business administration incl. our tra v el requests,
reim bursemen ts and the man y lab orders :)
All of the CS departmen t sta, for helping us PhD studen ts in our times of need, but also with PhD
studen t activities, lunc heons, etc.
Lizsl De Leon Sp edding for b eing the b est studen t advisor an y one could wish for, and b eing a h uge
supp ort to all us CS PhD studen ts.
Ap ologies to an y one I forgot to men tion here. If y ou kno w me, y ou kno w m y memory is quite
bad with names, and strangely selectiv e at times.. Thanks!!!
Finally; thanks to m y family for allo wing me to pursue m y career across Europ e and the glob e,
for not questioning m y life decisions, and supp orting me from the other side of the w orld!
Dankjew el :)
100 CHAPTER 12. A CKNO WLEDGEMENTS
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14 | Appendix
In this c hapter w e sho w some of the results that w ere left of former c hapters to impro v e readabilit y .
On the next page, w e start with all on-b oard mo dels from the eld trials. This is follo w ed b y all
the b o x plots of the async hronous surfacing trials, and more extensiv e tables with results for the
async hronous trials.
110
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14.1 Field trials results - nal predictive mean and v ariance
14.1.1 F ull runs
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 1
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 1
0.1
0.2
0.3
0.4
0.5
Pred. variance
Figure 14.1: F ull run, `GP , Marc h 31 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
This is the same as Figure 5.4.
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 2
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Pred. variance
Figure 14.2: F ull run, `GP , April 28, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 3
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
full lGP run (Depth) 3
0.1
0.2
0.3
0.4
0.5
0.6
Pred. variance
Figure 14.3: F ull run, `GP , July 21, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
CHAPTER 14. APPENDIX 111
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14.1.2 Half runs
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 1
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 1
2
4
6
8
10
12
Pred. variance
Figure 14.4: Half run, `GP , Marc h 31, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
This is the same as Figure 5.5.
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 2
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 2
2
4
6
8
10
Pred. variance
Figure 14.5: Half run, `GP , April 28, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 3
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 3
1
2
3
4
5
Pred. variance
Figure 14.6: Half run, `GP , Ma y 18, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
112 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 4
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 4
5
10
15
20
25
30
Pred. variance
Figure 14.7: Half run, `GP , Ma y 24, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 5
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 5
1
2
3
4
5
6
7
8
9
Pred. variance
Figure 14.8: Half run, `GP , July 7, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short GP run (Depth) 6
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short GP run (Depth) 6
1
2
3
4
5
6
Pred. variance
Figure 14.9: Half run, GP, July 21, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 7
0
5
10
15
20
25
Depth (m)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Depth) 7
0.5
1
1.5
2
2.5
3
Pred. variance
Figure 14.10: Half run, `GP , Aug. 8, 2017. Predictiv e mean
Yx
(left) and v ariance
2
Yx
(righ t).
CHAPTER 14. APPENDIX 113
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14.1.3 Chlorophyll half runs
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 1
4
5
6
7
8
Chl ( g/L)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 1
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Pred. variance
Figure 14.11: Half run, `GP , Apr. 28, 2017. Pred. mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 2
5
10
15
20
25
30
35
Chl ( g/L)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 2
0.5
1
1.5
2
2.5
3
3.5
4
Pred. variance
Figure 14.12: Half run, `GP , Ma y 18, 2017. Pred. mean
Yx
(left) and v ariance
2
Yx
(righ t).
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 3
5
10
15
20
25
30
Chl ( g/L)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 3
1
2
3
4
5
6
Pred. variance
Figure 14.13: Half run, `GP , Ma y 24, 2017. This is the same as Figure 5.6.
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 4
20
40
60
80
100
120
140
Chl ( g/L)
-117.81 -117.809 -117.808 -117.807
34.088
34.0885
34.089
short lGP run (Chl) 4
500
1000
1500
2000
2500
3000
3500
4000
Pred. variance
Figure 14.14: Half run, `GP , July 7, 2017. Pred. mean
Yx
(left) and v ariance
2
Yx
(righ t).
114 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
14.2 Asynchronous surfacing strategies results
This section con tains all the plots of the async hronous surfacing results, separated in to three
subsections: median RMSE plots in Section 14.2.1, RMSE b o xplots in Section 14.2.2, and the
cum ulativ e v ariance b o xplots in Section 14.2.3.
14.2.1 Median RMSE
0 1 2 3 4 5 6 7 8 9 10 11121314151617181920 21
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.15: Median RMSE for scenario a) for A UV 1
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0 1 2 3 4 5 6 7 8 9 10 11121314151617181920 21
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario b)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.16: Median RMSE for scenario b) for A UV 1
0 1 2 3 4 5 6 7 8 9 10 11121314151617181920 21
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario c)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.17: Median RMSE for scenario c) for A UV 1
116 CHAPTER 14. APPENDIX
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0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario d)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.18: Median RMSE for scenario d) for A UV 1
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.19: Median RMSE for scenario e) for A UV 1
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0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario f)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.20: Median RMSE for scenario f ) for A UV 1
118 CHAPTER 14. APPENDIX
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0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.21: Median RMSE for scenario a) for A UV 2
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario b)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.22: Median RMSE for scenario b) for A UV 2
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0 1 2 3 4 5 6 7 8 9 10 11121314151617181920 21
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario c)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.23: Median RMSE for scenario c) for A UV 2
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario d)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.24: Median RMSE for scenario d) for A UV 2
120 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
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10
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10
3
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4
median RMSE
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.25: Median RMSE for scenario e) for A UV 2
0 1 2 3 4 5 6 7 8 9 101112131415161718192021
timesteps (per 600s)
10
0
10
1
10
2
10
3
10
4
median RMSE
scenario f)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.26: Median RMSE for scenario f ) for A UV 2
CHAPTER 14. APPENDIX 121
Stephanie Kemna A daptiv e Sampling with A UV s
14.2.2 RMSE boxplots
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
RMSE
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.27: RMSE b o xplots for scenario a) for A UV 1
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
RMSE
scenario b)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.28: RMSE b o xplots for scenario b) for A UV 1
122 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
RMSE
scenario c)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.29: RMSE b o xplots for scenario c) for A UV 1
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
1
10
2
10
3
RMSE
scenario d)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.30: RMSE b o xplots for scenario d) for A UV 1
CHAPTER 14. APPENDIX 123
Stephanie Kemna A daptiv e Sampling with A UV s
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
RMSE
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.31: RMSE b o xplots for scenario e) for A UV 1
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
1
10
2
10
3
RMSE
scenario f)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.32: RMSE b o xplots for scenario f ) for A UV 1
124 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
RMSE
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.33: RMSE b o xplots for scenario a) for A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
2
10
4
RMSE
scenario b)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.34: RMSE b o xplots for scenario b) for A UV 2
CHAPTER 14. APPENDIX 125
Stephanie Kemna A daptiv e Sampling with A UV s
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
RMSE
scenario c)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.35: RMSE b o xplots for scenario c) for A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
10
10
20
RMSE
scenario d)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.36: RMSE b o xplots for scenario d) for A UV 2
126 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
1
10
2
10
3
RMSE
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.37: RMSE b o xplots for scenario e) for A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
1
10
2
10
3
RMSE
scenario f)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.38: RMSE b o xplots for scenario f ) for A UV 2
CHAPTER 14. APPENDIX 127
Stephanie Kemna A daptiv e Sampling with A UV s
14.2.3 Cumulative v ariance boxplots
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
cumulative pred. variance
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.39: Cum ulativ e v ariance b o xplots for scenario a) for A UV 1
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
cumulative pred. variance
scenario b)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.40: Cum ulativ e v ariance b o xplots for scenario b) for A UV 1
128 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
cumulative pred. variance
scenario c)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.41: Cum ulativ e v ariance b o xplots for scenario c) for A UV 1
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
cumulative pred. variance
scenario d)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.42: Cum ulativ e v ariance b o xplots for scenario d) for A UV 1
CHAPTER 14. APPENDIX 129
Stephanie Kemna A daptiv e Sampling with A UV s
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
cumulative pred. variance
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.43: Cum ulativ e v ariance b o xplots for scenario e) for A UV 1
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
cumulative pred. variance
scenario f)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.44: Cum ulativ e v ariance b o xplots for scenario f ) for A UV 1
130 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
cumulative pred. variance
scenario a)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.45: Cum ulativ e v ariance b o xplots for scenario a) for A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
cumulative pred. variance
scenario b)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.46: Cum ulativ e v ariance b o xplots for scenario b) for A UV 2
CHAPTER 14. APPENDIX 131
Stephanie Kemna A daptiv e Sampling with A UV s
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
cumulative pred. variance
scenario c)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.47: Cum ulativ e v ariance b o xplots for scenario c) for A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
0
10
2
10
4
cumulative pred. variance
scenario d)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.48: Cum ulativ e v ariance b o xplots for scenario d) for A UV 2
132 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
cumulative pred. variance
scenario e)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.49: Cum ulativ e v ariance b o xplots for scenario e) for A UV 2
0 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 1718 1920 21
timesteps (per 600s)
10
1
10
2
10
3
10
4
cumulative pred. variance
scenario f)
timed, no hub
Voronoi, no hub
timed, with hub
altruistic, with hub
gain-based, with hub
Figure 14.50: Cum ulativ e v ariance b o xplots for scenario f ) for A UV 2
CHAPTER 14. APPENDIX 133
Stephanie Kemna A daptiv e Sampling with A UV s
14.2.4 Number of surfacing events
T able 14.1: A v erage n um b er of surfacing ev en ts for A UV 1
strategy \ scenario a b c d e f
no h ub, timed 19.97 19.97 19.80 20.00 20.00 20.00
no h ub, v or 13.30 13.77 16.60 14.53 15.40 14.43
with h ub, timed 23.13 19.97 23.80 23.90 24.00 23.90
with h ub, altruistic 5.90 4.70 5.83 6.90 7.27 6.77
with h ub, gain-based 18.97 20.43 18.87 17.07 19.30 18.77
T able 14.2: A v erage n um b er of surfacing ev en ts for A UV 2
strategy \ scenario a b c d e f
no h ub, timed 19.97 19.97 20.00 20.00 20.00 20.00
no h ub, v or 13.30 13.77 16.60 14.53 15.33 14.43
with h ub, timed 18.30 15.83 18.30 18.97 18.97 18.60
with h ub, altruistic 6.77 4.73 6.90 7.17 7.33 6.50
with h ub, gain-based 18.53 20.33 18.63 16.53 18.73 18.43
134 CHAPTER 14. APPENDIX
A daptiv e Sampling with A UV s Stephanie Kemna
14.2.5 Final HP optimization GP size
T able 14.3: A v erage size do wnsampled GP at nal HP optimization for A UV 1
strategy \ scenario a b c d e f
no h ub, timed 9357.53 9162.30 9611.30 9463.70 9551.50 9719.53
no h ub, v or 9063.23 8642.13 8895.70 9449.37 8065.03 9369.13
with h ub, timed 9176.80 8939.87 9362.13 9673.03 9196.53 9748.30
with h ub, altruistic 10173.80 9560.00 10455.10 10241.40 10260.70 10284.60
with h ub, gain-based 9481.33 8771.43 9448.27 9779.87 9143.30 9463.43
T able 14.4: A v erage size do wnsampled GP at nal HP optimization for A UV 2
strategy \ scenario a b c d e f
no h ub, timed 9349.27 9160.40 9612.03 9472.00 9551.50 9719.33
no h ub, v or 9064.63 8642.13 8887.20 9449.37 8858.80 9356.00
with h ub, timed 9184.50 8948.40 9260.07 9658.97 9175.73 9724.00
with h ub, altruistic 10294.43 9216.67 10393.87 10312.90 10142.37 10288.23
with h ub, gain-based 9422.23 8888.27 9360.23 9683.13 9218.90 9509.97
CHAPTER 14. APPENDIX 135
Stephanie Kemna A daptiv e Sampling with A UV s
14.2.6 First surfacing event
T able 14.5: A v erage time of rst surfacing ev en t for A UV 1
strategy \ scenario a b c d e f
no h ub, timed 1298.08 1296.87 1348.12 1296.47 1293.74 1333.47
no h ub, v or 1980.47 1905.53 1967.94 2325.26 1950.51 2480.51
with h ub, timed 1259.41 1251.17 1293.68 1240.23 1226.12 1262.32
with h ub, altruistic 1256.19 1255.47 1268.14 1250.26 1239.50 1270.80
with h ub, gain-based 1244.92 1256.84 1297.85 1227.13 1246.34 1282.22
T able 14.6: A v erage time of rst surfacing ev en t for A UV 2
strategy \ scenario a b c d e f
no h ub, timed 1285.33 1298.58 1347.41 1295.66 1292.98 1332.67
no h ub, v or 1979.75 1904.64 1967.12 2324.53 1949.72 2479.84
with h ub, timed 1279.45 1250.46 1297.95 1286.46 1284.77 1299.65
with h ub, altruistic 1270.28 1281.46 1285.34 1281.99 1265.72 1300.93
with h ub, gain-based 1278.01 1289.21 1330.12 1294.74 1284.44 1313.77
136 CHAPTER 14. APPENDIX

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Asset Metadata

Creator Kemna, Stephanie (author)

Core Title Multi-robot strategies for adaptive sampling with autonomous underwater vehicles

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Computer Science

Publication Date 10/09/2018

Defense Date 04/30/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag adaptive sampling,aquatic robotics,autonomous systems,autonomous underwater vehicles,Autonomy,informative sampling,marine robotics,multi-robot systems,OAI-PMH Harvest,robotics,unmanned underwater vehicles

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Sukhatme, Gaurav S. (committee chair), Ayanian, Nora (committee member), Caron, David A. (committee member)

Creator Email kemna@usc.edu,stephaniekemna@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-76169

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Identifier etd-KemnaSteph-6802.pdf (filename),usctheses-c89-76169 (legacy record id)

Legacy Identifier etd-KemnaSteph-6802.pdf

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Document Type Dissertation

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Type texts

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Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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