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include via point task with manipulators of various DOFs as well as the task of pushing a
door to open with the simulated CBi humanoid robot. In the last section 6.8 we discuss
the performance of PI2 in the aforementioned tasl and we conclude.
6.1 Learnable nonlinear attractor systems
6.1.1 Nonlinear point attractors with adjustable land-scape
The nonlinear point attractor consists of two sets of differential equations, the canonical
and transformation system which are coupled through a nonlinearity (Ijspeert, Nakan-ishi,
Pastor, Hoffmann & Schaal submitted),(Ijspeert, Nakanishi & Schaal 2003). The
canonical system is formulated as 1
. x˙ t = −2xt. That is a first - order linear dynamical
system for which, starting from some arbitrarily chosen initial state x0 , e.g., x0 = 1, the
state x converges monotonically to zero. x can be conceived of as a phase variable, where
x = 1 would indicate the start of the time evolution, and x close to zero means that the
goal g (see below) has essentially been achieved. The transformation system consist of
the following two differential equations:
'z˙ =2z)z
$$
g +
f
2z)z
%
− y
%
− 2zz (6.1)
'y˙ =z
Essentially, these 3 differential equations code a learnable point attractor for a move-ment
from yt0 to the goal g, where ) determines the shape of the attractor. yt, y˙t denote
181
Object Description
| Title | Iterative path integral stochastic optimal control: theory and applications to motor control |
| Author | Theodorou, Evangelos A. |
| Author email | etheodor@usc.edu; theo0027@umn.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Computer Science |
| School | Viterbi School of Engineering |
| Date defended/completed | 2011-01-11 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-04-29 |
| Advisor (committee chair) | Schaal, Stefan |
| Advisor (committee member) |
Valero-Cuevas, Francisco Sukhatme, Gaurav S. Todorov, Emo Schweighofer, Nicolas |
| Abstract | Motivated by the limitations of current optimal control and reinforcement learning methods in terms of their efficiency and scalability, this thesis proposes an iterative stochastic optimal control approach based on the generalized path integral formalism. More precisely, we suggest the use of the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parameterized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton Jacobi Bellman (HJB) equation, policy improvements can be transformed into an approximation problem of a path integral which has no open algorithmic parameters other than the exploration noise. The resulting algorithm can be conceived of as model-based, semi-model-based, or even model free, depending on how the learning problem is structured. The new algorithm, Policy Improvement with Path Integrals (PI2), demonstrates interesting similarities with previous RL research in the framework of probability matching and provides intuition why the slightly heuristically motivated probability matching approach can actually perform well. Applications to high dimensional robotic systems are presented for a variety of tasks that require optimal planning and gain scheduling.; In addition to the work on generalized path integral stochastic optimal control, in this thesis we extend model based iterative optimal control algorithms to the stochastic setting. More precisely we derive the Differential Dynamic Programming algorithm for stochastic systems with state and control multiplicative noise. Finally, in the last part of this thesis, model based iterative optimal control methods are applied to bio-mechanical models of the index finger with the goal to find the underlying tendon forces applied for the movements of, tapping and flexing. |
| Keyword | stochastic optimal control; reinforcement learning,; robotics |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3804 |
| Contributing entity | University of Southern California |
| Rights | Theodorou, Evangelos A. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Theodorou-4581 |
| Archival file | uscthesesreloadpub_Volume14/etd-Theodorou-4581.pdf |
Description
| Title | Page 195 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | include via point task with manipulators of various DOFs as well as the task of pushing a door to open with the simulated CBi humanoid robot. In the last section 6.8 we discuss the performance of PI2 in the aforementioned tasl and we conclude. 6.1 Learnable nonlinear attractor systems 6.1.1 Nonlinear point attractors with adjustable land-scape The nonlinear point attractor consists of two sets of differential equations, the canonical and transformation system which are coupled through a nonlinearity (Ijspeert, Nakan-ishi, Pastor, Hoffmann & Schaal submitted),(Ijspeert, Nakanishi & Schaal 2003). The canonical system is formulated as 1 . x˙ t = −2xt. That is a first - order linear dynamical system for which, starting from some arbitrarily chosen initial state x0 , e.g., x0 = 1, the state x converges monotonically to zero. x can be conceived of as a phase variable, where x = 1 would indicate the start of the time evolution, and x close to zero means that the goal g (see below) has essentially been achieved. The transformation system consist of the following two differential equations: 'z˙ =2z)z $$ g + f 2z)z % − y % − 2zz (6.1) 'y˙ =z Essentially, these 3 differential equations code a learnable point attractor for a move-ment from yt0 to the goal g, where ) determines the shape of the attractor. yt, y˙t denote 181 |
