University of Southern California Dissertations and Theses

Data-driven robotic sampling for marine ecosystem monitoring

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Data-driven robotic sampling for marine ecosystem monitoring

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Content Data-driven Robotic Sampling for Marine Ecosystem Monitoring by Jnaneshwar Das A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Computer Science) Committee: Prof. Gaurav S. Sukhatme (Chair) Computer Science Prof. Stefan Schaal Computer Science Prof. David A. Caron Biological Sciences May, 2014 Copyright 2014 Jnaneshwar Das Dedicated to my mother Jayanti Das, father Biraja Shankar Das, and brother Bishweshwar Das. ii Acknowledgements First of all, I would like to thank my Ph.D. advisor Professor Gaurav Sukhatme for his guidance, support, and for being a staunch advocate of this work. Gaurav gave me the freedom to nd and pursue the questions I cared about, and I could not have asked for a better mentor and role model. I look forward to our interactions in the future. I am grateful to members of my thesis proposal and defense committees, Professor David Caron, Professor Laurent Itti, Professor Cyrus Shahabi, Professor Yan Liu, Pro- fessor Stefan Schaal, and Kanna Rajan for their scrutiny and guidance. Lizsl De Leon ensured that all ocial paperwork was handled smoothly through the years, with timely reminders, and each conversation accompanied by her warm sense of humor. I am indebted to her for making my life easy. When I began graduate school, I knew very little about the marine world. My early work with Professor David Caron's lab in the Department of Biological Sciences gave me the background and condence for the years of work that followed. David has been an enthusiastic supporter of robotics for the marine sciences, and working with researchers from his group, I developed an appreciation for the challenges of scientic eld work. I thank Beth Stauer, Erica Seubert, Lindsay Darjany, Alyssa Gellene, and Ellen Smith for their support during our collaborations, and for being excellent company during the eld experiments we have carried out together. I would like to thank Professor Burt Jones and members of his lab { Ivona Cetini c, Bridget Seegers, and Matthew Ragan for their help with deployments in Southern Cali- fornia Bight. A signicant portion of my thesis work has been carried out at the Monterey Bay Aquarium Research Institute (MBARI), where I had the privilege of working with a remarkable group of researchers. I am particularly grateful to Kanna Rajan, the Principal Investigator of the Autonomous Systems Group, for his guidance and support since 2009. With Kanna's help, I got an opportunity to work on a wide range of research projects, including participation in multiple large-scale eld campaigns. Fr ed eric Py, John Ryan, Julio Harvey, Rishi Graham, and Thom Maughan have been my core collaborators, and I thank them for their endless support through the years. Numerous other MBARI researchers have helped me at various stages of my thesis work, including Sergey Frolov, Mike McCann, Monique Messi e, Tom O'Reilly, Brent Roman, Kevin Gomes, Fred Bahr, Yanwu Zhang, Francisco Chavez, Jim Bellingham, Robert Vrijenhoek, Hans Thomas, and Chris Wahl. I am grateful to the crew of R/V Zephyr and R/V Rachel Carson for their crucial role during eld experiments. My countless trips to MBARI would not have been possible without the help of friends in the San Francisco Bay Area. Umang Jaipuria, Ramya Naidu, Arjun Kulothungun, Asim iii Bhalerao, Sharath Gowda { thanks for hosting me (always) on short notice, and making my trips up north so much fun! Life at graduate school is incomplete without the support of labmates. True to the tradition of apprenticeship, I was fortunate to have excellent mentors at RESL in my early years. Srikanth Saripalli, Gabe Sibley, Marin Kobilarov, Jonathan Kelly, Karthik Dantu, and Sameera Poduri introduced me to the nuances of state-estimation, controls, and multi-robot systems. Jon, your steadfastness and sense of humor in the face of adversity have been exemplary. Whenever weary and confused, I still ask myself, what would Jonathan Kelly do? The ups and downs of grad school were shared with my peers at RESL { Arvind Pereira, Hordur Heidarsson, Megha Gupta, Christian Potthast, Harshvardhan Vath- sangam, Stephanie Kemna, Max P ueger, David Inkyu Kim, Supreeth Subbaraya, and Jon Binney. Together, we shared many delirious moments over margaritas at La Barca, and for that and everything else, I thank you. Some of my earliest eld experiments at RESL were carried out under the guidance of Bin Zhang and Amit Dhariwal, and I thank them for their help. Carl Oberg has been a strong in uence on how I approach experiment logistics. Carl, thanks for teaching me the proper way to do things! I have also been fortunate to have the guidance of excellent postdoctoral mentors, Ryan Smith and Geo Hollinger, during the nal years of my thesis work. I am grateful to them for their time and patience. Sharing our lab space with another lab made the days and nights in RESL a lot more fun. I thank everyone at the Interaction Lab, past and present, especially Dylan Shell, David Feil-Seifer, Ross Mead, and Eric Wade for being great co-labmates. Across the corridor at CLMC lab, I forged strong bonds with a number of people. Mrinal Kalakrishnan has been my friend and sounding board since undergrad years, and I consider myself extremely lucky to have him around through grad school. Peter Pastor and I explored Los Angeles together, with priceless memories etched in Venice Beach and various other odd places. Conversations over lunch, coee, and beer would not have been so entertaining and stimulating without the company of Ludovic Righetti, Jeannette Bohg, Franziska Meier, Alex Herzog, Manuel Wuthrich, and Vince Enachescu. Finally, I would like to thank my parents and my brother for their unconditional sup- port through the years. They believed in my mission, and their love and encouragement got me through the challenges of grad school. iv Table of Contents Acknowledgements iv List of Figures xiii List of Tables xiv Abstract xv Chapter 1 Introduction 1 1.1 Contributions and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2 Deployment Planning 6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Scientic Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Technical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.1 Hotspot detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.2 Hotspot Advection . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5.1 AUV deployment planning . . . . . . . . . . . . . . . . . . . . . . 11 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Chapter 3 Coordinated Tracking 16 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Technical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3.1 Tracking advecting patches . . . . . . . . . . . . . . . . . . . . . . 21 3.3.2 Scientic Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3.3 Lagrangian survey design . . . . . . . . . . . . . . . . . . . . . . . 22 3.3.4 Repeated static-plan surveys vs transformed surveys . . . . . . . . 33 3.4 Field Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4.2 June 2010 experiment: Repeated static-plan surveys . . . . . . . . 39 3.4.3 September 2010 CANON Experiment: Transformed surveys . . . . 40 3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.5.1 Intrinsic sources of error . . . . . . . . . . . . . . . . . . . . . . . . 44 v 3.5.2 Extrinsic sources of errors . . . . . . . . . . . . . . . . . . . . . . . 48 3.5.3 Survey quality metric . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.5.4 Analysis of September trial results . . . . . . . . . . . . . . . . . . 51 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Chapter 4 Autonomous Sampling 54 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.1.1 Problem Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.1.2 Contributions of this Work . . . . . . . . . . . . . . . . . . . . . . 55 4.1.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2 Technical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2.1 Probabilistic model . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2.2 Bayesian sequential optimization . . . . . . . . . . . . . . . . . . . 58 4.2.3 Optimal stopping theory . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.4 Field Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4.1 Ex-situ sample analysis . . . . . . . . . . . . . . . . . . . . . . . . 71 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Chapter 5 Oceanographic Decision Support System 73 5.1 Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Experiment Design and Implementation . . . . . . . . . . . . . . . . . . . 77 5.2.1 CANON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2.2 ODSS System Architecture . . . . . . . . . . . . . . . . . . . . . . 79 5.3 Usage and Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3.1 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3.2 Usage statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.4 Lessons Learned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.5 What about the future? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Chapter 6 Conclusions 90 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 BIBLIOGRAPHY 94 vi List of Figures 1.1 An algal bloom o the Scripps Institution of Oceanography Pier, La Jolla, Cal- ifornia. (Image credit: P. Alejandro D az and Ginny Velasquez) . . . . . . . . 2 1.2 Aquatic platforms with onboard water sample retrieval and storage capabilities 3 1.3 This thesis targets multiple pieces of an \oceanographic macroscope", with a transition from macro to micro scale features. Additionally, we developed web- based tools for situational awareness and experiment planning. . . . . . . . . 5 2.1 Algal bloom hotspots can be detected by processing outdated images from remote-sensing satellites. Thereafter, land-based measurements of surface-currents can be used to project the transport of these hotspots, resulting in an estimate of the nowcast, or current estimate of bloom location. . . . . . . . . . . . . . 7 2.2 Illustration of ltering of thresholded satellite imageI thresholded using 8-connectivity and pixel-weight to determine coherent hotspots. . . . . . . . . . . . . . . . 9 2.3 An hourly snapshot of surface-current, estimated from measurements by multiple land-based HF radar stations (shown as black triangles). . . . . . . . . . . . . 9 2.4 Projection of a bloom from October 2007. . . . . . . . . . . . . . . . . . . . 12 2.5 Projection of a bloom from October 2008. . . . . . . . . . . . . . . . . . . . 12 2.6 A hypothetical bloom onset (A), projection (B) and a viable AUV survey to capture the bloom's spatial extent. . . . . . . . . . . . . . . . . . . . . . . . 13 2.7 Results of bloom projection and AUV mission plans for 2007 and 2008 datasets. 14 3.1 Dynamics of algal blooms in California's Monterey Bay. Figure shows remote sensing images capturing the chlorophyll concentration at the ocean surface be- tween September 19th and October 8th, 2002. Due to atmospheric conditions, the images are temporally aperiodic. Algal hotspots characterized by red col- oration can be seen evolving as a result of biological growth and decay, and advection due to ocean currents. Marine scientists are interested in understand- ing the dynamics of these hotspots as they evolve, which necessitates being able to track them spatially as they are advected by ocean currents, and sampling within this patch frame of reference. (Image from [1]) . . . . . . . . . . . . . 17 3.3 Airborne remote sensing images showing short-term phytoplankton bloom dy- namics in the Monterey Bay in the month of August 2009. A phytoplankton bloom patch, marked in the left image with a +, is shown advecting eastward by 1 km in less than 80 minutes, suggesting currents of the order of 0:2 m/s. 20 vii 3.2 A lawnmower survey pattern of an AUV in the upper water-column showing chlorophyll uorescence within vertical saw-tooth (or 'yo-yo') proles. . . . . . 20 3.4 Illustration of a Lagrangian drifter being tracked on shore and at sea. The drifter has a oat section aected mostly by wind and a drogue section which is impacted by sub-surface currents. Drifter locations are transmitted via satellite. The support vessel is for launch, recovery and charging of the AUV. . . . . . . 21 3.5 The box survey pattern of an AUV which circumscribes a patch volume being sampled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.6 Illustration of the box survey pattern. For a box pattern with edge length l, implemented in three dimension, the AUV performs saw-tooth vertical proles along the edges with pitch angle. The AUV moves at a constant surge speeds a . The projected speed of the AUV on the horizontal plane while executing the saw- tooth proles is given by s a cos. We can design AUV plans in two-dimensions where the motion along the depth axis is encapsulated by the projection onto the horizontal plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.7 Enclosure-criterion satised in drifter frame. The goal of our study is to imple- ment surveys such that a drifter that represents a patch of water stays within the boundary of the survey. In the gure, p 0 1 :::p 0 5 denes the perimeter of a survey in the drifter frame. The enclosure criterion ensures that the drifter, marked by o 0 , stays inside the survey perimeter. . . . . . . . . . . . . . . . . . . . . . 24 3.8 Implementation of the box pattern for Lagrangian observation studies involves the AUV covering a trailing distance u, the survey length 4l and ensuring that the enclosure criterion is satised. o 1 represents the starting point of the drifter ando 2 its termination within a single pattern. For the enclosure criterion to be satised, the AUV has to cross the drifter ahead of its path in the earth frame. 27 3.9 Trajectory of a drifter advected in the vicinity of Monterey Bay in August 2006 for a period of 3.5 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.10 Distribution of speeds for a drifter deployed at the central Californian coast. The dotted line shows the upper-bound of 0.36 m/s on drifter speed for which the enclosure criterion is satised. This is based on our analysis of repeated static-plan box surveys performed by an AUV operating at nominal speed of 1.5 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.11 Illustration of transformed survey for the box pattern. The goal is to ensure that a box pattern is implemented in the advecting drifter frame of reference. The goal waypoints for the corners of the box pattern in the drifter frame are trans- formed to the earth frame to provide us with the AUV mission plan consisting of ve waypoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 viii 3.12 Illustration of a transformed survey for the box pattern for the case where the AUV is required to move at constant speed in the drifter frame. Given the ve goal waypoints and the corresponding time of arrival (p 0 1 ;t 0 1 );:::; (p 0 5 ;t 0 5 ) for the corners of the box pattern, our goal is to compute (p 1 ;t 1 );:::; (p 5 ;t 5 ). For this computation, we require a prediction of the drifter trajectory for the duration of the iteration. This is done using a linear projection of the drifter trajectory based on the last two position updates from the drifter. For the box pattern, the AUV will travel varying distancesd 1 ,d 2 andd 4 in the earth frame, for equal time intervals corresponding to each leg of the survey. . . . . . . . . . . . . . 31 3.13 Illustration of survey planning with constant AUV speed in the earth frame. . 32 3.14 An illustration of an iteration of transformed box survey with constant AUV ground speed in earth frame. Based on previously observed drifter positions, a linear projection of the drifter trajectory is computed for the duration of the iteration. In this gure, we assume the AUV is already at the initial waypoint p 1 at time t 1 which corresponds to the rst corner waypoint of the box pattern in the drifter frame. We know the desired waypoints for the other corners of the box pattern,p 00 2 ::p 00 5 . Using the solution to Eqn. 3.17, we obtain the locations and times of the other four waypoints, giving us the complete plan for the iteration, (p 1 ;t 1 ):::(p 5 ;t 5 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.15 Survey oset error, e offset , for repeated static-plan surveys is dened as the distance between the drifter frame origin and the centroid of the perimeter of the survey. Since in repeated static-plan surveys, the survey is distorted when visualized in the drifter frame, we usee offset as a measure of how well the survey tracks the drifter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.16 Simulation result for survey oset error and survey time for repeated static-plan and transformed surveys using the box pattern with an edge length of 1 km. AUV surge speed of 1:5 m/s and pitch angle of 30 o were used for this analysis. Drifter speeds between 0 m/s and 1:3 m/s was considered. The dashed vertical line shows the maximum drifter speed for which repeated static-plan surveys satisfy the enclosure criterion. Note that the survey oset error is zero throughout for the transformed survey. For transformed surveys, although the AUV can complete surveys as long as the drifter speed is less than projected AUV speed ( 1:2m=s), the survey time increases with increasing drifter speed, crossing 8 hours for drifter speeds 1:1 m/s. Hence, the upper bound on drifter speed for transformed surveys depends on the operational upper bound on survey time. . 36 3.17 The Dorado AUV being loaded on the R/V Zephyr for the 5 day o-shore drifter tracking experiment in September 2010. . . . . . . . . . . . . . . . . . . . . 37 3.18 Illustration of repeated static-plan lawnmower implemented in the June 2010 eld trial. The survey is described by the waypointsp 1 :::p 7 in the earth frame. The resulting survey in the drifter frame is described by p 0 1 :::p 0 7 . . . . . . . . 38 ix 3.19 AUV and drifter trajectories for the June 2010 drifter following experiment with the lawnmower pattern. AUV paths are shown for both the earth frame and the drifter frame. The top plot shows the survey oset error for each iteration. The middle plot shows the drifter frame of reference for each iteration, with the location of the origin being the location of the drifter at the end of every iteration. The drifter frame is oriented in the direction of drifter advection at the end of the iteration. The AUV track is shown relative to the drifter frame through the iteration in each case. The bottom plot shows AUV and drifter tracks for each iteration in the earth frame. For the earth frame, an overlay of the previous iteration is included. . . . . . . . . . . . . . . . . . . . . . . . 39 3.20 Histogram of drifter speeds observed during the June 2010 eld trial. Mean drifter speed of 0:08 m/s and a maximum drifter speed of 0:33 m/s was observed. 40 3.21 The September 2010 CANON experiment occurred 160 kms o California coast for a duration of ve days. In this period, the Dorado AUV performed a Lagrangian-box survey around an GPS-tagged drifter with an attached genomic sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.22 AUV and drifter paths during the September 2010 ve-day eld trial. The black dots show the beginning of every iteration when the latest drifter locations were sent to the AUV. Based on these updates, the AUV computes linear projection of the drifter trajectory at the beginning of every iteration and plans waypoints in the earth frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.23 Drifter speed and survey time statistics for the September eld experiment. Mean drifter speed of 0.245 m/s and maximum speed of 0.6 m/s was observed during ve-day experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.24 Iterations from Day 4 of the September trial illustrating the drifter frame views of the AUV path. In total, 9 iterations were conducted that day. Each of the plots shows the desired AUV trajectory (square with dotted edges with length 1000 m). The star shows the starting location of the AUV for each iteration, and the AUV path relative to the drifter is shown in solid line. . . . . . . . . 45 3.25 Illustration of AUV position and timing error. Since the AUV dead-reckons when underwater, with corrections from GPS only when it surfaces (every 30 mins), it can experience substantial localization error. This gure shows a scenario where the AUV surfaces ahead of its goal waypoint and compensates for the error, nally surfacing near the goal waypoint with both positional and timing error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 x 3.26 The earth frame (left plot), showing planned and observed AUV paths and the Drifter frame (right plot) showing the observed AUV path relative to the true drifter and observed AUV path relative to the projected drifter. In the earth frame, p 1 :::p 5 are the locations where the AUV surfaced. p 0 shows the location of the AUV at the beginning of the survey iteration. Thus, the AUV has to initially travel to the rst waypoint p 1 before beginning the survey iteration, resulting in additional error in the survey quality. The drifter was located at d 1 in the beginning of the survey iteration. The projected location of the drifter at the end of the iteration is d 5 , whereas the true location is d t . In the drifter frame, the corresponding surfacings of the AUV are at p 00 1 :::p 00 5 , and the survey center is at g 00 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.27 Distribution of survey oset error for the 45 iterations of the September eld trial. The mean error was 282 m, and maximum error of 1075 m (corresponding to one of the 3 iterations where the enclosure criterion was not satised). . . . 50 3.28 Descriptive statistics for timing error and surfacing errors in drifter and earth frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.29 Scatter plots for error-pairs along with the correlation coecient R. . . . . . . 52 4.1 AUV with onboard water sample collection system (ten `gulpers') that can be triggered by the onboard computer. . . . . . . . . . . . . . . . . . . . . . . 55 4.2 A campaign of 17 AUV surveys was carried out over 8 days in August 2005. We use chlorophyll uorescence, one of the in-situ measurements as the property of interest and emulate collection of samples with high uorescence. pk samples are randomly sampled from the rst p surveys (p = 2 for day 1), followed by training and update of a GP model to guide sampl collection in subsequent surveys. The inlay at bottom right shows the true chlorophyll uorescence for one of the surveys. The same pattern was repeated 17 times over 8 days. . . . 61 4.3 True (top) and predicted (bottom) chlorophyll uorescence from one of the sim- ulated AUV surveys. It shows the AUV carrying out vertical proles between the surface and a depth of 40m. The submodular secretary algorithm is used on utility from probabilistic abundance predictions, and black circles with white '+' show gulps taken within a segment. The black circles with black '+' show two gulps taken at a segment end due to lack of better candidates within the sampling window. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.4 Cumulative regret and regret of over the course of the 17-survey campaign, averaged over 100 simulated campaigns. . . . . . . . . . . . . . . . . . . . . 64 4.5 Summary statistics of regret and correlation coecient for 100 simulated cam- paigns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 xi 4.6 Survey 1/17 and survey 17/17 during one of the emulated campaigns. Top plots and bottom plots show prediction means and variances respectively for the input space. Circles on the top plots, and dots on the bottom plots show ex-situ sample locations. Circle sizes are proportional to the true value of chlorophyll uorescence, after ex-situ labeling. . . . . . . . . . . . . . . . . . . . . . . 66 4.7 Trained PN model used for the October 17 trial. The size of the circles is proportional to the measured PN abundance through lab analysis. . . . . . . . 67 4.8 Transect plot of the sampling survey with depth on x-axis and time on y-axis. Color shows predicted PN abundance, and the crosses show where gulps ere taken. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.9 Data points corresponding to in-situ measurements of temperature (x-axis) and uorescence (y-axis) taken by the AUV during the survey, along with the pre- dicted PN abundance (color), and the ulp locations in the temperature- uorescence space (numbered dots). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.10 The time series of predicted PN abundance from the deployment, with the threshold choices for each segment as determined by the submodular secretary. 70 4.11 Histogram of various signals from the October 17 trial. Vertical lines show where gulps were taken. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.12 Comparison of PN abundance predictions for the collected gulps, and the corre- sponding PN abundance measurements through lab analysis after the mission. 71 5.1 Spatiotemporal extent of a red-tide in the Monterey Bay, CA in 2007 shown in false color remote sensing data. . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.2 The Oceanographic Decision Support System (ODSS) in use during the CANON 2010 eld experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.3 The ODSS improves situational awareness of deployed assets though near-realtime assimilation of observations from the assets. . . . . . . . . . . . . . . . . . . 78 5.4 Communication channels and robotic assets in the sea during the October 2010 experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.5 ODSS architectural block diagram, highlighting its subsystems. The unshaded boxes show legacy subsystems that were coupled with with newly developed subsystems (shaded boxes). . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.6 A section of the ODSS showing sea-surface current from third party CeNCOOS [2] server. The Data Products panel is located on the top-left corner. . . . . . . . 81 5.7 Virtual functionalities within the ODSS. . . . . . . . . . . . . . . . . . . . . 83 5.8 Real-time chlorophyll concentration data updated every two minutes from the Wave Glider [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.9 ODSS during multi-AUV experiment highlighting the chlorophyll patch, AUV Dorado, and AUV Tethys. Tethys estimated the patch center marked as 'CHL PATCH', which was tracked by the tracking subsystem. The Dorado was then commanded to perform a survey around this patch, taking water samples at chlorophyll peaks [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 xii 5.10 Plot of daily platform activity measured in platform-days, and ODSS usage, measured in unique visiter count for the days of October 2010. . . . . . . . . 85 5.11 Asset deployment statistics for the 2010 eld experiment. . . . . . . . . . . . 86 6.1 Networked systems composed of heterogeneous robots can share in-situ measured data to eciently collect physical samples for ex-situ analysis. Such systems, consisting of satellites, UAVs, AGVs, ASVs, and AUVs will enable persistent monitoring for ecological and environmental studies. . . . . . . . . . . . . . 92 xiii List of Tables 2.1 Scores of qualitative evaluation of bloom projection. Fall bloom scores have been highlighted in bold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 xiv Abstract The marine environment is in a perpetual state of ux due to ocean currents. As a result, phenomena such as plankton blooms are constantly advected, making their observation challenging. Traditionally, measurements from remote-sensing satellites, ships, piers, and moorings have helped scientists study such phenomena. However, a sound understanding of bloom ecology and dynamics requires persistent sampling at spatio-temporal scales infeasible with existing methods. Advances in robotic sampling using autonomous under- water vehicles (AUVs) have opened up the arena for adaptive sampling at unprecedented scales, augmenting other methods of observation. This thesis presents a novel data-driven robotic sampling methodology for marine ecosystem monitoring, focusing on the observation of plankton blooms. The problem is addressed at multiple spatio-temporal scales to detect, track, and sample blooms with the goal of acquisition of physical water samples for ex-situ analysis of plankton abundance. This is essential for the understanding of plankton ecology and community structure since sensors onboard AUVs are incapable of measuring precise biological data in realtime, necessitating lab analysis of water samples. Starting at the macro scale (kilometers/days), this work demonstrates how remote sensing imagery and periodic measurements of surface currents facilitate detection and trajectory projection of plankton blooms to plan AUV deployments. Once deployed, the AUV needs to survey within the context of the advecting bloom. The thesis presents the design of Lagrangian surveys wherein a bloom is tagged with a GPS-tracked drifter, and surveys are designed and executed in the frame of reference of the advecting bloom. Re- sults from a eld experiment where a 1km x 1km patch of water was successfully tracked by an AUV over multiple days demonstrate the ecacy of this approach. Next, during such Lagrangian surveys, the AUV is required to carry out adaptive water sample acquisition for ex-situ analysis. The thesis describes a principled online sampling strategy that uses probabilistic regression models trained on previously collected data to predict abundance of desired plankton from realtime measurements of physical and chemical properties by the AUV's onboard sensor suite. Extensive simulations carried out by mining historical data, and a one-day eld trial targeting a toxinogenic plankton demonstrate the impact of the approach, in eect \closing the loop" on a a signicant science problem. Finally, the thesis describes an Oceanographic Decision Support System (ODSS), a web-based tool developed for situational awareness and data visualization during robotic sampling experiments of the kind presented in this work. Extensive use during a month-long eld campaign with multiple platforms and users demonstrate the importance of support tools in marine ecosystem monitoring. Through extensive experimental results, the thesis demonstrates robotic sampling for marine ecosystem monitoring at an unprecedented spatio-temporal scale, highlighting its role in biological hypothesis testing. Although the work presented is in the context of the marine environment, it is applicable to a variety of unstructured and extreme environments inaccessible to humans. xv Chapter 1 Introduction \How inappropriate to call this planet Earth when it is quite clearly Ocean." | Arthur C. Clarke Earth's oceans cover 71% of its surface and support a diverse and complex ecosys- tem that has a direct impact on terrestrial life. Interactions between the oceans and the atmosphere drive climate patterns, 50% of oxygen is produced in the oceans; yet, we know very little about them. This thesis examines robotic sampling for observation of coastal oceanographic phenomena such as algal blooms (Figure. 1.1), anoxic zones, thin phytoplankton layers, intermediate nepheloid layers, etc. Underwater robots or au- tonomous underwater vehicles (AUVs) play a critical role in the persistent observation of these dynamic phenomena, augmenting data from other platforms such as remote-sensing satellites, ships, piers, and moorings. AUVs have allowed marine scientists to observe physical properties of coastal oceans (e.g. temperature, salinity, turbidity, etc) with high spatio-temporal resolution. How- ever, autonomous observation of biological phenomena remains a challenge due to lack of sensors that can measure organism abundance in real-time. Take for instance Harmful Algal Blooms (HABs), the focus of our work because of their impact on coastal ecosys- tems. HABs are caused due to a population explosion of various genus of algae. To help estimate the abundance of these microscopic organisms rapidly, marine scientists are developing models that map environmental features to organism abundance [5, 6]. To build these models, water samples are collected manually - o-shore from ships and boats, and on-shore from wharfs and piers. The samples are subjected to molecular and morphological analysis to identify organisms of interest, and estimate their abundance. The modeling task is to determine the mapping from the environmental features to the measured organism abundance. More importantly,samples rich in specic kinds of algae are used to carry out lab cultures to observe response to various stimuli to determine con- ditions under which blooms can become toxic, for example. Learning a predictive model can facilitate the collection of samples with high abundance of a desired type of alga. 1 Figure 1.1: An algal bloom o the Scripps Institution of Oceanography Pier, La Jolla, California. (Image credit: P. Alejandro D az and Ginny Velasquez) 2 Water sample collection for ex-situ analysis has traditionally been carried out by sci- entists manually visiting various sites. Additionally, although the environmental features are sometimes measured in parallel for model learning, the decision to collect a sample is rarely guided by measured environmental features. Thus, the approach can suer from sampling bias that can result in the learned model having poor skill. (a) USC's Roboduck - an au- tonomous boat and \data- mule" (b) MBARI's upper-water column underwater robotGulper with onboard water-samplers Figure 1.2: Aquatic platforms with onboard water sample retrieval and storage capabilities The limitation of manual sample collection has been addressed through the develop- ment of a new breed of AUVs that allow collection and retrieval of water samples to shore (Figure 1.2 shows two such platforms). This eort, still in its early stages, currently lacks principled adaptive sampling policies that utilize prior organism abundance models, and in-situ measurement of environmental features to guide sample collection. This thesis develops techniques for deployment, tracking, and adaptive sampling of marine plankton blooms, with focus on intelligent collection of water samples with high organism abun- dance. We focus on the relationship between the physics and biology of the coastal ocean, and use it to develop adaptive sample retrieval policies that help marine scientists test biological hypothesis through lab cultures, and implicitly, through the characteristics of learned organism abundance models. The thesis statement is as follows. Data-driven robotic sampling methodologies benet targeted oceanographic studies for biological hypothesis testing. 3 1.1 Contributions and Outline The contributions of this thesis are in four areas. 1. Deployment planning Given synoptic hyperspectral imagery from remote-sensing satellites, and near- realtime surface current measurements from shoreside HF radar stations, a deploy- ment plan for an AUV has to be computed. This step involves planning at large spatio-temporal scales (kilometers, hours). 2. Coordinated Tracking Once an AUV has been deployed, it should carry out surveys autonomously while taking into account advective transport of the features of interest (blooms) due to ocean currents. This involves onboard deliberation, and decisions on intermedi- ate spatio-temporal scales (hundreds of meters, minutes), coordinated with realtime updates to track the transport of the bloom. 3. Autonomous Sampling Switching from macro to micro scale, persistent marine ecosystem monitoring ne- cessitates autonomous collection of physical water samples for ex-situ analysis, op- erating at small spatio-temporal scales (meters, seconds), and relying on principled approaches to predict hidden biological features that are not measurable in-situ. 4. Oceanographic Decision Support System (ODSS) A web-based situational awareness and data visualization tool that serves as the window to the eld experiments. We envision an oceanographic macroscope that allows multi-scale observation of dynamic oceanographic phenomena using heterogeneous platforms such as remote-sensing satellites, research vessels, moorings, surface and underwater robots, and airplanes. In addition, the macroscope consists of ship-board and shore-side labs (for analysis of col- lected samples), and scientists. Figure 1.3 highlights how our work contributes to this vision. The thesis is organized as follows. In Chapter 2, we discuss how to detect marine blooms and plan surveys using remotely sensed images, and near-realtime measurements of ocean surface currents. Once a bloom has been detected and an AUV has been de- ployed, the goal is to stay with the bloom as it advects due to ocean currents. In Chapter 3, we present Lagrangian survey design where an AUV carries out a desired survey pattern in the frame of reference of an advecting bloom using GPS-tracked drifters to tag the bloom. Chapter 4 presents principled approaches to carry out online water sample acqui- sition during Lagrangian surveys, guided by an onboard probabilistic model that predicts abundance of a target organism from realtime environmental measurements. Next, in Chapter 5, we describe the Oceanographic Decision Support System (ODSS), a tool de- veloped for situational awareness during large-scale robotic sampling experiments of the 4 Figure 1.3: This thesis targets multiple pieces of an \oceanographic macroscope", with a transi- tion from macro to micro scale features. Additionally, we developed web-based tools for situational awareness and experiment planning. kind addressed in this thesis. Finally, we summarize our work and present the vision for future eorts, extending robotic sampling for ex-situ analysis beyond the marine environ- ment. 5 Chapter 2 Deployment Planning \Prediction is very dicult, especially if it's about the future." | Niels Bohr 2.1 Introduction The drivers and mechanistic processes behind algal bloom initiation, evolution and col- lapse are not well understood in part due to the complex interactions between the members of the plankton communities and the surrounding environment. As a result, our capacity to assess the range of potential future scenarios that might result from ocean temperature changes, acidication, or nutrient shifts is highly limited. The causes and triggers for these blooms vary widely depending upon regional geography and consequent oceanog- raphy [1]. Accurately predicting the location and time of a HAB onset or demise is a dicult task, and an open problem. Also, prediction of bloom collapse is relevant to so- cietal needs, including early re-opening of sheries closed due to bloom toxicity, warning of possible intensication of harmful eects in a dying bloom, and predicting the onset of anoxic events. In this chapter, we AUV deployments can be planned to study an ongoing bloom by making use of synoptic data from remote sensing satellites and shoreside HF radar stations. We show how imagery from remote sensing satellites is used to detect algal bloom hotspots using ocean color as a proxy. However, these images can be outdated by days due to atmospheric constraints such as cloud cover, and hence, it is essential to determine an accurate estimate of bloom location at the time of deployment of an AUV. We show how trajectories of bloom patches detected from remote sensing satellite imagery can be obtained using surface current data measured by HF radar stations. Our experiments show promising results for coherent blooms, whose imagery are outdated by a few days, allowing in ecient deployment planning for AUVs. 6 Figure 2.1: Algal bloom hotspots can be detected by processing outdated images from remote- sensing satellites. Thereafter, land-based measurements of surface-currents can be used to project the transport of these hotspots, resulting in an estimate of the nowcast, or current estimate of bloom location. 2.2 Scientic Motivation To understand the bloom ecology (why and when they occur, and why they decay), it is necessary to sample bloom hotspots (regions with very high biochemical activity) with high spatio-temporal resolution. To plan survey missions, scientists rely on satellite im- agery, data from moorings and drifters, ocean models, and seasonal patterns in observing HABs with the goal to maximize the likelihood of sampling hotspots as well as to be able to stay with a patch of the water with such intense activity. However predicting the occurrence of a bloom is a dicult task given the complex variability in coastal waters coupled with rudimentary understanding of phytoplankton ecology [7]. Because of the non-localized nature of blooms, the size of the observation area, and the lack of under- standing of the exact dynamics, ship-based and AUV missions often under-sample bloom hotspots. Factors negatively impacting mission success include the lag in obtaining pro- cessed satellite data (usually a day with no occlusion due to clouds), and the spatial sparsity of mooring data. Additionally, plans are made in an ad-hoc, per deployment basis and cannot be generalized to be used in a continuous, repeatable manner. 2.3 Related Work In recent work [8, 9, 10] at USC Center for Integrated Networked Aquatic PlatformS (CINAPS) [11], gliders were used to track fresh water plumes based on ocean current predictions from the Regional Ocean Modeling System (ROMS) [12] model. [1] discusses 7 the eect of external forcing on blooms occurring in the Monterey Bay. Our eort is complementary and leverages the above eort in addressing a piece of the larger problem: how to detect algal hotspots from infrequent and lagged remotely-sensed satellite images, and project their trajectories using frequently measured surface current data. Our experiments target the Monterey Bay which is not only one of the most biologically diverse bodies of waters but the northeast bay frequently experiences extreme \red-tide" blooms, making it an ideal location for bloom studies. In this chapter we analyze the result of advecting hotspots from blooms that occurred between October 2007 and October 2008 at the Monterey Bay, and show an example of how such predictions can be used to plan survey missions for AUVs. 2.4 Technical Approach An algal bloom is dened as a region of water containing a high population density of phytoplankton, often covering areas of more than 50 km 2 . The path of a bloom through the ocean is in uenced by a) advection, the component of transport due to the eect of external forcing such as ocean currents b) diusion, the mixing of uid that occurs as a result of spontaneous movement from a region of higher to lower concentration, and c) biological growth and decay, the governing factors in bloom ecology. Remote sensing satellite data provide a synoptic view of the ocean, enabling esti- mation of algal bloom concentration in the top 5-10 m of water. However, usable data from remote-sensing satellites are only available on clear days. Depending on weather conditions, these images can have a lag of a day (best case), to upto a month if there is persistent cloud-cover. Our work has three goals, 1. Detecting and labeling distinct algal hotspots from remote-sensing images through image-processing. 2. Projecting the movement of the labeled hotspots over a scale of days using hourly surface-current measurements from land-based High-Frequency Radar stations (Fig- ure 2.3). 3. Determining a deployment plan for an underwater robot based on the projected hotspot locations. Here, we will brie y describe the technical approach to implement the three goals. 2.4.1 Hotspot detection We dene a bloom hotspot as the region in a satellite image M in which the pixels have uorescence valuesf greater than a specied threshold F . This is a proxy for a region of intense biological activity. We perform image thresholding on M with level F , resulting in a thresholded image I thresholded that may contain many small disconnected patches. 8 Figure 2.2: Illustration of ltering of thresholded satellite image I thresholded using 8-connectivity and pixel-weight to determine coherent hotspots. Hence, we isolate coherent patches in I thresholded using two steps. First, connected regions are de- tected by nding pixels satisfying 8-connectivity (connected on either of eight sides). From these distinct connected regions, the ones with a pixel weight of at least W pixels are selected. In our work, we choose W = 50. Since each pixel on the satellite image represents a 1 km 2 region, the nal detected patches are atleast 50 km 2 , representative of coherent algal hotspots. Figure 2.2 illustrates the detection of patches fromI thresholded image using 8- connectivity and pixel-weight based ltering. After this step, the resulting image will havek distinct re- gions. For purposes of asset placement, we want to track thek regions (or hotspots) separately. Hence, we perform a labeling step on the k regions where pixels in each connected component is given a label h i , where h i 2 H =fh 1 ;h 2 ;::;h k g. This concludes the detection and labeling step, and the k patches in the set H can now be advected using the approach discussed in the following section. 2.4.2 Hotspot Advection Figure 2.3: An hourly snapshot of surface- current, estimated from measurements by multi- ple land-based HF radar stations (shown as black triangles). The hotspot detection step results in H, a set of k hotspots in the outdated satellite image M. Now, we want to use hourly surface-current measurements (or velocity elds) from land-based HF radar stations, to advect the hotspot to current time for a nowcast. To do so, we want to advect pixels in each patch in H using the time- series of velocity elds (Figure 2.3 shows an hourly snapshot of the velocity eld). Since advecting each pixel within a patch over multiple time steps can be compu- tationally expensive, we choose a sparser representation of a patch. We sub-sample each patch h i 2 H, i 2 1;:::;k to se- lect points uniformly at a chosen resolu- tion. The selected sample points P = fp 1 ;p 2 ;:::;p N g provide a lower resolution representation of the hotspot, which can be advected using the velocity eld snapshots. We interpolate the velocity eld time-series so that for any location p = [x y] T (x, y are longitude and latitude, resp.), and timet, we have the velocityR p;t = [u v] T , whereu and 9 v are the East and North velocity components, respectively. A sample point is dened as s = [p f] T where p is the geographical location and f is the corresponding uorescence value. Each pointp within a patch is projected usingR p;t to obtain a new position of the sample point p t+1 =p t +R p;t+1 t. Algorithm 1: Hotspot detection and advection 1 Input: MODIS images M 1 and M 2 2 Time period T = timestamp(M 2 - M 1 ) 3 t = t M 1 4 I thresholded = threshold(M 1 ;F ) 5 H = connectedSegments(I threholded ) 6 h hotspots, H =fh 1 ;h 2 ;:::;h k g 7 foreach HotSpot h i do 8 sample points for HotSpot h i , 9 P i = resampleHotspot(h i ,resolution) 10 P i =fp 1 ;p 2 ;:::;p N g 11 foreach sample point p j = [x;y;t] do 12 while t<t m2 do 13 R p;t = [u;v] 0 14 p t+t =p t +R p;t t 15 p t+1 = pt + Rt :t 16 t =t + t 17 end 18 end 19 end The error covariances for the Open Mode boundary Analysis (OMA) interpolated velocity estimates are given as u and v for each data point in the grid. These are used to project the estimation error of the advected point. Each iterative step in advecting the patch is a linear transformation from p t to p t+1 . The new error is obtained by p t+1 = pt + Rt t. This algorithm for the detection and advection of bloom patches is summarized in Algorithm 1. We retain the original FLH value for each sample point throughout the advection and do not model error in FLH estimates. The FLH error exists because we do not consider diusion and bloom ecology. We plan to address this issue by modeling it as a Gaussian error that grows exponentially with time. Also, we assume that the surface current eld is constant within a neighborhood of the advected point. 10 2.5 Results We performed advection of FLH hotspots on a dataset of MODIS FLH images captured between September 2007 and November 2008. The period was chosesn such that we had both MODIS and HF Radar data. MODIS images are often unusable due to cloud cover or corrupted images. After rejecting the unusable images, we selected those that displayed hotspots of considerable intensity. We were also interested in studying the quality of the advection for dierent time periods. From the test cases, we identied 1, 2, 3, 4, and 5 day periods between MODIS images to ground truth our projections. In total, we selected 16 test cases spanning Fall 2007 to Fall 2008. The resulting projections were evaluated qualitatively by a physical oceanographer, and table 2.1 shows the results. We observed good predictions for stronger blooms, specif- ically blooms in Fall. The advection of bloom patches fail to predict blooms that are in the initial stages of growth. The projections were good for blooms that were well devel- oped and of high intensity. Figure 2.4 and Figure 2.5 show two two-day projections from the 16 test cases in this study. Hotspot Projection Test Cases Period(days) Case Evaluation Rating (max 5) 5 03/20/2008 3 4 06/02/2008 4 10/12/2008 4 3 10/09/2008 4 2 10/12/2007 4.5 02/15/2008 3 03/18/2008 2 03/25/2008 2 04/10/2008 2 04/26/2008 2 05/21/2008 3 10/10/2008 3.5 10/12/2008 3 10/14/2008 5 1 10/24/2007 4 10/09/2008 2 Table 2.1: Scores of qualitative evaluation of bloom projection. Fall bloom scores have been highlighted in bold. 2.5.1 AUV deployment planning Our aim next is to choose a survey area given the projection of the hotspot location. A compelling scenario for such an application is illustrated in Figure 2.6. Two day old 11 Figure 2.4: Projection of a bloom from October 2007. Figure 2.5: Projection of a bloom from October 2008. satellite data shows the onset of a bloom. Our objective is to project the blooms trajectory and then place a viable `lawnmower' AUV survey to ensure coverage. One application of such a survey could be nd hotspots in the water. By generating the survey using the projected hotspot location instead of directly using detected hotspots in the outdated satellite images, we hope to maximize our chances of nding an ongoing bloom. We are given a desired survey template specied by the bounding box dimensions (length and width). Our goal is to determine the best deployment plan, given by the location of the center of the survey template and its orientation. For a candidate survey area bounded by R, the sampling reward r is given by total signal intensity within the survey area. Since our goal is to attain maximum spatio-temporal sampling resolution at hotspots, our 12 Figure 2.6: A hypothetical bloom onset (A), projection (B) and a viable AUV survey to capture the bloom's spatial extent. objective is to maximize the total signal intensity in the region where we sample. For our implementation, we dene the sampling reward r as, r = n X i=0 e f i g R (p i ) (2.1) where g is given by, g(p) = ( 1; if p is inside rectangle R 0; if p outside rectangle R (2.2) and is a chosen constant. The weighing function over FLH was chosen to be exponential to reward higher values of f favorably by a factor . 13 We use a recursive-grid (described in algorithm 2) to determine the best location, followed by an exhaustive search to nd the best orientation. Algorithm 2: recursiveBestGrid(G,a,b) 1 Input: survey area parameters a and b and grid G 2 L and B are length and breadth of bounding-box B 3 if L=2<a OR B=2<b then 4 return G 5 end 6 L =L=2,B =B=2 7 m = arg max i (samplingReward(G i ;P )) 8 recursiveBestGrid(G m ,a,b) Algorithm 3: ndSurveyArea(P ,a,b) 1 Input: N projected sample points P =fp 1 ;p 2 ;:::;p N g 2 survey area parameters a and b 3 bounding-box of advected points B 4 G max = recursiveBestGrid(B,a,b) 5 [S p ;] = ndBestArea(G max ,a,b) Figs. 2.7a and 2.7b show the result of our search algorithm on the example bloom cases from October 2007 and 2008. The dotted box shows the initial bounding box and the solid box shows the nal survey area chosen by the search algorithm. (a) Rectangular survey area of known size that maximizes the contained FLH intensity of the bloom case 1 (10/12/2007). The nested grid ap- proach was used to search for the location and ori- entation of the rectangle that maximized the gain (FLH intensity). (b) Plot showing the survey rectangle for the Oc- tober 2008 bloom. Figure 2.7: Results of bloom projection and AUV mission plans for 2007 and 2008 datasets. 14 2.6 Conclusions The ability to detect and project a bloom hotspot, followed by the generation of a deploy- ment plan, is relevant for oceanographic eld experiments. This work can be integrated with systems such as the Oceanographic Decision Support System (ODSS) described in Chapter 5 as an always-on tool that provides the best deployment plan at any time, based on recent (< 5-day lag) satellite images (if available). Finally, note that the survey tem- plate places the AUV in the vicinity of the targeted hotspot. However once within the approximate area, the vehicle's adaptation and response to sensed parameters needs to be considered. This requires methodologies for bloom tracking and sampling, which are discussed in the following chapters. 15 Chapter 3 Coordinated Tracking \I would believe only in a God that knows how to dance." | Friedrich Nietzsche 3.1 Introduction Oceanographic features are often heterogeneous and dynamic, spread over large spatial scales with dynamic biological activity across the temporal spectrum, making autonomous tracking and sampling of these features with robotic platforms challenging. For instance, bio-geochemical features of interest in the coastal ocean such as phytoplankton blooms, and anoxic zones are constantly circulated by ocean currents. Currently, AUV-based surveys rely primarily on geographic waypoint track-line surveys [13] that are suitable for observing static features such as bathymetry, or slowly changing aquatic environments characterized by weak circulation [14]. When studying dynamic, rapidly evolving oceano- graphic features, such methods at best introduce error through insucient spatial and temporal resolution, and at worst completely miss the spatial and temporal domain of interest. In this chapter, we demonstrate methodologies for Lagrangian y observation of ad- vecting z oceanographic features. We describe two approaches, both utilizing GPS-tracked devices called drifters that advect with ocean currents and which have traditionally been used as proxies for advection [16]. They have been used for observation of coastal sur- face currents [17] and analysis of circulation elds for improvement of ocean models [18]; usually one or more of these drifters are deployed for such studies and used in concert Oxygen depleted regions in the ocean. y From [15]:The terms Lagrangian and Eulerian describe dierent frames of reference for speci- fying or observing uid properties. An Eulerian specication of a uid property is a function of space and time. The Eulerian frame of reference is probably most familiar to people; we stand on the shore and watch the river ow by us. A Lagrangian specication is a function of an identiable piece of uid and time. The Lagrangian frame of reference moves with the uid; we sit in an inner tube and oat down the river. z The horizontal transport of a patch of water. 16 Figure 3.1: Dynamics of algal blooms in California's Monterey Bay. Figure shows remote sensing images capturing the chlorophyll concentration at the ocean surface between September 19th and October 8th, 2002. Due to atmospheric conditions, the images are temporally aperiodic. Algal hotspots characterized by red coloration can be seen evolving as a result of biological growth and decay, and advection due to ocean currents. Marine scientists are interested in understanding the dynamics of these hotspots as they evolve, which necessitates being able to track them spatially as they are advected by ocean currents, and sampling within this patch frame of reference. (Image from [1]) with ship surveys. We make use of drifters to tag patches of interest. Updates on drifter location are received periodically via tracking satellite services such as Iridium. These updates are used to plan and implement surveys that take into account the movement of the patch due to ocean currents. This work is motivated by a multi-year inter-disciplinary eld program at the Mon- terey Bay Aquarium Research Institute called the Controlled, Agile and Novel Observing Network (CANON) [19]. The program focuses on understanding rapidly evolving coastal ocean processes that have signicant societal impact on local ecosystems. The initial emphasis is on phytoplankton blooms that have signicant consequences on marine ecol- ogy with the generation of toxins that in turn in uence the food web [20]. Figure 3.1 highlights the spatio-temporal dynamics of phytoplankton blooms in Monterey bay, as observed by images acquired by a remote-sensing satellite over a period of twenty days. The drivers and biogeochemical processes behind phytoplankton bloom initiation, evo- lution and collapse are poorly understood in large part due to the complex interactions between the members of the plankton communities (including phytoplankton) and the surrounding environment. This necessitates acquiring measurements at sucient spatial and temporal scales as the feature evolves. In the past, such studies have been carried out using an array of drifters equipped with onboard sensors to observe bio-geophysical properties such as temperature, uorescence, and salinity of advecting oceanographic features [21]. Using an array of drifters to study advecting features suers from some operational limitations. While it is not necessarily cost-eective to deploy multiple drifters with sensors capable of measuring features of 17 interest, some of the drifters can eventually drift in unanticipated directions due to non- coherence of ocean currents. This not only results in under-sampling of the feature, but additionally makes drifter retrieval non-trivial. Therefore, our work describes the problem and associated engineering challenges with providing the environmental context around an advecting drifter using a fully autonomous and controllable robot. We treat our problem as a simultaneous tracking and sampling task, where a single GPS-tracked drifter is used to tag a patch of water providing a frame of reference along with a survey template that is repeatedly undertaken by an autonomous platform around the advecting drifter. This methodology has certain advantages: a) the autonomous platform can be controlled to perform a survey of a desired size and pattern and b) the platform can be equipped with a suite of sophisticated sensors that can be exploited to sample various properties of the patch. In this work, the autonomous platform we have chosen to use is an AUV. We demonstrate two modes of performing the surveys a) repeating static-plan surveys to stay with the moving patch, and b) transformed surveys carried out in the frame of reference of an advecting patch. Starting with the scientic motivation for this eort, we rst lay the ground-work through analysis of past data and simulations. We derive the relationship between patch advection speed and survey dimension, and dene the requirement for successful tracking in the form of an enclosure criterion. Subsequently we describe two eld trials that demonstrate our approach. In our experiments, in addi- tion to the sensor suite onboard the AUV, a genomic sensor is attached underneath the drifter. This allows tracking of microbial variation at the patch center along with the environmental context at the perimeter of the patch observed by the AUV. The scientic validation of the experimental goals is outside the scope of this work. The contribution and novelty of this work is multi-fold. First, in the development of strategies to use autonomous robotic platforms for Lagrangian observations of an ad- vecting patch and doing so in real world settings in the open ocean. Second, we show the limitations of using extensions of static surveys which repeatedly reposition a robot with the advecting patch and in the process demonstrate the importance of observation frames of reference. Third, we analytically derive an envelope on patch speeds that can be tracked autonomously. And nally, we show ways to measure the performance of such robotic surveys. The chapter is organized as follows. Section 3.2 places this eort in the larger context of drifter based studies, sampling and robotic control. Section 3.3 is the core of the chapter and highlights the technical approach we follow. Section 3.4 shows the experimental setup in the eld. Section 3.5 analyzes a ve day eld experiment conducted in September 2010 in the open ocean followed by conclusions and some future work in Section 3.6. 3.2 Related work Drifters have traditionally been used for Lagrangian studies for measurement of biolog- ical processes in-situ at the appropriate temporal scales with ship-support [21], and for 18 physical oceanographic measurements of current ow and turbulence related to ocean modeling [18, 22]. Our work extends these applications from a pure drifter based La- grangian observation system to one which provides a larger environmental context as well as more control of the survey design using an autonomous robotic platform. Tracking of oceanographic features with AUVs has previously been addressed with the help of ocean models. Advection forecasts provided by regional ocean models in the form of virtual drifters have been used for planning trajectories for gliders to track the boundary and centroid of a patch of water [10, 23]. However, glider trajectories computed for virtual drifters are not guaranteed to track a physical patch of water since such model forecasts suer from high uncertainty. Further, the work is limited by the speed and motion of gliders which are highly restrictive and in uenced by currents which have resulted in focused demonstration of boundary and centroid tracking. In contrast, the goal of this work is to track a patch and sample within it rapidly. Tracking and rendezvous with moving targets has been covered in the robotics lit- erature, although the focus has been on interception and entrapment with multiple ro- bots [24], rather than sampling in the target frame-of-reference. In [25], landing of an Unmanned Aerial Vehicle (UAV) on a moving target is demonstrated. In [26], control strategies are demonstrated wherein a team of autonomous aircraft orbit a moving target while maintaining a specied distance (stando line-of-sight tracking). In [27], a terres- trial multi-robot system using low-level control is used to localize and encircle a moving target in a lab environment. In the ocean sciences, [28] discusses the use of drifters for tracking anticyclonic eddies in near coastal waters; however they use a lagrangian frame of reference to navigate their manned support vessel [29]. Feature tracking with AUVs has been discussed in the context of multiple gliders in the Monterey Bay by [30] while coordinated sampling with a eet of gliders is demonstrated in [14]. [31] proposes a methodology for iceberg relative terrain aided navigation for AUVs using sideways looking sonar maps generated by a ship. However the authors abstract out the iceberg deformation and its motion while relying on the closed structure of a solid body. Our work is distinct in that environmental observation and sampling drive the survey methodology using onboard planning techniques within the oceanographic domain. More importantly the focus of this work is on deriving the frames of reference for undertaking such observations which none of the prior work address. And to the best of our knowledge, our work presents the rst study where an autonomous robot samples in the Lagrangian frame of reference of an advecting oceanographic feature in the upper water-column. 3.3 Technical Approach AUVs are equipped with scientic payloads to enable sampling of bio-geochemical prop- erties of interest at desired sampling rates. Typically while sampling the upper water- column, track-line based surveys are carried out. 19 3 km August 26, 12:10 August 26, 13:20 Figure 3.3: Airborne remote sensing images showing short-term phytoplankton bloom dynamics in the Monterey Bay in the month of August 2009. A phytoplankton bloom patch, marked in the left image with a +, is shown advecting eastward by 1 km in less than 80 minutes, suggesting currents of the order of 0:2 m/s. Figure 3.2: A lawnmower survey pat- tern of an AUV in the upper water- column showing chlorophyll uores- cence within vertical saw-tooth (or 'yo- yo') proles. A prominent example is the `radiator' or `lawn- mower' pattern shown in Figure 3.2. It shows an aggregation of chlorophyll uorescence from phyto- plankton biomass during daytime operations when biological activity is concentrated in the upper por- tions of the shelf in Monterey Bay. The vertical saw- tooth proling path of the AUV illustrated in this gure is called a 'Yo-Yo' and allows observation of a three-dimensional snapshot of the water-column. The patterns are usually determined a priori accord- ing to scientic need. Existing AUV sampling methodologies use sur- vey patterns designed in the earth frame, i.e., they are not planned and carried out relative to the wa- ter mass. Hence, by design, these static-plan sur- veys are suitable for features that do not move out of the survey's region of coverage or are suciently slow for an AUV with typical speeds of 1:5 m/s to resolve adequately. The oceanographic features of interest in our study, however are not static; movement occurs either due to surface currents, the geography of the coastal shelf, wind driven conditions or all of the above. Figure 3.3 shows remote sensing imagery of chlorophyll concentration in the upper 5-10m of Monterey bay. Within an hour, the hotspots (regions with concentrated coloration) are shown advected eastward by a kilometer. The scientic goal of this work is to extend existing oceanographic sampling methodologies to perform Lagrangian observation studies to sample such ad- vecting features of interest. We propose approaching this problem in two ways: Track a patch We use GPS-tracked Lagrangian drifters, used as proxies for advection by marine scientists, to tag an identied patch of interest. 20 Figure 3.4: Illustration of a Lagrangian drifter being tracked on shore and at sea. The drifter has a oat section aected mostly by wind and a drogue section which is impacted by sub-surface currents. Drifter locations are transmitted via satellite. The support vessel is for launch, recovery and charging of the AUV. Sample the patch We extend existing oceanographic survey patterns to sample within the context of the advecting patch tagged by the drifter. Frequent position updates from the drifter are used to estimate the short-term trajectory of the patch, and two approaches are demonstrated to stay with the patch and sample around or within it. 3.3.1 Tracking advecting patches We use GPS-tracked drifters to tag the center of an advecting water patch. These patches are usually identied by using data from remote-sensing satellites, pilot AUV static- plan surveys, and ship-board measurements. Once detected, a bloom center is marked with a GPS-tracked drifter and position updates are obtained from the drifter at regular intervals of 2 mins via a satellite communication network such as Iridium. To improve the drifter's signature of patch advection, which may experience a range of sub-surface currents, drogues are often used to improve the surface and sub-surface expression for advection. Figure 3.4 illustrates the usage of a GPS-tracked Lagrangian drifter and its communication channels with shore, ship, and AUV. 21 3.3.2 Scientic Motivation Two primary science goals drive our work; the rst is to quantify a nutrient budget for a volume by estimating nutrient uxes across its boundaries. This requires a survey tem- plate that repeatedly circumscribes the volume boundary such as a box pattern shown in Figure 3.5. The second goal is to map the interior of the volume in order to understand the biological dynamics occurring within the volume of the patch, requiring a template that passes through the volume interior such as in the lawnmower pattern described earlier. Both goals are relevant to the overarching research objective to understand the environ- mental factors in uencing the growth and ecology of phytoplankton communities. The box pattern was chosen for our open ocean eld experiment, although the results can be gener- alized to other patterns. Vertical Yo-Yos Algal patch Survey Volume Nutrient Flux 100m 1 Km Figure 3.5: The box survey pattern of an AUV which circumscribes a patch volume being sam- pled. Our work extends existing static-plan sur- veys to the observation of advecting fea- tures of interest. To achieve this goal, we rst tag an identied patch of interest with a GPS-tracked drifter. The decision of where and when to tag a water patch is usually driven by a combination of oceano- graphic conditions such as wind, real-time surface currents, geographical conditions, historical data and remote sensing infor- mation when available. A specic assump- tion we make is that the AUV does not compute currents for executing the survey around the drifter primarily for two rea- sons. In-situ determination of current velocities using an ADCP (Acoustic Doppler Cur- rent Proler) is challenging given integration times and signal noise from this sensor. Second, drifter speed and bearing are computed shore-side and transmitted to the vehicle providing adequate information for the vehicle's onboard planner to generate a plan to meet the coverage goal of the experiment. Based on the scientic motivation above, our problem statement is as follows: Problem Statement Extend existing oceanographic surveys by an autonomous plat- form to observe an advecting patch of interest, such that the patch-center tagged by a GPS-tracked drifter, remains within the survey perimeter at all times. 3.3.3 Lagrangian survey design AUV surveys are characterized by the pattern in the horizontal plane (e.g. lawnmower, box, etc), the pitch angle for the yo-yo's and a depth-envelope specifying the maximum and minimum depths. For the purpose of planning, we will approximate the motion of the AUV to the horizontal plane by projecting its velocity by the pitch angle. Figure 3.6 22 s X Y Z o a s s p p Depth envelope l l X Y l p p o 1 2 3 4 1 2 3 4 p p p p Figure 3.6: Illustration of the box survey pattern. For a box pattern with edge length l, imple- mented in three dimension, the AUV performs saw-tooth vertical proles along the edges with pitch angle. The AUV moves at a constant surge speeds a . The projected speed of the AUV on the horizontal plane while executing the saw-tooth proles is given bys a cos. We can design AUV plans in two-dimensions where the motion along the depth axis is encapsulated by the projection onto the horizontal plane. 23 p' Drifter frame o' Y' X' 1 p' 2 p' 3 p' 4 p' 5 Figure 3.7: Enclosure-criterion satised in drifter frame. The goal of our study is to implement surveys such that a drifter that represents a patch of water stays within the boundary of the survey. In the gure, p 0 1 :::p 0 5 denes the perimeter of a survey in the drifter frame. The enclosure criterion ensures that the drifter, marked by o 0 , stays inside the survey perimeter. shows a box pattern that has a square prole in the horizontal plane with edge length l. The vertical saw-tooth patterns with pitch angle allows the AUV to sample the vertical faces of a cube which is essential for the nutrient ux study. In the following discussion, we will use this pattern as the template for analysis and design of our approach for the two modes. We begin by dening a few terms used in our design: Earth frame The geographic frame of reference which allows the specication of ev- ery location on Earth uniquely. Typically static-plan AUV surveys are planned in the earth frame in the form of track waypoints using a Longitude/Latitude based spherical coordinate system. Drifter frame The frame of reference relative to the advecting patch. Since the patch is tagged by a GPS-tracked drifter we set the origin of the patch frame to the drifter location and orient it to point along the direction of drifter advection. Repeated static-plan surveys These are static-plan surveys carried out repeatedly by catching up with the drifter after each iteration. Survey patterns are intended for earth frame, but we do our analysis by visualizing these in the drifter frame. Trailing distance To perform repeated-static plan surveys, the AUV needs to catch-up with the last observed location of the drifter on completion of the current static-plan iteration. The distance the AUV lags or trails behind its survey start location for the next iteration is called the trailing distance. Transformed surveys In contrast to repeated static-plan surveys that are designed in the earth frame, these patterns are designed relative to the patch frame or the drifter frame. Since the AUV operates in the earth frame, this entails transfor- mations between the advecting drifter frame and the earth frame. Enclosure criterion Ideally the drifter should remain within the perimeter of the pat- tern while the AUV is executing the pattern. The enclosure criterion ensures that 24 the AUV encapsulates and characterizes the volume by enforcing the constraint that the patch center marked by the drifter always stays within the perimeter of the sur- vey. Figure 3.7 shows the limiting condition for the enclosure criterion for repeated static-plan surveys with a box pattern. In Section 3.3.3, we will obtain the bounds on drifter speed for the satisfaction of the enclosure criterion for repeated static- plan surveys; transformed surveys by denition ensure satisfaction of the enclosure criterion. We have identied two ways of approaching our goal to perform Lagrangian obser- vation studies: a) repeated static-plan surveys and b) transformed surveys. In repeated static-plan surveys, we perform existing oceanographic surveys repetitively, repositioning the AUV to the latest location of the drifter once a survey or iteration is complete. In case of transformed surveys, we design the pattern in the drifter frame and transform it back to the earth frame to obtain the plan to command the AUV. To plan the surveys in both repeated static-plan surveys and transformed surveys, we require an estimate of the drifter path in the near-term ( 2 hours). Repeated static-plan surveys Repeated static-plan surveys are planned in the earth frame with respect to the current location of the drifter. Once the survey is complete, the latest drifter location is obtained and the AUV traverses to the new survey location and carries out another survey. We dene this as a survey iteration. Repeated iterations are carried out till the mission is over, or the drifter moves out of an area of interest. We will derive the maximum drifter speed for which static-plan surveys satisfy the enclosure criterion. Consider an AUV that is required to perform a static-plan box pattern around a drifter that is moving with a speed ofs d . We will consider a simple scenario where at the beginning of the n th iteration of the experiment, the drifter is moving in a straight line and the AUV is at a trailing distance of u n from the initial waypoint of the static-plan survey relative to the drifter's current location. Let the surge speed of the AUV be s a performing a straight line transect and the speed during the survey when it is performing a saw-tooth pattern with a pitch angle be s s , where s s = s a cos. For our analysis, we will assume that the AUV is lagging directly behind the drifter and for illustrative purposes, we will use a box pattern with edge lengthl. The total distance the AUV needs to travel as viewed on the horizontal plane is given by the sum of trailing distance u, and the survey length for the box pattern L survey . For the box pattern, L survey = 4l. Given u n , the trailing distance for the nth survey iteration of an experiment, we rst show that within a few survey iterations, the trailing distance converges tou . The total time taken by the AUV to complete the survey is given by: T s = u n s a + L survey s s (3.1) 25 un sa is the time taken for the AUV to reach the starting point at the AUV surge speed s a . Once the starting point has been reached, the AUV initiates the yo-yo's, resulting in the projected speed of s s . The time taken for completion of the survey is given by the second term Lsurvey ss . The trailing distance for the n + 1 th iteration is the distance the drifter travels while the AUV nishes the nth survey. For the n + 1 th iteration, the AUV hence lags or trails behind the starting waypoint for the iteration by this distance given by: u n+1 =T s s d (3.2) Substituting T s from Eqn. 3.1 to Eqn. 3.2 we get: u n+1 = u n s a + L survey s s s d (3.3) Taking a = s d sa and b =L survey s d ss in Eqn. 3.8, we get: u n+1 = u n s d s a +L survey s d s s = au n +b = a(au n1 +b) +b = a 3 u n2 +b(1 +a +a 2 ) The trailing distance for the n + 1 th iteration is hence of the form: u n+1 =a i u ni+1 +b i1 X k=0 a k (3.4) where 0in + 1. On taking i =n + 1 in the above equation, we get: u n+1 =a n+1 u 0 +b n X k=0 a k (3.5) On taking the limiting case where n!inf, Eqn. 3.5 gives us the asymptotic trailing distance u : u =u 0 lim n!inf a n+1 +b lim n!inf n X k=0 a k (3.6) But a< 1 for s d <s a , hence: u = b n X k=0 a k 26 o o o Earth frame Drifter frame X Y o' Y' X' m l/2 u* l/2 p 1 p 2 p 3 p 4 p 0 p 5 p' 1 p' 2 p' 3 p' 4 p' 5 p' 0 1 2 Figure 3.8: Implementation of the box pattern for Lagrangian observation studies involves the AUV covering a trailing distanceu, the survey length 4l and ensuring that the enclosure criterion is satised. o 1 represents the starting point of the drifter and o 2 its termination within a single pattern. For the enclosure criterion to be satised, the AUV has to cross the drifter ahead of its path in the earth frame. For a< 1, P inf k=0 a k = 1 1a : u = b 1a (3.7) Substituting values of a and b: u = L survey s a s d s s (s a s d ) (3.8) Hence, for survey length L survey , AUV surge speed s a , drifter speed s d < s a , and pitch-angle , the trailing distance converges asymptotically to u = Lsurveys d cos(sas d ) . The asymptotic trailing distance is hence independent of the initial trailing distance u 0 and depends only on the drifter speed s d . Note that the maximum drifter speed observed in historic drifter data is 0:6 m/s, about half of the maximum AUV surge speed of 1:5 m/s. We use the above result to determine the maximum drifter speed for which the enclo- sure criterion is satised in the drifter frame. For the enclosure criterion to be satised, the AUV has to cross the drifter ahead of its path in the earth frame, as illustrated in 27 Figure 3.8. Hence, for the box pattern with edge length l, the drifter must travel less than l=2 in the time the AUV takes to intercept the drifter. u s a + l=2 s s s d < l=2 (3.9) u s a + l 2s s < l=2s d (3.10) Using Eqn. 3.8 with L survey = 4l and solving for s d , s d < s a (1 + 30 cos + cos 2 ) 1=2 s a (1 cos) 14 (3.11) Figure 3.9: Trajectory of a drifter ad- vected in the vicinity of Monterey Bay in August 2006 for a period of 3.5 days. For s a = 1:5m=s, = =8, Eqn. 3.11 results in s d < 0:36 m/s. This sets the upper bound on the drifter speed for which we can successfully complete repeated static-plan surveys while satisfying the en- closure criterion in the drifter frame. We obtained drifter logs from a deployment in Monterey Bay dur- ing August 2006 lasting 18 days [32]. From this data-set, we utilized a 3.5 day section during which the drifter traveled a total of 80 km near Monterey Bay as shown in Figure 3.9. The computed distribution of drifter speeds ob- served during this period for use in our analysis is shown in Figure 3.10. The dotted-line in this gure marks this upper-bound of 0:36 m/s for which the enclosure criterion is satised. As highlighted by the cumulative frequency curve in Figure 3.10, for 30% of the speeds the vehicle won't be able to satisfy the enclosure criterion. This poses a limitation in the use of repeated static-plan surveys for Lagrangian observation studies, since it cannot be guaranteed that the drifter stays within the perimeter of the survey at all times. To address this limitation, we present an alternative approach in the following discussion that by design ensures that the enclosure-criterion is satised for a wider range of drifter speeds. Transformed Surveys Instead of repeating static-plan surveys planned in the earth frame of reference based on periodic updates of patch trajectory, we can design the surveys in the drifter frame of reference. We call these transformed surveys since the waypoints of the surveys are planned in the drifter frame of reference and then transformed back to the earth frame. As opposed to repeated-static plan surveys where we observed an upper-bound of 0:36 28 Figure 3.10: Distribution of speeds for a drifter deployed at the central Californian coast. The dotted line shows the upper-bound of 0.36 m/s on drifter speed for which the enclosure criterion is satised. This is based on our analysis of repeated static-plan box surveys performed by an AUV operating at nominal speed of 1.5 m/s. m/s, transformed surveys by design ensure that the enclosure criterion is satised. The key idea is as follows. Given a desired survey pattern, for example a `lawnmower' or a `box', we acquire the frame of reference of the advecting patch from the GPS-tagged drifter. Since AUVs are commanded using waypoints in the earth frame, we want to plan waypoints and AUV operation parameters (speed, pitch angle), which will result in the desired survey being executed in the drifter frame of reference. Hence, this approach requires transformations between the advecting drifter frame of reference and the static earth frame. Figure 3.11 illustrates the transformation between earth and drifter frame for the box pattern. There are two ways of implementing transformed surveys. The rst is to perform a survey at a constant speed in the drifter frame. However, we will show that due to the transformations between the advecting drifter frame and the static earth frame, such surveys require the AUV to travel in the earth frame at variable speeds. To simplify command and control and to utilize the maximum AUV speed at all times (in the previous case, the maximum AUV speed is utilized only for sections of the survey), we describe a second approach that involves running the AUV at a constant speed (ideally the maximum operational speed of the AUV). This however results in a survey pattern in the drifter frame with variable speed. We discuss both the cases below, and show experimental results for the latter in Section 3.4. Constant AUV speed in the Drifter frame One goal is to perform the template at constant speed relative to the drifter, ensuring uniform sampling rate in the drifter frame. In Figure 3.12, we show a box pattern with ve corner waypoints forming the complete survey. Given the desired speed at which we want the AUV to sample relative to the 29 p o o o Earth frame Drifter frame X Y o' Y' X' Easting Northing 1 p 2 p 3 p 4 p 5 p' 1 p' 2 p' 3 p' 4 p' 5 1 2 Figure 3.11: Illustration of transformed survey for the box pattern. The goal is to ensure that a box pattern is implemented in the advecting drifter frame of reference. The goal waypoints for the corners of the box pattern in the drifter frame are transformed to the earth frame to provide us with the AUV mission plan consisting of ve waypoints. drifter and the length of the survey, the corner waypoints are denoted by p 0 i = [x 0 i ;y 0 i ; 1] T . Additionally, since the AUV appears to travel at constant speed in the drifter frame, we can compute the time t i when the AUV should be at each waypoint. If is the angle between the drifter frame and the earth frame and the drifter is at o i at each time-step t i , we can construct the homogeneous transformation matrix [33] H d w that transforms the waypoints in the drifter frame to the earth frame, given by, H d w = cos sin o ix sin cos o iy 0 0 1 (3.12) Given p 0 i , a coordinate in drifter frame, the corresponding coordinate in the earth frame can then be given by: p i =H d w p 0 i (3.13) Given the current AUV coordinate in the earth frame and the destination computed using Equation 3.13, we can then compute the required projected AUV speed to achieve the target in the drifter frame at the desired time instant. As illustrated in Figure 3.12, the AUV needs to travel varying distancesd 1 ,d 2 andd 4 in the earth frame, for equal time intervals for each leg of the box pattern. Consequently, the maximum required projected 30 Figure 3.12: Illustration of a transformed survey for the box pattern for the case where the AUV is required to move at constant speed in the drifter frame. Given the ve goal waypoints and the corresponding time of arrival (p 0 1 ;t 0 1 );:::; (p 0 5 ;t 0 5 ) for the corners of the box pattern, our goal is to compute (p 1 ;t 1 );:::; (p 5 ;t 5 ). For this computation, we require a prediction of the drifter trajectory for the duration of the iteration. This is done using a linear projection of the drifter trajectory based on the last two position updates from the drifter. For the box pattern, the AUV will travel varying distances d 1 , d 2 andd 4 in the earth frame, for equal time intervals corresponding to each leg of the survey. 31 (a) Illustration of AUV navigation between two waypoints of the box pattern using con- stant speed in earth frame. As the drifter moves from o 0 to o 00 , the AUV moves at con- stant ground speed fromp 1 top 2 . This results in the AUV moving fromp 00 1 top 00 2 in the drifter frame. Given the drifter speed s d , the initial AUV location p and the goal location of the AUV in drifter frame,p 00 2 , we need to compute the corresponding goal location in the earth frame, p 2 . Earth frame X Y Easting Northing o' p X' Y' p - p o'-o'' Initial drifter location Initial drifter location o'' X'' Y'' 1 p 2 p'' 2 1 2 (b) Computation of AUV target waypoint for transformed survey with constant AUV speed in the earth frame. Given an initial AUV lo- cation in the earth frame, p 1 , the goal is to compute the waypoint p 2 in the earth frame that corresponds to a desired coordinate in the drifter frame, q 00 . Figure 3.13: Illustration of survey planning with constant AUV speed in the earth frame. AUV speed in the earth frame constrains the maximum speed at which sampling can be done in the drifter frame of reference. Constant AUV speed in the Earth frame In the case of transformed surveys with constant AUV speed in drifter frame, we observe that the optimal AUV speed is not utilized for the duration of the survey. Depending on their power consumption, every AUV has an optimal speed that allows the vehicle to cover a maximum distance on a single survey [34]. In the case of the Dorado AUV used in our experiments, this speed is 1:5 m/s for a total mission duration of 18 hours on a single charge. For this reason we consider the case where we want the AUV to move at a constant speed in the earth frame. Given the initial AUV coordinate, initial drifter coordinate, latest drifter velocity, AUV pitch angle and commanded AUV speed we need to compute the required AUV trajectory in the earth frame. As shown in Figure 3.13b, let o represent origin of the earth frame. Leto 0 ando 00 represent the origins of the initial and nal drifter frames, also representing the coordinates of the drifters. Let the initial location of the AUV be p 1 . Given a goal of p 00 2 in the drifter frame, we want to compute p 2 , i.e. the AUV coordinate in the earth frame. 32 We start with the observation that the time taken by the AUV to travel from p 1 to p 2 in the earth frame is equal to the time taken for the drifter to advect from o 0 to o 00 . Hence, jp 1 p 2 j s a = jo 00 o 0 j s d (3.14) The goal waypoint in the earth frame, p 2 , can be obtained by transforming p 00 2 from the drifter frame to the earth frame. This is given by, p 2 =p 00 2 H o 00 o (3.15) Where, H o 00 o is the homogeneous transform dened by, H o 00 o = cos(=2) sin(=2) o 00 x sin(=2) cos(=2) o 00 y 0 0 1 (3.16) Eqn. 3.14 then becomes: jp 1 p 00 2 H o 00 o j s a = jo 00 o 0 j s d (3.17) On solving Eqn. 3.17, we obtain the nal drifter coordinate o 00 . Using the solution for o 00 in Eqn. 3.15, we compute the nal goal of the AUV in the earth frame for the given target p 00 2 in the drifter frame. Given the current velocity of the drifter s d , the goal is to compute waypoints to implement the survey pattern in the drifter frame, assuming linear motion of the drifter. Figure 3.14 illustrates an iteration of the experiment, where the initial position of the drifter is d 1 at time t 1 . Subsequently a survey plan using the waypoints p 1 :::p 5 are computed in the earth frame with arrival-times of t 1 :::t 5 . 3.3.4 Repeated static-plan surveys vs transformed surveys Having computed the upper bounds on drifter speed for repeated static-plan surveys and having formulated the approach for transformed surveys, we now compare the two approaches in simulation. We will start by dening two metrics that will allow us to compare the performance of each approach: a) survey oset error and b) survey time. We dene the survey oset error as the distance between the drifter and the center of the survey in the drifter frame. This metric will be used as a measure of how well our approach performs for various drifter speeds. As illustrated in Figure 3.15, if o 0 is the drifter frame origin and g 0 is the centroid of the perimeter of the survey in the drifter frame, then the oset error is dened by: e offset =jo 0 g 0 j (3.18) 33 p ,t 1 1 p ,t 2 2 p ,t 3 3 p ,t 4 4 p ,t 5 5 d ,t 1 1 d ,t 5 Direction of drifter advection 5 Figure 3.14: An illustration of an iteration of transformed box survey with constant AUV ground speed in earth frame. Based on previously observed drifter positions, a linear projection of the drifter trajectory is computed for the duration of the iteration. In this gure, we assume the AUV is already at the initial waypoint p 1 at time t 1 which corresponds to the rst corner waypoint of the box pattern in the drifter frame. We know the desired waypoints for the other corners of the box pattern, p 00 2 ::p 00 5 . Using the solution to Eqn. 3.17, we obtain the locations and times of the other four waypoints, giving us the complete plan for the iteration, (p 1 ;t 1 ):::(p 5 ;t 5 ). p' p' p' p' Drifter frame o' p' Y' X' e offset g' 1 2 3 4 5 p' 0 Figure 3.15: Survey oset error,e offset , for repeated static-plan surveys is dened as the distance between the drifter frame origin and the centroid of the perimeter of the survey. Since in repeated static-plan surveys, the survey is distorted when visualized in the drifter frame, we use e offset as a measure of how well the survey tracks the drifter. 34 We compute g 0 by determining the centroid of the closed polygon formed by the perimeter of the survey template, as observed in the drifter frame. In Figure 3.15, this is given by the centroid of the polygon consisting of the vertices p 0 1 :::p 0 5 . We dene the survey time to be the total time taken for each survey to be completed. Each completed survey is an iteration of the Lagrangian observation experiment and denes how often the AUV is able to sample the advecting patch. A shorter survey time is therefore desirable. With AUV surge speeds a and survey speeds s (Section 3.3.3), from Eqn. 3.1, the survey time for the repeated static-plan surveys is given by: T s = u s a + L survey s s (3.19) whereu is the asymptotic trailing distance of the AUV for a drifter speeds d , derived earlier in Eqn. 3.8. Using u from Eqn. 3.8 in Eqn. 3.19, the survey time for repeated static-plan surveys is given by: T s =L survey s d s s (s a s d ) + 1 s s (3.20) Survey time for transformed surveys involves a solution to Eqn. 3.17 for computation of goal waypoints for each iteration. For the following analysis, we computed the time for the transformed surveys empirically in simulation. While an analytical solution can be derived, we do not present that result in this work. We analyzed the survey time and oset error for drifter speeds s d < 1:3 m/s in simulation for both repeated static-plan and transformed surveys. For each run of the simulation, the drifter was advected with a constant speed on a straight line while the AUV performed a box pattern using repeated-static plan and transformed surveys. En- vironmental perturbations and navigational errors were not emulated for this simulation. For each drifter speed, the repeated static-plan survey was run for six iterations so that the trailing distance converged. Results are shown in Figure 3.16 for standard AUV operational parameters, i.e. commanded AUV speeds a of 1:5 m/s, yo-yo pitch angle of 30 o and box width l of 1 km. The survey oset error (Eqn. 3.18) is zero throughout for the transformed surveys since by design it is implemented in the drifter frame. On the other hand, this error increases monotonically with the drifter speed, reaching 4:9 km at a drifter speed of 1 m/s. The survey time is higher for repeated-static plan surveys in comparison with trans- formed survey plans for all drifter speeds above zero. In the case of repeated static-plan surveys, the drifter stays within the perimeter of the survey only for drifter speeds lower than 0.36 m/s. This corresponds to 70% of the observed drifter speeds in historical data and as a consequence, Lagrangian observations are not successful for 30% of the observed drifter speeds. Hence, for the ve-day September 2010 Lagrangian eld experiment, we used the transformed survey approach. Specically, we used constant AUV speed in the earth frame to utilize the optimal operational speed of the AUV at all times. 35 0 2 4 6 8 Survey time (hours) Repeated static−plan surveys Transformed surveys 0 0.2 0.4 0.6 0.8 1 1.2 0 2 4 6 8 10 Survey offset error (Km) Drifter speed (m/s) Figure 3.16: Simulation result for survey oset error and survey time for repeated static-plan and transformed surveys using the box pattern with an edge length of 1 km. AUV surge speed of 1:5 m/s and pitch angle of 30 o were used for this analysis. Drifter speeds between 0 m/s and 1:3 m/s was considered. The dashed vertical line shows the maximum drifter speed for which repeated static-plan surveys satisfy the enclosure criterion. Note that the survey oset error is zero throughout for the transformed survey. For transformed surveys, although the AUV can complete surveys as long as the drifter speed is less than projected AUV speed ( 1:2m=s), the survey time increases with increasing drifter speed, crossing 8 hours for drifter speeds 1:1 m/s. Hence, the upper bound on drifter speed for transformed surveys depends on the operational upper bound on survey time. 36 Figure 3.17: The Dorado AUV being loaded on the R/V Zephyr for the 5 day o-shore drifter tracking experiment in September 2010. 3.4 Field Trials We describe results from two eld trials; a single-day deployment in June 2010 in Monterey Bay and a ve-day o-shore experimentation in September 2010 with two research vessels following a drifter with an attached bio-geochemical sensor. We brie y describe the experimental setup including onboard AUV autonomy followed by the description of the deployments and the results. 3.4.1 Experimental setup Both eld trials in 2010 were carried out using MBARI's Dorado AUV (Fig. 3.17) a 4 m long propelled vehicle with a nominal speed of 1:5 m/s. Onboard autonomy is handled using a hybrid plan-execution controller T-REX which provides a goal-directed interface to the AUV allowing a user to give high-level objectives that are resolved in-situ by the system while allowing adaptation to unexpected situations during plan execution. T-REX is 37 p p p p p p l p' p' p' p' p' p' p' Earth frame Drifter frame 1 2 3 4 5 6 p 7 1 2 3 4 5 6 7 Figure 3.18: Illustration of repeated static-plan lawnmower implemented in the June 2010 eld trial. The survey is described by the waypoints p 1 :::p 7 in the earth frame. The resulting survey in the drifter frame is described by p 0 1 :::p 0 7 . built around the sense-plan-act paradigm and uses at its core a constraint-based temporal planner to synthesize plans in-situ and execute these plans in the context of a dynamic environment. Re-planning occurs onboard when a partial plan has been invalidated by an unexpected situation (e.g. battery depleted faster than expected) or new objectives are injected as goals. These objectives could have been produced in-situ (e.g sensor data collected exhibit opportunistic science) or externally provided to the vehicle via a remote connection. To cope with typical planning complexity, T-REX divides the large planning problem into multiple control loops that resolve and execute their own plans within their specic functional and temporal scope. In the context of Lagrangian studies, such a goal- directed approach along with the ability to send on-the- y new objectives in the form of drifter updates forms the basis for autonomous tracking. While the overall capability of autonomous tracking is the subject of this work, details of T-REX are outside its scope and can be found in [35, 36, 37]. The Dorado is deployed and retrieved using the support vessel R/V Zephyr. A typical mission involves two AUV operations personnel along with the ship's crew. The vessel is equipped to communicate with the AUV when it is on the surface and in near vicinity via a radio link. When underwater the vessel communicates with the AUV using an acoustic link primarily for tracking. The AUV comes with a full suite of sensors including two Seabird Conductivity Temperature Depth (CTD) sensors, a Hobilabs 2 channel backscat- ter, a Teledyne ADCP, a Laser Optical Phytoplankton Counter, an ISUS Nitrate sensor, a Paroscientic pressure sensor, a uorometer for measuring colorded disolved organic matter among other instruments. For this experiment only CTD data was of relevance. 38 Figure 3.19: AUV and drifter trajectories for the June 2010 drifter following experiment with the lawnmower pattern. AUV paths are shown for both the earth frame and the drifter frame. The top plot shows the survey oset error for each iteration. The middle plot shows the drifter frame of reference for each iteration, with the location of the origin being the location of the drifter at the end of every iteration. The drifter frame is oriented in the direction of drifter advection at the end of the iteration. The AUV track is shown relative to the drifter frame through the iteration in each case. The bottom plot shows AUV and drifter tracks for each iteration in the earth frame. For the earth frame, an overlay of the previous iteration is included. 3.4.2 June 2010 experiment: Repeated static-plan surveys This initial experiment lasted 7 hours with repeated static-plan surveys using the lawn- mower pattern carried out in Monterey Bay, California. Fig. 3.18 shows the lawnmower survey pattern used for this trial. The experiment was initiated with a drifter deployed at the patch center and the AUV in near vicinity. Every 10 minutes, the GPS-tracked drifter transmitted its location to the vessel via the Iridium satellite network. At the beginning of a survey iteration, an operator on the vessel transmitted the drifter location, course and speed to the AUV. Although this step could have been automated, it was desired to have a human in the loop for the rst trial for operational safety reasons. T-REX on the vehicle computed the waypoints based on the lawnmower pattern and executed the survey. On completion of the survey, the AUV was commanded again for the next iteration by the operator on the support vessel. The AUV and drifter trajectories are shown in Fig. 3.19. Results The drifter experienced low speeds as shown in the histogram in Fig. 3.20, with a mean of 0:08 m/s, and a maximum of 0:33 m/s. Hence, we were unable to validate the behavior of repeated-static plan surveys under limiting conditions discussed earlier. Additionally, the drifter showed a sudden change in direction, undergoing a 'U-turn' within an hour (iteration 3 in Fig. 3.19) resulting in the AUV having to travel a smaller distance to move 39 0 0.2 0.4 0.6 0.8 1 0 7 14 21 28 35 Drifter speed (m/s) Frequency (%) 0 20 40 60 80 100 Cumulative Frequency (%) Cumulative freq. curve Figure 3.20: Histogram of drifter speeds observed during the June 2010 eld trial. Mean drifter speed of 0:08 m/s and a maximum drifter speed of 0:33 m/s was observed. to the initial waypoint for iteration 4. Overall, this experiment was a proof-of-concept for Lagrangian observation study and allowed us to test the communication channels from drifter and AUV and validate tracking and sampling of a patch for multiple iterations. The groundwork was useful in the longer experiment carried out o-shore in September 2010. 3.4.3 September 2010 CANON Experiment: Transformed surveys Based on the results of the June experiment, a longer ve-day deployment was carried out in September 2010, 160 kms o the California coast (Fig. 3.21a). A specialized drifter was developed with a genomic sensor hanging 20 m below, performing in-situ identication of micro-organisms (Fig. 3.21b). The experiment was supported by crews on two support vessels, the R/V Western Flyer and the R/V Zephyr. The Flyer visited the drifter every four hours to carry out a series of ship-based sampling experiments and lab analysis on water samples to ground-truth the drifter sensor data. The Zephyr was meanwhile focused on Lagrangian observation studies using the AUV. The goal was to monitor the nutrient budget at the perimeter of a 1km X 1km water patch around the advecting drifter while the AUV was to perform a transformed box pattern described in Section 3.3.3 around the drifter. A number of logistical issues were kept in mind while designing and executing the experiment. Each iteration began 40 (a) Location of the September 2010 CANON experiment (b) The drifting genomic sensor in the foreground, being followed by the R/V Western Flyer. The AUV was monitored by a second vessel, the R/V Zephyr. Figure 3.21: The September 2010 CANON experiment occurred 160 kms o California coast for a duration of ve days. In this period, the Dorado AUV performed a Lagrangian-box survey around an GPS-tagged drifter with an attached genomic sensor. with the latest drifter update (position and velocity) received from the drifter through an Iridium satellite link. This was transmitted to the AUV for in-situ adaptation. With this input, T-REX computed the ve waypoints necessary for an iteration of the box pattern using the formulation in Eqn. 3.17, with the AUV traveling at constant velocity in the earth frame. Waypoints were computed once at the beginning of the survey with the AUV surfacing once for every survey, with each survey lasting 1 to 1:5 hours. Results In total 60 iterations were attempted over the course of 5 days, out of which 45 were completed successfully (some iterations had to be canceled midway or restarted due to operational reasons). Fig. 3.22 shows the overall track lines of the drifter and the peram- bulating AUV over the course of the experiment. The gure shows the AUV and drifter trajectory for ve days of the experiment, with gaps in between days when the AUV was being recharged. Each deployment lasted 12 hours. The black dots in the gure show the beginning of each iteration when drifter updates were received by the AUV. During the experiment, a mean survey time of 1:2 hours was observed. The survey time for each iteration depended on two factors: a) projected drifter speed, which could vary across dierent iterations depending on the latest drifter speed observed and b) the distance to the initial waypoint of the survey. This distance is dependent on how well the previous iteration is carried out, which in turn depends on various factors such as AUV localization error, drifter projection error and AUV timing error. These are discussed in Section 3.5. 41 86 km iter 5 iter 7 iter 8 iter 28 iter 36 iter 37 iter 45 iter 47 Figure 3.22: AUV and drifter paths during the September 2010 ve-day eld trial. The black dots show the beginning of every iteration when the latest drifter locations were sent to the AUV. Based on these updates, the AUV computes linear projection of the drifter trajectory at the beginning of every iteration and plans waypoints in the earth frame. 42 (a) Distribution of survey time for the 45 itera- tions of the September eld trial. (b) Distribution of drifter speeds during the 5 days of September 2010 experiment. Figure 3.23: Drifter speed and survey time statistics for the September eld experiment. Mean drifter speed of 0.245 m/s and maximum speed of 0.6 m/s was observed during ve-day experiment. 43 Fig. 3.23a shows the distribution of survey time. For the 45 iterations conducted, the enclosure criterion was satised for the true drifter for 42 iterations and with respect to the projected drifter for 44 iterations. This corresponds to a 93.3% success for tracking the patch over the ve day eld trial spanning. Fig. 3.24 shows the AUV path in the drifter frame for Day 4 of the experiment where 9 iterations of the box pattern were completed. The gure shows the desired AUV path around the drifter in the horizontal plane (1 km x 1 km square). Since each iteration was performed using the projected drifter path we show both the AUV path relative to the projected and true drifter trajectory. The paths are plotted corresponding to the origin of the drifter frame for each iteration either corresponding to the projected or the true drifter. This highlights the error in the path the AUV followed for each case, i.e. with respect to the projected drifter and true drifter path. In Section 3.5, we describe the sources of error with a discussion of the contribution of each to the overall quality of the surveys. 3.5 Analysis In the previous discussion of the September eld trial, we observed the error in the AUV trajectory around the drifters attributable to a number of sources. These can be from errors due to the state-estimation on board the AUV and error due to the projection of the drifter trajectory during an iteration which can vary from the true trajectory of the drifter. In this section, we analyze these errors and their contribution to the quality of the surveys using two metrics: survey oset error and mean surfacing error in the drifter frame. We start by dening the types of errors, followed by the description of the quality metrics. We then show the relationship between these errors and the survey metrics analyzed empirically, followed by a summary of the results. For the Lagrangian surveys we presented in this chapter, we classify the sources of error into two: intrinsic sources that result from errors in AUV state estimation and onboard planning and extrinsic sources due to logistical constraints and human-in-the-loop operation. 3.5.1 Intrinsic sources of error The quality of surveys depends primarily on sources of error inherent in AUV operations and the assumptions made in the design of the survey. The former is due to the state- estimation performed onboard the AUV which provides it with an estimate of its current location and velocity. The latter is the assumption we make about the drifter trajectory during an iteration, namely that the drifter will continue to travel in a straight line with the speed and in the direction computed from the last two position updates. We will now discuss these two error sources. 44 Figure 3.24: Iterations from Day 4 of the September trial illustrating the drifter frame views of the AUV path. In total, 9 iterations were conducted that day. Each of the plots shows the desired AUV trajectory (square with dotted edges with length 1000 m). The star shows the starting location of the AUV for each iteration, and the AUV path relative to the drifter is shown in solid line. 45 1 1 p ,t 21 21 p , t 2 2 p ,t 2 2 p' ,t' Ideal path Actual path e surfacing e = t' - t timing 2 2 completion line Figure 3.25: Illustration of AUV position and timing error. Since the AUV dead-reckons when underwater, with corrections from GPS only when it surfaces (every 30 mins), it can experience substantial localization error. This gure shows a scenario where the AUV surfaces ahead of its goal waypoint and compensates for the error, nally surfacing near the goal waypoint with both positional and timing error. State-estimation error AUVs suer from localization error due to environmental perturbations such as sub- surface currents and constraints on obtaining absolute position measurements. Since GPS location xes are not available underwater, AUVs surface at regular intervals (every 20 to 30 minutes for the Dorado). While frequent GPS-xes are essential to reduce the navigational error, multiple yo-yo's are usually performed before surfacing. This is done to ensure continuous recording of scientic data as well as to minimize surface time especially in high-trac areas. When underwater, the AUV dead-reckons using its depth sensor, onboard compass and inertial navigation system (INS). The accumulated position error between surfacings can be up to 500 m for 30 minutes. During the September eld trial, a median surfacing error of 220 m was observed for the goal waypoints in the earth frame. For our work, AUV state-estimation error aects Lagrangian surveys in two ways: surfacing error in the earth frame and timing errors. Figure 3.25 illustrates how the AUV navigates to a goal waypoint. In this gure, the AUV is at location p 1 at time t 1 and is tasked to navigate to goal location p 2 at time t 2 . Dorado's onboard controller performs straight line navigation between commanded way- points (as projected on the horizontal plane) at constant speed. The controller considers the goal reached when the AUV has crossed a 'completion line' through the goal location, perpendicular to the AUV's direction of travel. Given the goal location and time, the controller computes and executes its parameters of traversal (surge speed, pitch angle, heading) targeting to surface when the goal waypoint is reached. The nature of the AUV controller makes it explicitly target reaching the goal location, with no guarantees on the time of arrival at the location. Based on the state estimator output and the onboard controller, the AUV could surface at timet 21 at locationp 21 , with the belief that the goal p 2 has been reached. However, there could be a large error in the surfacing location and 46 4.85 4.855 4.86 4.865 x 10 5 4.0076 4.0078 4.008 4.0082 4.0084 4.0086 4.0088 4.009 4.0092 4.0094 x 10 6 Easting (m) Northing (m) Iteration 8 : Initial drifter lag: 91m AUV planned path AUV observed path Projected Drifter True Drifter − 1500 − 1000 − 500 0 500 1000 1500 − 1500 − 1000 − 500 0 500 1000 1500 Planned Waypoints w.r.t projected drifter AUV path w.r.t projected drifter AUV path w.r.t true drifter Survey center (w.r.t true drifter trajectory) p'' 0 p'' 1 p'' 2 p'' 3 p'' 4 p'' 5 p 0 p 1 p 2 p 3 p 4 p 5 o'' d 1 d t d 5 g'' Figure 3.26: The earth frame (left plot), showing planned and observed AUV paths and the Drifter frame (right plot) showing the observed AUV path relative to the true drifter and observed AUV path relative to the projected drifter. In the earth frame, p 1 :::p 5 are the locations where the AUV surfaced. p 0 shows the location of the AUV at the beginning of the survey iteration. Thus, the AUV has to initially travel to the rst waypoint p 1 before beginning the survey iteration, resulting in additional error in the survey quality. The drifter was located at d 1 in the beginning of the survey iteration. The projected location of the drifter at the end of the iteration is d 5 , whereas the true location isd t . In the drifter frame, the corresponding surfacings of the AUV are at p 00 1 :::p 00 5 , and the survey center is at g 00 . the goal location. As a result the AUV attempts to correct its course to nally reach the waypoint, accumulating some error in surfacing, but a signicant error in its timing. Consider an iteration from the September experiment shown in Figure 3.26. It shows the AUV path in earth and drifter frames, along with the actual drifter and projected drifter path. The planner onboard the AUV computes its trajectory in the form of ve waypoints corresponding to the corners of the survey, along with the arrival times at those waypoints. This trajectory in the earth frame corresponds to the desired survey template being implemented in the drifter frames. To measure the error due to the two factors discussed above, we use the following error metrics for each iteration of a survey: a) mean surfacing error in the earth frame (MSE-EF), and b) the mean timing error (MTE). The former captures mean error in surfacing for the ve waypoints in the earth frame while the latter captures the mean error in the time of arrival for these ve waypoints. If (p 1 ;t 1 ):::(p 5 ;t 5 ) are the desired waypoints and times of arrival for the ve waypoints 47 in the earth frame for an iteration of the survey and the AUV achieves (p 1 ;t 1 ):::(p 5 ;t 5 ), then the mean surfacing error in earth frame (or MSE-EF) is given by: e MSEEF = 1 5 5 X i=1 jp i p i j (3.21) The mean timing error is similarly given by: e MTE = 1 5 5 X i=1 (t i t i ) (3.22) Drifter trajectory projection error For each iteration of our experiment, we estimate the latest observed drifter velocity and the linearly-projected drifter trajectory assuming constant velocity for the duration. Change in drifter speed and course during an iteration results in the true drifter trajectory being dierent from the AUV's projection. This can be observed in Figure 3.26 where we can notice the dierence between the linear projection of the drifter path and the true drifter path in the earth frame. The path-plan for the AUV is designed for the projected trajectory of the drifter resulting in an error in the drifter-frame survey with respect to the true trajectory of the drifter. We measure this error as the distance between the nal projected drifter location and the true drifter location at the end of every iteration and call it the drifter projection error. 3.5.2 Extrinsic sources of errors Some errors can be attributed to operational choices. During complex eld campaigns, many platforms exist in close proximity for an extended period of time. Experiment design decisions are consequently made to reduce operational hazards and chance of equipment damage (e.g. AUV collisions with vessel hull due to improper surfacings). Although the communication channels were set up to be fully-automated, human-in-the-loop operation was desired to ensure a) situational awareness among operations personnel and b) vali- dation of plans to avoid errors due to environmental perturbations not accounted for in experiment design such as excessive drifter speeds, strong sub-surface currents, and error in drifter position data. The impact of human-decision making was kept to the minimum; an additional check was added before onboard planning was initiated at the beginning of a survey. Also, to ensure the ship's crew were cognizant of where the AUV might surface, waypoints were not recomputed after initial generation. AUV plans therefore were not adaptive during an iteration even if the onboard capability existed. The key extrinsic sources of errors were as follows: Lag in drifter position update During the experiment, there was a lag of 15 mins for drifter location data sent to the AUV. This delay was due both to the update rate 48 via the communication network from the drifter ( 10 mins) as well as operational delays due to human in-the-loop commanding for safety. Wait time at surface while acquiring GPS x Additional delays adding up to imprecise drifter speeds being fed to the AUV occurred because the AUV itself required up to two minutes to obtain a GPS x when on the surface. During this period, the AUV is drifting in the earth frame, resulting in errors in survey plans which were implemented in the drifter frame. Distance to rst waypoint of an iteration In the transformed survey approach, we make the assumption that the last waypoint of one iteration is coincident with the rst waypoint of the next iteration. However, since the waypoints are planned based on the linear projection of latest drifter velocity, there is always a residual distance between where one iteration ends and the next should begin. We do not, however, compensate for this error in our survey plan which results in a timing error in starting the iteration. 3.5.3 Survey quality metric To evaluate the quality of our surveys, we use two metrics: the survey oset error and the mean surfacing error of the AUV in the drifter frame. The survey oset error (dened in Section 3.3.4) is a measure of how close the center of the transformed survey is to the origin of the drifter frame. The smaller the survey oset error the better, zero being the ideal case. Figure 3.27 shows the distribution of survey oset error for the 45 iterations of the September eld trial. The mean error was 282 m and the maximum 1075 m. For 3 of the 45 iterations, the enclosure criterion wasn't satised and these corresponded to the top three survey oset errors of 1075 m, 793 m and 734 m respectively. By denition, iterations with high survey oset error are prone to a non-satisfying enclosure criterion. The mean surfacing error in the drifter frame or MSE-DF is a measure of how close the geometry of the survey is to that of the desired survey pattern. If the implemented survey is highly distorted due to errors in the experiment, for e.g. because of the AUV surfacing far away from intended waypoints, then MSE-DF will be high. If (p 00 1 ;t 00 1 ):::(p 00 5 ;t 00 5 ) are the desired waypoints and times of arrival for the ve waypoints in the earth frame for an iteration of the survey and the AUV achieves (p 00 1 ;t 00 1 ):::(p 00 5 ;t 00 5 ), then the mean surfacing error in drifter frame (or MSE-DF) is given by: e MSEDF = 1 5 5 X i=1 jp 00 i p 00 i j (3.23) Figure 3.28 shows the distributions of the surfacing error in the earth frame, the surfacing error in drifter frame, and the timing error for the iterations of the September eld trial. 49 0 200 400 600 800 1000 1200 0 5 10 15 20 25 30 Survey offset error (m) Frequency (%) Figure 3.27: Distribution of survey oset error for the 45 iterations of the September eld trial. The mean error was 282 m, and maximum error of 1075 m (corresponding to one of the 3 iterations where the enclosure criterion was not satised). Figure 3.28: Descriptive statistics for timing error and surfacing errors in drifter and earth frames. 50 3.5.4 Analysis of September trial results We analyzed which sources of error contributed the most to the quality of surveys during the September eld trial using the quality metrics and the intrinsic errors described earlier. Our goal is to determine the contribution of the various sources of error (mean surfacing error in the earth frame (MSE-EF), mean timing error (MTE) and drifter projection error) to the overall quality of the survey measured using mean surfacing error in drifter frame (MSE-DF), and the survey oset error. MSE-DF captures the eect of distortion of the survey, whereas the survey oset error captures the distance between the implemented patch center, and the desired the patch center (the drifter location). We look at the correlation of various error terms with these two metrics. For the 45 iterations from September, MSE-EF and MTE were computed using Eqn. 3.21 and Eqn. 3.22 respectively. The quality metrics, survey oset error and MSE-DF were computed using Eqn. 3.23 and Eqn. 3.18 respectively. The rst two contributions are measured with the MSE-DF metric. It correlates most with MSE-EF, with a correlation coecient R = 0:62. MSE- DF is correlated with the mean timing error (MTE) with R = 0:56. We also analyzed the correlation between the error terms themselves; MSE-EF being correlated to MTE with R = 0:33. As mentioned earlier, survey oset error is used as a measure of the survey quality with regard to the true drifter trajectory. It is correlated with the drifter projection error with R = 0:60, to mean timing error with R = 0:25 and to MSE-EF with R = 0:15. Hence, the survey oset error is aected the most by our assumption of linear-drifter trajectory projection. Figure 3.29 shows the correlation coecient between MTE and MSE-DF, MSE-EF and MSE-DF, MTE and MSE-EF and drifter projection error and survey oset error. We summarize by drawing two conclusions from the above analysis. First, since the survey oset error is most strongly correlated to the drifter projection error, by improving the projection method, we hope to improve the overall accuracy of our experiments. Second, MSE-DF, which is a measure of the error in survey quality purely due to the eect of AUV localization error x is correlated to both MSE-EF and the timing error as expected. This is the inherent error in tracking the drifter due to the state-estimation error of the AUV. Hence, with better state-estimation and with a reduction of the AUV localization error, we can improve how the AUV implements the desired survey pattern in the drifter frame. 3.6 Conclusions In this chapter, we demonstrated methodologies to observe advecting oceanographic fea- tures with an autonomous underwater vehicle and a GPS-tracked drifter. The drifter was used to tag a feature (or patch) of interest and the AUV was used to survey the patch using various survey patterns. We proposed two approaches: a) repeating static-plan x Note that for this error metric, we perform our computation relative to the projected drifter 51 Figure 3.29: Scatter plots for error-pairs along with the correlation coecient R. 52 surveys, and b) transformed surveys where the planning is done in the drifter (or patch) frame of reference. A series of eld trials were conducted targeting the two approaches. The work provides marine scientists with an approach to observe and understand biological phenomena within an advecting mass of water. We started by extending current static-plan surveys that allow tracking of a drifter by repositioning the AUV to the latest drifter location at the end of every survey. An enclosure-criterion was specied as the constraint necessary for successful tracking of a tagged patch. We derived the upper-limit on the drifter (or patch) speed for which this criterion is satised for repeated static-plan surveys by an autonomous robot. In addition, we dened quality metrics that allow us to evaluate the performance of our approach and simulations were carried out to compare the performance of repeated static- plan and transformed surveys. Through these simulations, we showed that transformed surveys are ideal for Lagrangian observation studies with an AUV. Our method was validated in a 5-day o-shore eld trial where the AUV successfully tracked and sampled a patch of water tagged by a GPS-tracked drifter. During this period, 45 iterations were carried out, each lasting for more than an hour and the enclosure criterion was satised 93:3% of the time (42 iterations). The novelty of our work is four-fold; rst, we show that there are limitations in using extensions of static surveys repeatedly repositioned with the advecting patch. Second, we quantitatively derive an envelope on the speeds of patches that can be tracked au- tonomously. Third, we provide important ways to measure the performance of such surveys analytically. And nally, we demonstrate the concept of autonomous Lagrangian experiments in the eld with an inter-disciplinary team. The key lesson learned from Lagrangian studies presented in this chapter is that by ensuring a desired template is implemented in the drifter frame of reference, one can guarantee that an autonomous platform is able to track an advecting patch continuously. This work therefore, provides the empirical basis for tracking biological activity within an advecting patch of water, where acquiring measurements at sucient spatial and tem- poral resolution is important. To the best of our knowledge, this work presented the rst set of experiments where Lagrangian observation studies were carried out with an autonomous platform successfully tracking a patch of water over multiple days. In the following chapter, we present a data-driven online sampling strategy for AUVs to acquires physical water samples adaptively, while carrying out Lagrangian surveys discussed in this chapter. 53 Chapter 4 Autonomous Sampling \Maybe all one can do is hope to end up with the right regrets." | Arthur Miller 4.1 Introduction Robotic sampling is attractive in many eld robotics applications that require persistent collection of physical samples for ex-situ analysis. Examples abound in the earth sciences in studies involving the collection of rock, soil, and water samples for lab analysis. In marine ecosystem monitoring, accurate measurement of plankton abundance requires lab analysis of water samples, but predictions using physical and chemical properties measured in real-time by sensors aboard an autonomous underwater vehicle (AUV) can guide sample collection decisions. We minimize cumulative regret of plankton samples acquired by an AUV over multiple surveys in batches ofk water samples per survey. Samples are labeled at the end of each survey, and used to update a probabilistic model that guides sampling in subsequent surveys. During a survey, the AUV makes irrevocable sample collection decisions online on a sequential stream of candidates, with no knowledge of the quality of future samples. Our experimental results are based on extensive retrospective studies by mining his- torical eld data to emulate 100 campaigns, each composed of 17 surveys. Beginning with no prior, successive surveys by the AUV result in samples that are progressively higher- abundance in a pre-specied type of plankton. Additionally, from a one-day eld trial beginning with a prior learned from data collected and labeled in an earlier campaign, the AUV eld survey resulted in samples with a high-abundance of a pre-specied type of plankton - a potentially toxinogenic alga of interest to marine ecologists. This is the rst time such a eld experiment has been carried out in its entirety in a data-driven fashion, in eect `closing the loop' on a signicant and relevant ecosystem monitoring problem. 54 4.1.1 Problem Outline Consider an Autonomous Underwater Vehicle (AUV) equipped with k physical samplers (Fig. 4.1), tasked to obtain water samples with high values of a property b2R that can only be measured oine (ex situ). The AUV measures environmental feature vectors fz 1 ;:::; z N g; z 2 R D at corresponding geographic locationsfx 1 ;:::; x N g; x 2 R 3 . The set of locations X =fx 1 ;:::; x N g constitutes a geographic survey. Two practical considerations constrain the problem. First, since labeling requires lab analysis to measure the value ofb in each of thek water samples, it can only be performed oine when the AUV is brought onshore at survey termination. Second, N >>k. We present an approach to Figure 4.1: AUV with onboard water sample collection system (ten `gulpers') that can be trig- gered by the onboard computer. minimize cumulative regret associated with the samples collected over multiple surveys (a campaign), using a predictive model g :R D 7!R;b =g(z) that maps the environmental feature vector z to the hidden property b. Regret for a single sample b i , is dened as b + b i , where b + is the value for the best sample (in hindsight). Samples are acquired online in response to the measurement z, with no knowledge of the future. 4.1.2 Contributions of this Work The contributions of this work are as follows. We formulate and solve the autonomous physical sample collection problem over multiple environmental surveys in a principled manner. In this setting, any samples collected can only be labeled in batches ex situ. We frame sample collection as a cumulative regret minimization problem using theoretically sound techniques from probabilistic modeling, Bayesian sequential optimization, and op- timal stopping theory. Samples are labeled at the end of each survey, and used to update a probabilistic model that guides sampling in subsequent surveys. During a survey, the AUV makes irrevocable sample collection decisions online on a sequential stream of can- didates, with no knowledge of the quality of future samples. We present a framework to mine previously collected data to emulate campaigns allowing comparative evaluation 55 of multiple sampling strategies. The results show that using a regret minimization over multiple surveys performs better than other strategies consistently, both for oine sce- nario where we have full knowledge of a survey in advance, and online, where sampling decisions are made sequentially. Finally, we demonstrate results from a one-day eld trial, that resulted in water samples with a high-abundance of a pre-specied type of plankton - a potentially toxinogenic alga of interest to marine ecologists. This is the rst time such a system has been demonstrated in its entirety in a data-driven fashion, in eect `closing the loop' on a signicant and relevant ecosystem monitoring problem. While the experimental context for our work is marine ecosystem monitoring, it is well-suited for autonomous and persistent robotic observation of any property that cannot be measured in-situ, but possesses observable covariates, thus opening up the potential for advanced autonomous robotic exploration of unstructured environments that are inaccessible to humans. Additionally, an important contribution of this work is the learning of organism abundance models that don't require geographical parameters (i.e. latitude, longitude, and depth) as inputs. In dynamic environments such as the coastal ocean, the online geography-agnostic approach addresses the rapid change in the geographic distribution of the property of interest b due to environmental factors such as water currents. This is especially important when considering the age of the training dataset, which can be many weeks old. By using a model with environment specic parameters, we focus on the \en- vironmental niche" of the organism, allowing population prediction using environmental covariates only. Our results demonstrate how organism rich samples can be successfully acquired by ignoring spatial parameters, with the environmental covariates capturing the environmental conditions under which the organism has been observed to thrive. 4.1.3 Related Work Autonomous robotic sampling has been explored for monitoring terrestrial and marine environments for a variety of applications [38, 39, 40, 41, 42, 4, 43, 44, 45, 46]. A large body of work exists for active learning on directly observable elds, i.e. in situ sampling to improve model accuracy. For example, near-optimal maps of in-situ measurable elds such as temperature and pH have been computed by maximizing information-gain from sensors placed in sequential and batch settings [47, 48]. Extended to mobile sensors, informative-paths have been computed for robots to maximize information from additional measurements [49, 50, 51, 52]. In the ecological modeling literature, hidden phenomena such as algal blooms have been predicted from environmental parameters such as temperature, salinity, upwelling index, rainfall index, etc. [53]. Most recently, ecosystem modeling has been addressed using the maximum entropy method (MAXENT) to model geographic distribution of terrestrial species from environmental covariates of presence-only samples. [54]. Related to adaptive sampling for in situ elds, various approaches have been explored for ex situ sampling in marine ecological applications. Thresholds on measurable elds dened by scientists along with novel use of vertical structure of chlorophyll uorescence, 56 an in-situ measurable proxy for algal biomass, has allowed AUVs to precisely acquire samples from chlorophyll peaks [4] for ex-situ analysis of plankton community structure. Samples have been acquired at thermal fronts characterized by a sudden change in prop- erties such as temperature in the horizontal scale [55]. However, these approaches are not data-driven, and require specication of parameters that can vary over time for each survey, inhibiting scaling to persistent monitoring applications. Model driven approaches to acquire ex situ samples have been explored on scientist labeled datasets identifying an oceanographic phenomena called intermediate nepheloid layer (INL), allowing in situ pre- diction of INL probability using directly measurable inputs. Rules for spacing the samples geographically, and appropriate thresholds have allowed targeting of high probability INL samples for analysis in the lab [42, 56]. 4.2 Technical Approach The autonomous ex-situ sampling problem for a campaign of T surveys (or trials) is as follows. Given an initial set of random samples from p pilot surveys, B pilot =fB 1 ;B p g, nd a policy that adaptively acquiresB campaign =fB p+1 ;:::;B S g from subsequent surveys, where B i =fb 1 ;:::;b k g is the ex-situ sample set from the i th survey, labeled after the survey. Decision needs to be made online, in response to environmental feature vector z measured in-situ at geographic location x, and current set of samples fori th survey, while jB i j<k. The goal is to minimize cumulative regret of the samplesfB pilot ;B campaign g. We use Gaussian process regression [57], a Bayesian function approximation technique to learn a probabilistic model g :R D 7!R;b =g(z) + where is a Gaussian noise term, to predict the hidden property of interest b from the in-situ measured environmental feature vector z. The probabilistic predictions of the GP model is used in a Bayesian sequential optimization setting to a maximize long term reward, i.e. minimize cumulative regret over multiple surveys. Finally, since sample collection is performed online, we use optimal stopping theory to choose sample batches ofk candidates sequentially. We discuss the three subproblems in this section. 4.2.1 Probabilistic model We rst learn the mapping from z = [temperature, salinity,...] 2R D , measured at geo- graphic locations x = [latitude, longitude, depth]2R 3 , to a desired property of interest, in our application plankton abundance b2R. GP regression assumes that the samples from the function to be estimated are nor- mally distributed with the covariance between samples given by a `kernel' or covari- ance function. Unbiased GP regression (demeaned input) is dened completely by the kernel function, which controls how quickly the input space gets decorrelated. This enforces smoothness constraints in the trained function, where the observed values for closer input samples are more correlated than the ones farther apart. The training data T = < z 1 ;b 1 >;< z 2 ;b 2 >;:::;< z N ;b N >, is drawn from a Gaussian process, 57 b i =g(z i ) + (4.1) where is the Gaussian noise term. With this prior, we can compute the posterior mean and covariance for the test data points with the following equations, (z ) = k(K + 2 n I) 1 b (4.2) 2 (z ) =k(z ; z ) + k(K + 2 n I) 1 k (4.3) where K is the covariance or Gram matrix, generated using with a kernel function k chosen to be a squared-exponential function dened as, k(z p ; z q ) =e 1 2 2 jzpzqj 2 (4.4) where is the decorrelation length scale. We used the GPML toolbox [58] for MATLAB to learn the dominant input variables and hyperparameters from training data. For a measured environmental feature vector z, the model predicts the abundance through the posterior distribution p(b jT; z ) = N b j(z ); 2 (z ) , where (z ) and 2 (z ) are the mean function and variance function, representing the learned GP model. We train the GP regression model on shore, and use it on board the AUV for realtime predictions of the mean plankton abundance, and the associated prediction variance. 4.2.2 Bayesian sequential optimization The GP model provides probabilistic prediction of plankton abundance for observed part of the input space. Bayesian sequential optimization concerns the computation of the utility of candidate samples to minimize cumulative regret of the acquired samples over multiple surveys. The balance between improving the model accuracy globally by ex- ploring points with high variance, and exploiting the known model to maximize reward (high-abundant samples) is discussed in the machine learning literature as the multi-armed bandit problem [59]. The goal is a to develop a sampling policy that chooses the next best sample, taking into account the balance between exploration and exploitation, i.e. using the mean and the variance of the abundance predictions. Given a prediction of mean and variance for a candidate input data point, the sampling policy concerns maximization of a utility function h( t1 (z); 2 t1 (z)) over the input space. z t = arg max z2Z h( t1 (z); 2 t1 (z)) (4.5) where h is a utility function we need to determine. We use Gaussian Process Upper Condence Bound (GP-UCB), a sequential stochastic optimization strategy that uses a GP regression model to minimize cumulative regret over T trials, with regret bounds [60, 61]. Using the learned GP regression model, instead of seeking the maximum of the mean or the variance independently, the GP-UCB algorithm prescribes the following utility function. z t = arg max z2D t1 (z) + 1=2 t t1 (z) (4.6) 58 where z t is the sampling candidate for the t t h trial, and t is a constant that grows logarithmically with each trial, given by t = 2 log( jDjt 2 2 6 ) (4.7) where D is the number of input dimensions, t is the time-step (or iteration), and is a parameter that denes the probability of the regret bound being satised. By targeting points that maximize a combined function of mean and variance, the GP-UCB algorithm strikes a balance between exploration and exploitation, with the goal of keeping the av- erage regret within bounds after T trials. The GP-UCB algorithm expects update of the model, i.e. functions t1 (z) and 2 t1 (z) after each trial. In our problem however, the model can only be updated once a batch of k samples have been retrieved and labeled after a survey. Hence, we consider each survey to be a single trial with the k ex situ samples used for the model update at theend of each survey. The modied batch-update GP-UCB algorithm is as follows. Algorithm 4: Batch-update GP-UCB algorithm 1 SetAlgoLined Data: Input dimension D, GP Prior =0, 0 , k 2 for t 1 to T do 3 Choose top k arguments Z t =z 1 :::z k corresponding to top k peaks of t1 (z) + 1=2 t t1 (z); 4 Sample set B t =g(Z t ) + t ; 5 Perform Bayesian update to obtain t and t ; 6 end We dene the average regret R t of a sample set from a trial B t as the average dif- ference between the sum of abundance of acquired samples, and the best sum possible (in hindsight). For a trial t, R t = ( k i=1 b i k i=1 b i )=k, where b i is the i th top ranked sample in hindsight, and b i is the i th acquired sample. To evaluate the performance of a sampling algorithm, we use cumulative regret over T surveys, dened as R = T t=1 R t . A lower cumulative regret shows better long term reward collection by the algorithm. 4.2.3 Optimal stopping theory The goal is to choose the global maximum of the utility function h, s t = t1 (z ) + 1=2 t t1 (z ), where z denotes a candidate from all possible candidates available during a survey. Additionally, we want to choose the top k samples. However, since the AUV does not have access to information on candidates a priori, we need an algorithm to pick the k top candidates online. Three factors are considered for this task. First, the AUV should not be too greedy, missing future hotspots. Conversely, the AUV should not be too conservative returning with fewer than k samples, resulting in an opportunity cost. Finally, we don't want to manually set thresholds since that would inhibit scaling. We propose the use of optimal stopping theory that deals with the question of when to take a particular action. The hiring (or secretary) problem have been studied in the context of 59 image collection and online auctions [62, 63, 64]. For the classic secretary problem, there are n applicants who have signed up for an interview. After interviewing each candidate one can rank them relative to all other candidates seen so far. One must either hire or reject the candidate immediately after the interview. One is not allowed to go back and hire a a previously rejected candidate. The optimal solution in this setting is to observe rst n/e candidates without hiring. Select the next best. Single best candidate selected 1/e, or 37% of the time. Algorithm 5: Submodular secretary algorithm to maximize utility ofk online water samples Data: Gulp set B =; , number of gulpers k, Total survey samples expected N, stopping parameter r, current trial = t Result: Gulp set B 1 Segment duration N w = N k ; 2 Observation duration N o = Nw r ; 3 Start Survey: n=0; 4 Set segment= 1; 5 while survey time n less than N do 6 while not at end of segment do 7 read current env param vector z n ; 8 use GP model to compute utility of sample u n = t1 (z n ) + 1=2 t t1 (z n ); 9 if within observation window then 10 check and update best candidate to u n if utility better than previous candidate; 11 else 12 add candidate at n to B if better than observation window best candidate; 13 end 14 end 15 if no better candidate found within sampling window, add current candidate to B; 16 Increment segment; 17 end For the scenario where we want the topk best choices (or candidates), an extension of the secretary problem, the Submodular secretary problem allows selection ofk secretaries, represented by the set B so as to maximize the expectation of a submodular function which denes eciency of the selected secretarial group based on their overlapping skills. The candidates are rated in this case, as opposed to ranked. With the goal of maximiz- ing the sum of all elements of the set, a constant factor approximation exists under i.i.d 60 assumptions [65]. The solution with a constant factor guarantee of 1 1 e 11 (under i.i.d as- sumptions) is to split all candidates intok equal sections, and use the secretary algorithm described above on each section. For our application, we split the prespecied survey duration into k equal segments, and apply the secretary algorithm in each segment. The pseudocode for this algorithm is presented below. 4.3 Simulation Studies We evaluate our autonomous ex-situ sampling approach by mining previously collected AUV data during an eight day campaign from 2005 consisting of atleast two surveys per day (Figure 4.2), and 17 surveys in total. We simulate ex-situ sample collection on in-situ measured parameter, chlorophyll uorescence, a proxy for algal biomass that are hidden from the AUV by the simulaiton framework during surveys. The goal is to acquire k simulated `gulps' per survey to maximize the sum of chlorophyll uorescence, revealed at the end of each survey. For the whole campaign, this corresponds to minimizing cumula- tive regret of the ex-situ samples over multiple trials. To compute a predictive model for Figure 4.2: A campaign of 17 AUV surveys was carried out over 8 days in August 2005. We use chlorophyll uorescence, one of the in-situ measurements as the property of interest and emulate collection of samples with high uorescence. pk samples are randomly sampled from the rst p surveys (p = 2 for day 1), followed by training and update of a GP model to guide sampl collection in subsequent surveys. The inlay at bottom right shows the true chlorophyll uorescence for one of the surveys. The same pattern was repeated 17 times over 8 days. chlorophyll uorescence, we use p pilot surveys to collect pk random samples. The value oracle reveals the true chlorophyll uorescence of the acquired samples (equivalent to a lab analysis of the batch of samples) at the end of each survey. Using the pk records, 61 we use the GPML toolbox [58] for MATLAB [66] to learn a GP regression model. In subsequent surveys this model is used to guide sampling with the goal of minimizing cumulative regret of the whole campaign. Thek samples acquired during each subsequent survey forms the setB =fb 1 ;b 2 ;:::;b k g. An optimal set B + is computed oine on the whole survey resulting in k samples with maximum abundance (global chlorophyll uorescence peaks) . We also compute a set B r that consists of k random samples without replacement from the whole survey. To determine how well the sampling policy performs in an exploitation-exploration setting over multiple surveys, we use average regret of acquiring the set B or B r , instead of the optimal set B. To observe the accuracy of the learned predictive model with the envi- ronmental parameters as inputs, we compute the correlation coecient for predicted and observed values of chlorophyll uorescence for the whole survey. Figure 4.3: True (top) and predicted (bottom) chlorophyll uorescence from one of the simulated AUV surveys. It shows the AUV carrying out vertical proles between the surface and a depth of 40m. The submodular secretary algorithm is used on utility from probabilistic abundance predictions, and black circles with white '+' show gulps taken within a segment. The black circles with black '+' show two gulps taken at a segment end due to lack of better candidates within the sampling window. 62 Based on the nature of labeling and the model update, we identify three cases. First, we stop labeling after the pilot surveys, and use the resulting model for all subsequent sampling decisions. In our results, this is indexed as INI. Next, if we continue labeling after each survey, we can update the model using a data only from the previous p surveys (with p=2, we call this WIN). Finally, if we use all data from previous surveys to keep the GP model updated, we have the case ALL. For each of the three update methods, we use three utility functions { i.e. mean, variance, and GP-UCB. Random sampling, is also carried out for a baseline, resulting in ten methods in total. We emulate 100 campaigns for each method, by starting with a new set of k samples drawn randomly from the rst p pilot surveys. Figure 4.4 shows the regret and cumulative regret of each survey, averaged over hun- dred campaigns. We observe that the lowest cumulative regret is obtained when the GPUCB algorithm is used with a model updated with all data up to previous survey (ALL-GPUCB). The worst performance is when random sampling is used during each survey. When using all data, the GPUCB approach outperforms the other model update methods. Survey 12 has high regret with random sampling, suggesting a stronger hotspot than other surveys. ALL-GPUCB shows a trend of lower regret with each survey. An interesting observation is that when only the pilot survey model is used for all future surveys, a variance driven policy outperforms all methods but ALL-GPUCB. We hypothesize that due to the chlorophyll uorescence being a low probability event, the initial sample distribution represents the region unlikely to contain chlorophyll. Targeting regions with high variance (sparser training data) explores regions more likely to contain a chlorophyll hotspots. Figure 4.5 shows the summary of campaign results for the then methods. An additional insight from our results is that the GP-UCB algorithm captures a known characteristic of the backscatter-temperature space in a data-driven manner, while demonstrating the lowest cumulative regret. Backscatter is a measure of particle size, and hence shows strong correlation with algal biomass. However, due to presence of suspended particles of comparable size as of algae at greater depths, backscatter can result in over estimation of chlorophyll uorescence value, especially in deeper waters. The GPUCB algorithm results in a model with the peak at high temperature, high backscatter region of the temperature-backscatter input space (Figure 4.6). This results in precise acquisition of chlorophyll uorescence samples by targeting high backscatter samples that are also near the surface, hence warmer. 4.4 Field Experiment We describe a eld experiment carried out in October 2013, targeting Pseudo-nitzschia (PN), a genus of phytoplankton known to cause potentially toxic blooms. The goal was to acquire 9 water samples rich in PN, during 1 km x 1 km Lagrangian surveys (described in Chapter 3) with the AUV in north Monterey bay. We discuss the experiment design 63 (a) Oine sampling with full knowledge of survey. The GP-UCB algorithm has the lowest cumulative regret (left plot) at the end of the campaign, and also has progressively lower regret as the campaign proceeds (right plot). An insightful observation was that on using a variance-driven sampling policy (INI- VAR) trained from data from pilot surveys results in superior performance than other sampling strategies. Additionally, we note that at survey 12, a strong phytoplankton hotspot results in high cumulative regret for the random sampling strategy. The GP-UCB policy however demonstrates reduction in regret for this survey. (b) Online sampling using submodular secretary algorithm. The cumulative regret of the GP-UCB algo- rithm is lowest at the end of the campaign, although in the online case, the performance is poorer than in the case with full knowledge. Figure 4.4: Cumulative regret and regret of over the course of the 17-survey campaign, averaged over 100 simulated campaigns. 64 (a) Oine sampling with full knowledge of survey. (b) Online sampling using submodular secretary algorithm. Figure 4.5: Summary statistics of regret and correlation coecient for 100 simulated campaigns. 65 Figure 4.6: Survey 1/17 and survey 17/17 during one of the emulated campaigns. Top plots and bottom plots show prediction means and variances respectively for the input space. Circles on the top plots, and dots on the bottom plots show ex-situ sample locations. Circle sizes are proportional to the true value of chlorophyll uorescence, after ex-situ labeling. 66 (a) PN model mean. (b) PN model variance. Figure 4.7: Trained PN model used for the October 17 trial. The size of the circles is proportional to the measured PN abundance through lab analysis. and summarize the preliminary lab analysis of the water samples collected that showed high abundance of PN. A training dataset was composed from molecular analysis results of 87 water sam- ples collected by the AUV during a eld campaign in October 2010 (same season) using the chlorophyll peak-capture algorithm [4]. Along with measured PN abundance, the in situ measurements of temperature, salinity, chlorophyll uorescence, dissolved oxygen, backscatter, and nitrate conc. from AUV's onboard sensor suite was recorded in the train- ing dataset. The hyperparameters for the kernel function, and the input variables were chosen using 4-fold cross validation, resulting in chlorophyll uorescence and temperature as the dominant input parameters for prediction of PN. Figure 4.7 shows the predicted mean and variance of PN over the range of chlorophyll uorescence and temperature captured in the training dataset. With the prior training model, the goal was to acquire samples with high abundance of PN. Since we had a single survey to to do so, we use an exploitation only sampling policy ( = 0). The trial is to demonstrate the utility of data-driven ex-situ sampling to a relevant science problem. A deployment lasting six hours was carried out in north Monterey bay, during which we ran the GP model for PN on board the AUV, so that for every measured environmental feature vector z , the AUV computed a real valued prediction for PN abundance b . The variance for the samples were not used since we used a mean-driven sampling strategy. 67 Figure 4.8: Transect plot of the sampling survey with depth on x-axis and time on y-axis. Color shows predicted PN abundance, and the crosses show where gulps ere taken. Based on the expected amount of time to be spent at the surface (for communicating with other platforms, which was one of the experiment goals unrelated to this work), we subtracted time out of the total estimated duration to consider the eective survey duration. Since the AUV spent a longer than expected on the surface due to variability in surface data transmission time, our algorithm collected 8 gulps out of the tasked 9. The ninth gulp was not triggered since the last segment was not completed within the preset duration based on which the segment lengths were computed. The total duration of the survey was set to be 2:18hrs, with total expected in situ data points N = 15725. The submodular secretary algorithm splits this window into 9 segments, resulting in the segment size N w = 1747, 14min. We used stopping parameter r = 3, resulting in the observation window length for each segment to be 5min. A moving-average lter is used by the submodular secretary algorithm to lter out spikes in the sensor data while carrying out threshold updates, with a tolerance of 0.2 O.D. This tolerance is also used when making ring decisions to avoid erroneous gulps resulting from data spikes. Figure 4.8 shows the AUV transect and the predicted PN mean. Black crosses show the locations where gulps were taken. We observe that 5 out of 8 gulps were taken in the PN hotspots (the region in red showing high predicted abundance). Out of the remaining three, sample 5 appears to be at the boundary of the PN hotspot, at a depth of 14m, and the remaining two, samples 6 and 8, in deeper waters with low predicted abundance. The corresponding distributions of the gulp locations in the environmental parameter space (temperature, uorescence) are shown in Figure 4.9. This gure re ects the distribution of gulps with respect to the PN prediction model used. Gulp numbers 1,2,3,4, and 7 were taken close to the PN prediction peak, demonstrating the performance of the submodular secretary algorithm in targeting prediction peaks. 68 Figure 4.9: Data points corresponding to in-situ measurements of temperature (x-axis) and uorescence (y-axis) taken by the AUV during the survey, along with the predicted PN abundance (color), and the ulp locations in the temperature- uorescence space (numbered dots). The submodular secretary algorithm's sample collection decisions are shown in Fig- ure 4.10 that shows the gulp locations with respect to the predicted PN signal and the adaptive threshold updates. The periodic variations in the predicted PN abundance cor- responds to the movement of the AUV through the predicted PN layer (abundant between depths of 4m to 10m). The solid line shows how the threshold are picked, with updates happening in the rst 6min (observation window) of each segment of total duration 18min, and the sampling happening in the remaining 12min (sampling window). When a better candidate is not found in the sampling window, samples are taken at the end of the window. Spikes in data are ltered during threshold update, hence the chosen thresholds ignore extreme values. Samples acquired at the end of segments have a benet demonstrated in Figure 4.11, showing the distribution of gulps in the histogram of uorescence and temperature mea- sured by the AUV (input variables to the model), and the predicted PN abundance (output variable). Out of the three samples taken at segment ends, two were at the mode of the predicted PN. Since the PN hotspot only occupies a small portion of the water col- umn (the tail of the distribution with high predicted abundance), the mode corresponds to predictions of negligible abundance. Statistically, samples at window ends are likely to be at the mode. Also, in the histogram of uorescence and temperature, we see that the distribution of samples that were acquired within the sampling window is close to the peaks of the PN prediction model showed in Figure 4.7. This can also be observed 69 Figure 4.10: The time series of predicted PN abundance from the deployment, with the threshold choices for each segment as determined by the submodular secretary. (a) Chlorophyll uorescence. (b) Temperature. (c) Pseudo-nitzschia predic- tions. Figure 4.11: Histogram of various signals from the October 17 trial. Vertical lines show where gulps were taken. 70 (a) Predicted PN abundance, measured in Optical Density, a unit corresponding to molecular meth- ods. (b) Measured PN abundance, estimated as cell count through microscopy (morphological method). Figure 4.12: Comparison of PN abundance predictions for the collected gulps, and the corre- sponding PN abundance measurements through lab analysis after the mission. in Figure 4.9 that shows the location of AUV measurements and gulp locations in the environmental parameter space. 4.4.1 Ex-situ sample analysis Following the experiment, the eight samples were analyzed in a marine microbiology lab for PN cell count. The comparative results of predicted PN abundance and the measured PN cell count are shown in Figure. 4.12. The results are promising. We see strong similarity in the trends of the predicted and the measured PN abundances for the acquired samples. Note that the methods used for determining PN abundance in the training dataset (molecular), and in the estimation of the true abundance in the acquired dataset (morphological) are dierent. Nevertheless, the sample analysis results show that using the approach proposed in this work, we were able to train a model, run it onboard the AUV to predict organism abundnace in real time, and acquire samples that were not only rich in the organism of interest, but the predictions matched the measurements through lab analysis. We believe this is an important contribution for the following reasons. First, we were able to design and carry out an experiment entirely in a data-driven fashion. Predictive models were trained from lab analyzed water sample data from a previous season (experiment carried out in October 2013, but data from experiments in October 2010). Second, the methods used are theoretically sound, from the machine learning literature, providing guarantees on the performance of the algorithms. Third, scientists can observe the nature of the predictive models, and the behavior of the sampling algorithms through rich visuals, facilitating retrospection, especially if a large number of platforms are used for such experiments. 71 Finally, by assimilating the observed organism abundance from the data acquired during the experiment back into the training dataset, we can `close the loop' on the methodology. We want to point out that the methodology for sample analysis after the experiment was dierent from the one used for to generate the training dataset. Nevertheless, samples have been stored to carry out further analysis using molecular methods, which will provide us data in the same units as in the training dataset. 4.5 Conclusions In this chapter, we addressed the problem of acquiring ex-situ samples adaptively for ex- situ analysis, where labels can only be obtained oine, in batches of k samples per trial. Using marine ecosystem monitoring as a test domain, we presented a principled approach to minimize cumulative regret of acquired samples during the course of a eld campaign consisting of multiple surveys. By training a probabilistic model to predict the hidden property of interest of ex-situ samples (plankton abundance in our test application), we use Bayesian sequential optimization to maximize the utility of batches of k samples labeled after each survey. Optimal stopping theory considerations were used to maximize the utility of the batch of samples online. We presented a framework for emulating sampling campaigns by mining previously collected AUV data. The results for 100 campaigns with dierent initial conditions demonstrate the lowest cumulative regret for surveys carried out adaptively using the GP-UCB sampling policy, with model updated on all available data. Performance online, using the submodular secretary algorithm, shows the same trends. A one-day eld trial carried out with a previously trained model resulted in high-abundance samples of a potentially toxinogenic algae of interest to marine scientists for lab cultures and other studies. This is the rst time such a eld experiment has been carried out in its entirety in a data-driven fashion, in eect `closing the loop' on a signicant and relevant ecosystem monitoring problem. In the concluding chapter, we brie y discuss our vision of extending the ex-situ sampling problem beyond the marine domain to other extreme environments inaccessible to humans. 72 Chapter 5 Oceanographic Decision Support System \In preparing for battle I have always found that plans are useless, but planning is indispensable." | Dwight D. Eisenhower 5.1 Introduction and Motivation With the advent of sophisticated onboard sensors and marine robotic platforms, scien- tic eld experiments have become increasingly reliant on autonomous systems. An early multi-robot deployment, the Autonomous Ocean Sampling Network (AOSN)[67], demon- strated the utility of ensembles of robots in the coastal ocean targeting a specic set of questions in physical oceanography. The goals included resolving various phenomena such as ocean circulation, frontal dynamics, ocean heat ux, and subduction. Networked buoys, propelled AUVs, and gliders were utilized in conjunction with predictions from ocean cir- culation models. Future capabilities in intelligent control, docking, power management, advanced materials, and data management were clearly articulated. Initial deployments starting in the Arctic with a single platform were followed by subsequent deployments with multiple AUVs and gliders in the Monterey Bay. Mixed-initiative deployments Recent developments in robotic control, data systems, and sensor hardware have led to greater emphasis on software, both on-board and on- shore. Adaptive control techniques [30, 35] have allowed AUVs and surface craft to sample precisely in the coastal ocean. Yet, human-in-the-loop operations are necessitated given the tremendous cognitive and experiential skills of a trained scientist, the need to substantially augment ocean model skill, and limits to machine intelligence. Further, the need to understand dynamic coastal ocean biogeochemical processes which have poor computational analogs has highlighted the need for mixed-initiative robotic control in this domain. 73 Figure 5.1: Spatiotemporal extent of a red-tide in the Monterey Bay, CA in 2007 shown in false color remote sensing data. 74 Multiple-robots for synopticity Often, these coastal processes have large variations in spatial and temporal scales (from millimeters to kilometers in extent, in the order of hours to weeks and potentially months). A prominent example of such a process is coastal algal bloom ecology. As shown in Fig. 5.1, such blooms are dynamic, patchy, and could cover large coastal zones (> 50 Sq Km.). Persistent observation of such dynamic events dictates the use of multiple long-duration mobile robotic platforms [68] that can be retar- geted based on evolving observational needs, or simply used for tracking an advecting feature such as an algal hotspot. Smart robots are not enough Using robotic assets for adaptive environmental sam- pling has been the focus of a large body of work in computer science including [69, 51, 70]. Often, observation of dynamic and patchy environmental phenomena calls for the multi- week collaboration of multiple institutions with a wide range of assets resulting in in- creased observation scales and spatio-temporal resolution. For such experiments, besides onboard autonomy and adaptive sampling strategies, it is necessary to develop tools to engender planning and collaboration techniques that allow seamless knowledge transfer between participants, whether on ship or shore. Our work is situated in the context of a multi-year inter-disciplinary program called Controlled, Agile and Novel Observing Network (CANON) [19]. The program focuses on understanding rapidly changing ocean processes that have signicant impact on marine ecosystems. The initial emphasis is on phytoplankton blooms that have a wide impact on marine ecology e.g., via generation of conditions harmful to other organisms in the case of Harmful Algal Blooms (HABs). One of the goals of CANON is to develop and demonstrate technologies that allow the quantitative characterization of dynamic biological processes, in situ. This will enable a new mode of ocean observation, specically by focusing on spatial and temporal scales typical of microbial processes. By using a multi-vehicle robotic system that is capable of executing a sampling strategy over an extended period, we can observe the episodic nature of biological processes at sea in ways that have hitherto not been possible. In con- trast to previous multi-platform eld programs that have focused on the physical ocean, employing models with resolutions of kilometers, our system will allow exploration of ocean ecosystems with sub-kilometer and hourly resolution. By concentrating on the episodic, out-of-equilibrium events, where local perturbations produce detectable biolog- ical responses, we expect to capture both the causality and the dynamics of biological processes. This information is crucial to understanding how the coastal ocean works and projecting how they will adapt in the face of climate change. Using lessons learned from prior work including previous eld deployments, we have designed, developed, and deployed a shore-side Oceanographic Decision Support System (ODSS). The ODSS is a web-based portal used to assimilate information from a collection of sources at sea such as AUVs, moorings, radar stations, and remote-sensing satellites Horizontal transport of a patch of water due to currents. 75 (a) Screenshot of ODSS taken during the CANON 2010 eld experiment. Multiple assets are shown in the interactive asset map in the center, with the dash- board panel to the right showing asset statistics, and the panel on the left allowing visualization of data products, mission plans, and past deployments (b) The ODSS (on screen) being used at a daily planning-meeting during the October 2010 CANON eld experiment Figure 5.2: The Oceanographic Decision Support System (ODSS) in use during the CANON 2010 eld experiment. to provide a synthesis of views useful for predicting the movement of bloom patches in the connes of northern Monterey Bay. The system-of-systems provided situational awareness, data visualization, collaborative information sharing and planning capabilities for the rst of CANON eld programs in Monterey Bay in October 2010. Our work on ODSS is driven by a vision of how marine eld robotics will likely be conducted in the future and the necessary computational infrastructure that will augment decision making, onshore as well as on-board. This view was inspired by past eorts in mixed initiative planning and control for NASA's Mars Exploration Rovers program [71, 72], a data portal for AOSN [73], and JPL's Ocean Portal for Southern California Bight [74]. While the latter two provide data driven visualization and collaboration capabilities, the former provided inferential capabilities without an incoming data stream. Ultimately ODSS will combine these capabilities and more uniquely, provide an event response capability that could trigger the deployment of a robot and/or adapt its sampling strategy, all from a scientist's desktop on shore. Data returned from robotic assets at sea will be ltered for signals associated with a feature of interest along with information on its contextual environment. The association between the signal and a prospective event will be undertaken through tagging by experts, and machine learning techniques used in recommender systems[75]. Adaptive sampling strategies using an onboard autonomous system T-REX [35, 37, 76], and working with shore-side human and automated capability can then become an extension of the human senses. 76 This chapter describes the use of ODSS within the context of the CANON 2010 eld experiment. We discuss the challenges faced, lessons learned and present examples of how marine robotics will be served by such mixed-initiative decision support systems in the future. Section 5.2 describes the rationale behind ODSS and a description of its architecture. Section 5.3 discusses a few case studies highlighting the evolution of ODSS during CANON 2010, followed by asset deployment and usage statistics. Finally, we summarize the lessons learned in Section 5.4 and wrap up our work with our vision for marine experiments in the future. 5.2 Experiment Design and Implementation In this section, we will start by describing CANON and its goals, followed by a discussion on the need for ODSS and a description of its architecture and evolution. 5.2.1 CANON The month-long CANON eld experiment in October 2010 involved multiple platforms with diverse capabilities and payloads, multiple science goals and multiple principle in- vestigators (PIs). Platforms included autonomous underwater vehicles (AUVs), surface robots, research vessels, manned airplanes, moorings and Lagrangian drifters. Most ve- hicles required charging cycles at regular intervals; others like the solar powered Wave Glider or the Tethys long-range AUV (LRAUV) were persistent over the span of weeks. Experiment goals A core goal for the CANON eld initiative in October 2010 was to observe the evolution of phytoplankton blooms in Monterey Bay. These blooms are dynamic, moved around by ocean currents while impacted by its ecological life-cycle. They can be observed using data from remote-sensing satellites that capture the algal biomass in the upper 1 to 2m of the water column. However, this data is infrequent and dependent on weather conditions and often needs to be augmented by ship-based observation. Hence, once a bloom is detected, robotic assets are deployed to map the extent of the bloom, which is then tagged by Lagrangian drifters serving as proxy for the blooms advection. These GPS tracked devices help in the redeployment of assets based on observed advection patterns. Forecasts for a few physical and biological phenomena are obtained from ocean models to aid this process. Conception and evolution of ODSS The ODSS was conceptualized to help main- tain situational awareness during the CANON experiment, designed to be agile to respond to rapidly changing bloom dynamics. As the experiment progressed, new insights were developed and use-cases formulated, leading to the recommended inclusion of many fea- tures into ODSS. These features were desirable to support multi-robot, mixed-initiative experiments planned for CANON. Fig. 5.3 illustrates the evolution of ODSS in response 77 Situational Awareness Asset deployment Data products (observed by assets/ external products) generates requires increases goal Figure 5.3: The ODSS improves situational awareness of deployed assets though near-realtime assimilation of observations from the assets. to the experimental needs of CANON. While monitoring assets in real-time helped deci- sion making, visualization of scientic data products was desirable to improve situational awareness. This entailed viewing where robotic and manned assets were located, along with the data they were observing in the water-column, and potentially what they would likely observe based on predictive ocean models. In addition, ODSS served as a collabora- tive space where data, ideas and processed information would be shared and be persistent. As the experiment progressed, the complexity of dealing with evolving science hypotheses and the correlation between where the robots were sampling became increasingly tenuous. This was one driver for the desire to coordinate multiple robots out in the eld; the other and equally important need was that of observing a eld with a large spatio-temporal extent. Planning deployments Deployment planning occurred on a daily basis during the experiment to re-target assets to track the advecting patches. Daily morning planning meetings were prefaced either by data available from overnight missions or from short AUV missions targeting last known patch positions especially since remote-sensing data was sporadic due to weather constraints. Fig. 5.4 shows one such planning meeting with the ODSS on the screen, overlaid with mapped data products from the previous day's deployments. The data were analyzed and deliberated in these meetings and a consensus arrived at on where, how and with what assets to sample. These plans were disseminated in text and diagrams via the on-line discussion mechanism of a standalone component of ODSS called the Collaborative Science (CoSci) portal. In the future, more structured 78 Figure 5.4: Communication channels and robotic assets in the sea during the October 2010 experiment. methods of plan generation, dissemination, and integration will be included into the ODSS. In particular, we recognize the need for logistical planning capabilities in ODSS to capture deployment constraints on available research vessels, personnel and robotic assets. 5.2.2 ODSS System Architecture The ODSS was rapidly prototyped to generate an application with substantial back-end connectivity to existing MBARI databases and subsystems. Ease of use was the key to advocacy and acceptance by the science users, hence development of a web based cross-platform and cross-OS usage was targeted. Feedback from the users during the eld experiment has been assimilated into a more formally engineered system design for subsequent years use. Front-end Design Fig. 5.5 shows the ODSS's system architecture. At the core is a server that hosts the browser-based front-end and communicates with other subsystems that handle asset track- ing, science data access and shore-side intelligence allowing a loose coupling between var- ious subsystems some of which were legacy. For instance, an asset tracking system was already in place; the ODSS requirement was to interact with it to display up-to-date robot locations on an interactive map. The core web component of the ODSS, including 79 Figure 5.5: ODSS architectural block diagram, highlighting its subsystems. The unshaded boxes show legacy subsystems that were coupled with with newly developed subsystems (shaded boxes). the web-server and the front-end, was developed using a standardized toolkit [77], cho- sen over other available web-stacks primarily for the rich user-experience of the front-end and cross-browser support. The interactive front-end allowed overlay of science data with asset information to provide consolidated views of the experiment status. The various features of the ODSS front-end are as follows: Asset Tracking A core functionality for situational awareness is monitoring of assets during deployment and movement. An interactive map displays all active assets with their current locations and a Dashboard provided a summary of asset locations with advertised parameters such as speed and latitude/longitude. Additionally, asset tracks were highlighted with a history of up to a week. Fig. 5.2 shows a screenshot of the ODSS during the Fall experiment showing 6 hour tracks on the map, with a listing on the dashboard. Data Products Overlay of scientic data products such as sea-surface temperature, sea-surface current, etc. allowed scientists to view current sea state and ongoing oceano- graphic phenomena within the context of deployed assets. This consolidated view fa- cilitated asset re-tasking based on the observations of features of interest. Some of the science data products were available from third-party servers and others were cataloged and stored in CoSci. The ODSS provided a mechanism to toggle multiple data products on the interactive map. Fig. 5.6 shows a screenshot of ODSS with the data products panel and the sea-surface current product on the asset map. Mission Plans Mission plans specifying the basic deployment information for specic assets with the survey path to follow, could be overlaid on the ODSS on-demand. This 80 Figure 5.6: A section of the ODSS showing sea-surface current from third party CeNCOOS [2] server. The Data Products panel is located on the top-left corner. 81 allowed planners to view the overall coverage and at times, repeat previously executed plans if necessary. Asset Playback An important request from science collaborators was for instant recall of asset locations; knowing the past was important for planning future data gathering. This feature of ODSS allowed playback of the asset movement between specied start and end dates and used for analysis of asset deployment and movement for prior missions. Back-end Subsystems The ODSS design leveraged legacy systems used for collating and archiving data products. While these systems were in use as standalone entities, harnessing their power as part of the human-in-the-loop decision making process was novel. Tracking subsystem The ODSS was built on top of MBARI's asset tracking subsys- tem, an existing infrastructure to track and log locations of research vessels, moorings and other near-shore equipment in real-time. Robotic assets that took part in the eld experiment were tracked either via satellites or via radio links to shore. Asset informa- tion was stored in a tracking database and obtained either directly from the database, or through an HTTP API. For our deployment, the tracking subsystem stored information for a variety of assets such as propelled AUVs, gliders, moorings, Lagrangian drifters, research vessels, surface crafts and a research aircraft carrying an imaging sensor. This in turn allowed retrieval of information from past experiments and missions and useful for the playback functionality. Science data repository The ODSS' Data Products feature uses data cataloged by CoSci, which consists of a back-end data aggregator that periodically crawls multiple external servers to fetch and store data products of interest. The list of data sources to aggregate was initialized before the experiment and continually appended during the experiment as new collaborators joined the eort and derived data products became available. ODSS obtains a select list of data products from CoSci for overlaying on the interactive map. Additionally, CoSci includes a data visualization portal that allows direct access to scientic data products it acquired and which was integrated into the ODSS. 5.3 Usage and Impact To highlight the evolution and use of the ODSS, we articulate three dierent case studies, followed by a summary of asset deployment and usage statistic. 82 (a) Virtual drifter functionality (b) A validation tool for all assets to check distance-to-shore Figure 5.7: Virtual functionalities within the ODSS. 5.3.1 Case Studies Forecasting and planning A virtual drifter functionality was required early in the eld experiment to perform a Lagrangian patch tracking experiment involving the Dorado AUV. The goal was to extend Lagrangian observation studies carried out in June and September 2010 [78] to coastal waters where surface current forecasts are available, aided by HF Radar measurements and surface ocean current models. Traditional methods would call for a physical drifter to be dispatched in the vicinity of the study area, as a stand-in for a patch centroid, for tracking by manned vessels. Using the virtual drifter, the projected trajectory of waypoints of the patch was marked within the ODSS, and sent to the Dorado AUV; the automated planner onboard sub-sampled the virtual drifter waypoints and planned the vehicle trajectory. This feature was also used to analyze the estimated trajectory of a hotspot to guide future asset and AUV deployment as shown in Fig. 5.7a. An interactive validation tool was also developed to aid human operators to check for constraints such as distance to shore for safe operation. This was particularly useful when deciding to target a virtual drifter track for the Dorado and allowed operators to cross- check AUV tracks with potential violations of near-shore operating constraints. Fig. 5.7b shows a screenshot of validations on all platforms on the ODSS map. Visualization of real-time science data from robotic assets Most platforms operating in the eld experiment provided data with a lag of a few hours. AUV data was typically received every few hours over satellite and data on manned vessels were recovered once they returned to shore each day. The Wave Glider [3] a unique solar powered surface platform took measurements at two depths and transmitted them back in near real-time. Fluorometry and location information from this platform was fed to 83 Figure 5.8: Real-time chlorophyll concentration data updated every two minutes from the Wave Glider [3]. Figure 5.9: ODSS during multi-AUV experiment highlighting the chlorophyll patch, AUV Do- rado, and AUV Tethys. Tethys estimated the patch center marked as 'CHL PATCH', which was tracked by the tracking subsystem. The Dorado was then commanded to perform a survey around this patch, taking water samples at chlorophyll peaks [4]. the ODSS (Fig. 5.8) to serve both as a demonstration of real-time streaming on the asset map as well as for early detection of bloom hotspots. Multi-AUV drifter tracking experiment A key objective of this deployment was to track a water patch with multiple assets. An opportunity to have two AUVs with dierent payloads and characteristics tracking a patch came late in the experiment. The Tethys AUV was deployed within a known algal hotspot and tasked with tracking the patch and publishing the updated patch center every hour with the Dorado AUV observing the contextual environment in a 3km X 3km box around this centroid. Further, since the patch was suciently close to shore, operational constraints on the Dorado AUV were placed necessitating it be commanded from shore. The patch centroid sent from Tethys was updated on the tracking subsystem 84 Figure 5.10: Plot of daily platform activity measured in platform-days, and ODSS usage, mea- sured in unique visiter count for the days of October 2010. and displayed on ODSS; a human operator observed the patch location on the ODSS and commanded the Dorado AUV running T-REX, to perform surveys around the identied patch center while taking water samples using its onboard samplers. The operator's role was to be a lter; to ensure that the centroid was over sucient depth on the shelf and not heading towards shore and then dispatching the centroid location. T-REX on the Dorado AUV then synthesized the survey plan automatically and then executed the plan without human intervention. Fig. 5.9 shows a screenshot of ODSS during the multi-AUV patch tracking experiment, showing the chlorophyll patch. An inlay of the dashboard status for the patch shows the patch location, course, and speed. 5.3.2 Usage statistics We generated deployment statistics for the eld experiment by using data logged by the tracking sub-system. We measured the asset activity in 'platform-days', i.e. the sum-total duration each asset was deployed and active. Then, we determined the visitor-count to ODSS from the access logs of its web-server. This was computed using well-established techniques to monitor web site usage. Each session by a user from a particular IP address is considered to be a unique visit. Fig. 5.10 shows the plots of asset activity and ODSS visitor count for each day of October 2010. We observe a strong correlation between the experiment activity and ODSS usage, highlighting the role the ODSS played during the experiment. Additionally, we plotted the total distance traveled and time active for each asset; Fig. 5.11a shows the combined plot of the total distance traveled and the active deploy- ment time for each asset. This gure highlights the diverse nature of assets taking part and also the temporal extent of observations, with the research vessel R/V Point Sur 85 (a) Total distance traveled and active operational time for platforms (b) Asset tracks Figure 5.11: Asset deployment statistics for the 2010 eld experiment. being active for around 22 days, covering 2100 km. For visualization of the spatial cov- erage of all assets during the experiment, we generated Fig. 5.11b using Google Earth [79], highlighting intense activity in northern Monterey Bay. 5.4 Lessons Learned The October eld experiment was a preliminary step towards understanding the key functionalities necessary for scientically driven eld experiments in the coastal ocean. While the basic requirements of situational awareness, data collation and analysis were evident a priori, the process behind such large scale experimentation in the domain have never been closely analyzed for projection towards future computational needs. We oer some key lessons learned for the eld of marine robotics: Multi-vehicle coordination and control is a central need for science - As marine robotics plays an increasingly important role in science and robots are more ubiqui- tous in eld experimentation, scientists are likely to challenge design scales of such experiments. Current deployments might be multi-institutional/multi-PI; however the currently informal models of experiment design are giving way to more or- ganized, event-driven and reactive operation across a meso-scale (> 50 Sq. km). Dynamic processes varying in time will also be the subject of study requiring a mix of vehicles with varying payloads and speeds thru the water-column. The scale of experimentation is therefore likely to increase with more robotic assets in the water and with increasing need to coordinate their deployment and sampling. 86 Event Response scenarios will often drive experimentation - With our relatively poor understanding of coastal ocean processes and the challenges current ocean models pose in prediction, increasing reliance on Machine Learning and Data Mining techniques will play a critical role in data driven experimentation. Such computation techniques, whether on shore on onboard, will provide rapid assessment towards evolving science goals and will require new approaches to statistical interpretations of ensemble sensor data. Sampling and retrieval for lab analysis is an important aspect of vehicle control - Traditional ship-based approaches to water sampling are not sustainable; robots and robot control will play an important role in furthering this aim in large scale eld experimentation. This requires an important problem of \when and where to sample" to be coupled with in-situ sensor readings and the environmental context. Adaptive sampling approaches will need to be investigated which consider an en- semble of robots as one adaptable system to observe biogeochemical activity along diering scales. What-if scenarios are integral - During the course of our Fall experiment, eort was expended to decide on the placement of the various assets. Science participants are already asking for multiple scenario ows for \what if" analysis; with increasing use of multiple and heterogeneous robots in such experimentation, this need will be critical to fulll. While some predictive ocean modeling capability will be useful with enhanced model skill in the future, simpler techniques such as the \virtual drifter" for patch tracking can and should be leveraged. Asynchronous (human) communication is highly desirable - Historically, scienti- cally driven robotic eld experiments, whether in the marine or terrestrial domains, have focused on technologists and scientists to be co-located [80, 81, 82, 83, 84]. In part this has been driven by the ne tuning of the technology for deployment and coordination with science to ensure that appropriate science data are returned; analysis of science data was by and large post-facto of the experiment. With ma- rine robots becoming more robust as well as prevalent in the sciences, the focus of attention has turned to software, both for control as well as data gathering and analysis and one that can be modied based on ongoing needs. This in turn has lessened the need for close person-to-person coordination on deployment aspects, but increased the spotlight on data centric activities which do not necessarily re- quire in-person presence. This trend towards remote and geographically disparate operations has also shown a side benet associated with that of participation and inclusion in science teams. Handling data from disparate sources is inevitable - Payloads and platforms in the ocean sciences are often customized towards longer term science or technology goals. Participants in large-scale eld deployments often arrive with diering platforms and sensor payloads. However, such large eld deployments are not just about gathering 87 data but also continuous scientic analysis to spot and respond to dynamic events in the coastal ocean. Data obtained in-situ are often sent via dierent communication streams (locally via freewave or 802.11, via 3G or Iridium or Globalstar satellites) in diering formats (e.g raw text, binary, comma separated CSV les, with or without meta-data tags). Since communications especially in coastal deployments is less onerous, the expectations of situational awareness requires that data be gathered in near or quasi real-time with continuing/continuous science analysis. This requires that support tools onshore be capable of coalescing data in ways that are inter- pretable by humans to drive a (near) real-time response to evolving science and technology needs. Situational awareness is important; but so is knowing the intent of activity in the past - Marine science driven eld experiments are brief bursts of activity in a nom- inal academic calendar. To maximize the time and expense involved, continuous deployment and operation are highly desirable. This results in having a continuous stream of experiments and results that need to be planned for. Activities in the present are therefore informed by the near past; to understand the current state of deployment of assets, therefore it is critical to understand and archive the mo- tivation and intent of the recent science and technology drivers. In this context, disparate assets and their associated operational and logistical constraints need to be tracked over the temporal window of the evolving experiment and the scientic or technological intent needs to be recorded for subsequent use. Responding to evolving needs drives rapid software prototyping - The above need in turn drives another requirement; namely that mechanisms be in place to allow for dierent approaches for data interpretation which in turn require that tools be rapidly prototyped to keep pace with such evolving needs during experimentation. 5.5 What about the future? Marine robotics is a viable and healthy eld not only because it oers a challenging domain in which to undertake the science of robotics, but because there are important and complex science themes like global climate change that need better tools for human understanding. Littoral homeland security in the wake of recent events has shown the importance of autonomous surface robots while traditional mine counter measure scenar- ios are increasingly driven by underwater robotic devices. Given our experience in an inter-disciplinary eld experiment for an extended period of time with multiple heteroge- neous marine robots, we believe we can look forward at least a decade to predict how such oceanographic experiments will impact the eld of marine robotics while looking back to the past 50 years. Oceanography is already at a cusp; robotics will further enable and transform the move from an expeditionary to an observatory mode at a faster pace. Multiple robots 88 coordinated from shore via communication networks (Inter/intra nets, satellite commu- nication links, local area networks) will be the norm with increasing reliance on visual means of command and control. Scientists will no longer be constrained to be co-located to assign operations personnel (or graduate students) the task of commanding the assets; they would do so themselves, with the robots becoming extensions of the human senses. Drag and drop interfaces within browsers or standalone applications will be used for tar- geted planning and control of AUVs and other autonomous platforms, while shore-based algorithms would generate plan sketches for mixed-initiative coordination plans where multiple assets are involved. Major advances in data interpretation, visualization and event tracking driven by advances in automated Machine Learning techniques will drive event-response scenarios. More tightly integrated lab automation with eld experiments via ODSS like technologies will allow model-derived priors to drive such statistical based inference while also providing faster ground truth authentication for hypotheses generated by scientists from autonomously retrieved water samples. Communications under water might still be a challenge; but shore-side support coupled with portable network nodes will provide a variety of local area network support for vehicles when on the surface. With these advances, we see a great need to focus on multi-vehicle sampling tech- niques; adaptive sampling strategies will need to scale for those from single to multiple vehicles. Advances in ocean model driven deployments will increase with increasing model skill, but vehicle autonomy and control will continue to drive data-driven exploration. Ultimately roboticists will drive and be driven by scientic oceanographic and military challenges more substantially by participating and being entrained to participate in large eld deployments. 89 Chapter 6 Conclusions \The best way to observe a sh is to become a sh." | Jacques-Yves Cousteau 6.1 Summary This thesis developed data-driven robotic sampling methodologies for marine ecosystem monitoring. We approached the task in three parts { deployment planning, coordinated tracking, and autonomous sampling. Additionally, we described an oceanographic decision support system that facilitates situational awareness during large-scale eld experiments. In this chapter, we summarize the contributions of this thesis, and brie y discuss our plans for future work. First, in Chapter 2, we described how outdated (1-5 days) synoptic imagery from remote-sensing satellites is used to detect plankton blooms. Subsequently, nowcasts for blooms are obtained by using near-realtime hourly surface-current measurements from land-based HF radar stations to project trajectories for the bloom hotspots detected from the (outdated) satellite image. Using the nowcast projection, ecient deployment plan for the AUV are determined. We described the results of analysis on historical datasets consisting of 1-5 day projections of blooms, demonstrating the advantage of carrying this approach for deployment planning. Second, in Chapter 3 we showed how once an AUV is deployed within a bloom hotspot, it can stay with the hotspot as it gets advected by ocean currents. To do so, we tagged a patch of water (hotspot) with a GPS-tracked drifter and designed Lagrangian surveys to sample in the frame of reference of the advecting patch. We discussed the results of a eld experiment where a patch of water tagged with a GPS-tracked drifter was tracked over a period of ve days with an AUV. The accuracy of tracking was discussed, along with a description of the sources of errors in the navigation and operational aspects of the experiment. The work presented in the chapter is rst of its kind, allowing contin- uous monitoring of advecting features of interests such as plankton bloom hotspots over multiple days. 90 In Chapter 4, we addressed autonomous sampling once an AUV is deployed and to carry out Lagrangian surveys. We presented a data-driven sampling algorithm for ex-situ analysis of physical water samples, treating plankton abundance that cannot be measured in situ as a hidden feature that can be predicted using a probabilistic regression model trained on past data, with observable environmental parameters as its input. This model was used onboard the AUV to to predict microorganism abundance in real time. An on- line sampling policy used these predictions to make irrevocable decisions to sequentially collect a xed number of water samples over a course of a deployment. We carried out an extensive simulation study on real eld data from a week long campaign in 2005 consisting of 17 consecutive AUV deployments, providing empirical evidence for the utility of our sampling approach. We also presented results from a eld deployment that targeted a genus of phytoplankton known to cause potentially toxic blooms. A probabilistic regres- sion model was trained on a dataset of lab analyzed water samples from AUV missions carried out during a previous season. This trained model was used on board the AUV to target the phytoplankton of interest, and samples were analyzed on shore. Preliminary lab analysis results were promising, showing abundance of the target organism, and fa- cilitating lab cultures. This was the rst time such a eld experiment had been carried out in its entirety in a data-driven fashion, in eect `closing the loop' on a signicant and relevant ecosystem monitoring problem. Finally, in Chapter 5, we described the Oceanographic Decision Support System (ODSS) in Chapter 5, and demonstrated how it plays a key role in large-scale eld ex- periments for situational awareness, data visualization, and experiment design. This tool has had an impact on eld campaigns since it was developed in 2010, with latest versions being used regularly at MBARI, providing a window to eld experiments for planning and analysis, both on shore and on ships. We presented usage statistics that arms our view that such tools are critical to marine ecosystem monitoring experiments. 6.2 Future work The sampling methodology presented in the context of marine ecosystem monitoring scales naturally to a variety of other domains. We envision heterogeneous robot teams that will enable scientists to acquire physical samples from air, water, and land for com- plex ecological and environmental studies (Fig. 6.1). This will be guided by in-situ mea- surable properties at multiple spatio-temporal scales. For example, synoptic sensing by unmanned aerial vehicles (UAVs) using onboard hyper-spectral cameras can guide autono- mous ground vehicles (AGVs) to ideal locations for collection of soil samples. We identify three challenges in collaborative sample collection for ex-situ analysis. First, we need to choose sensors for each robot of the team to allow in-situ measurement of appropriate covariates to guide physical sample collection. Second, methods need to be developed to predict the hidden property of interest of the physical samples, using data measured by multiple robots. Finally, the metric for quality of samples need to be dened. In our marine ecosystem monitoring work, we formulated the problem of sample collection 91 Figure 6.1: Networked systems composed of heterogeneous robots can share in-situ measured data to eciently collect physical samples for ex-situ analysis. Such systems, consisting of satellites, UAVs, AGVs, ASVs, and AUVs will enable persistent monitoring for ecological and environmental studies. 92 for ex-situ analysis as a cumulative regret minimization problem, i.e. high-abundance plankton samples have lower regret. We believe robotic sampling for ex-situ analysis will open up the arena of large- scale persistent monitoring for environmental sciences, disaster mitigation, and commerce. Such systems will enable execution of tasks such as aerobiological sampling with UAVs, soil and rock sample analysis with AGVs, to cite two examples, in a data-driven fashion. Mitigating environmental disasters such as chemical spills and toxic plumes require collec- tion and analysis of physical samples of air, soil, and water from an aected geographical area. For these dynamic events, robotic sampling for ex-situ analysis is an essential ca- pability. Commercially, such systems will benet sheries and agriculture, both of which require persistent monitoring of properties that require collection of physical samples of water or soil. 93 BIBLIOGRAPHY [1] J. P. Ryan, H. M. Dierssen, R. M. Kudela, C. A. Scholin, K. S. Johnson, J. M. Sullivan, A. M. Fischer, E. V. Rienecker, P. R. McEnaney, , and F. P. Chavez, \Coastal ocean physics and red tides: an example from Monterey Bay, California," Oceanography, vol. 18, pp. 246{255, March 2005. [2] \The Central and Northern California Ocean Observing System (CeNCOOS)." http: //www.cencoos.org/. [3] S. Willcox, J. Manley, and S. 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Abstract (if available)

Abstract The marine environment is in a perpetual state of flux due to ocean currents. As a result, phenomena such as plankton blooms are constantly advected, making their observation challenging. Traditionally, measurements from remote‐sensing satellites, ships, piers, and moorings have helped scientists study such phenomena. However, a sound understanding of bloom ecology and dynamics requires persistent sampling at spatio‐temporal scales infeasible with existing methods. Advances in robotic sampling using autonomous underwater vehicles (AUVs) have opened up the arena for adaptive sampling at unprecedented scales, augmenting other methods of observation. ❧ This thesis presents a novel data‐driven robotic sampling methodology for marine ecosystem monitoring, focusing on the observation of plankton blooms. The problem is addressed at multiple spatio‐temporal scales to detect, track, and sample blooms with the goal of acquisition of physical water samples for ex‐situ analysis of plankton abundance. This is essential for the understanding of plankton ecology and community structure since sensors onboard AUVs are incapable of measuring precise biological data in realtime, necessitating lab analysis of water samples. ❧ Starting at the macro scale (kilometers/days), this work demonstrates how remote sensing imagery and periodic measurements of surface currents facilitate detection and trajectory projection of plankton blooms to plan AUV deployments. Once deployed, the AUV needs to survey within the context of the advecting bloom. The thesis presents the design of Lagrangian surveys wherein a bloom is tagged with a GPS‐tracked drifter, and surveys are designed and executed in the frame of reference of the advecting bloom. Results from a field experiment where a 1km x 1km patch of water was successfully tracked by an AUV over multiple days demonstrate the efficacy of this approach. Next, during such Lagrangian surveys, the AUV is required to carry out adaptive water sample acquisition for ex‐situ analysis. The thesis describes a principled online sampling strategy that uses probabilistic regression models trained on previously collected data to predict abundance of desired plankton from realtime measurements of physical and chemical properties by the AUV’s onboard sensor suite. Extensive simulations carried out by mining historical data, and a one‐day field trial targeting a toxinogenic plankton demonstrate the impact of the approach, in effect ""closing the loop"" on a a significant science problem. Finally, the thesis describes an Oceanographic Decision Support System (ODSS), a web‐based tool developed for situational awareness and data visualization during robotic sampling experiments of the kind presented in this work. Extensive use during a month‐long field campaign with multiple platforms and users demonstrate the importance of support tools in marine ecosystem monitoring. ❧ Through extensive experimental results, the thesis demonstrates robotic sampling for marine ecosystem monitoring at an unprecedented spatio‐temporal scale, highlighting its role in biological hypothesis testing. Although the work presented is in the context of the marine environment, it is applicable to a variety of unstructured and extreme environments inaccessible to humans.

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Creator Das, Jnaneshwar (author)

Core Title Data-driven robotic sampling for marine ecosystem monitoring

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Computer Science

Publication Date 05/01/2014

Defense Date 12/19/2013

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

Tag adaptive sampling,autonomous underwater vehicles,AUVs,environmental monitoring,experiment design,field robotics,machine learning,marine robotics,OAI-PMH Harvest,robotic sampling,robotics,software systems,underwater robots

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Language English

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Advisor Sukhatme, Gaurav S. (committee chair), Caron, David A. (committee member), Schaal, Stefan (committee member)

Creator Email jnaneshwar.das@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-409762

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