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List Of Figures
6.1 Comparison of reinforcement learning of an optimized movement with mo-tor
primitives. a) Position trajectories of the initial trajectory (before
learning) and the results of all algorithms after learning – the different
algorithms are essentially indistuighishable. b) The same as a), just us-ing
the velocity trajectories. c) Average learning curves for the different
algorithms with 1 std error bars from averaging 10 runs for each of the
algorithms. d) Learning curves for the different algorithms when only two
roll-outs are used per update (note that the eNAC cannot work in this case
and is omitted). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.2 Comparison of reinforcement learning of an optimized movement with mo-tor
primitives for passing through an intermediate target G. a) Position
trajectories of the initial trajectory (before learning) and the results of
all algorithms after learning. b) Average learning curves for the different
algorithms with 1 std error bars from averaging 10 runs for each of the
algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.3 Comparison of learning multi-DOF movements (2,10, and 50 DOFs) with
planar robot arms passing through a via-point G. a,c,e) illustrate the
learning curves for different RL algorithms, while b,d,f) illustrate the end-effector
movement after learning for all algorithms. Additionally, b,d,f)
also show the initial end-effector movement, before learning to pass through
G, and a “stroboscopic” visualization of the arm movement for the final
result of PI2 (the movements proceed in time starting at the very right
and ending by (almost) touching the y axis). . . . . . . . . . . . . . . . . 200
6.4 Reinforcement learning of optimizing to jump over a gap with a robot dog.
The improvement in cost corresponds to about 15 cm improvement in
jump distance, which changed the robot’s behavior from an initial barely
successful jump to jump that completely traversed the gap with entire
body. This learned behavior allowed the robot to traverse a gap at much
higher speed in a competition on learning locomotion. . . . . . . . . . . . 202
x
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 10 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | List Of Figures 6.1 Comparison of reinforcement learning of an optimized movement with mo-tor primitives. a) Position trajectories of the initial trajectory (before learning) and the results of all algorithms after learning – the different algorithms are essentially indistuighishable. b) The same as a), just us-ing the velocity trajectories. c) Average learning curves for the different algorithms with 1 std error bars from averaging 10 runs for each of the algorithms. d) Learning curves for the different algorithms when only two roll-outs are used per update (note that the eNAC cannot work in this case and is omitted). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 6.2 Comparison of reinforcement learning of an optimized movement with mo-tor primitives for passing through an intermediate target G. a) Position trajectories of the initial trajectory (before learning) and the results of all algorithms after learning. b) Average learning curves for the different algorithms with 1 std error bars from averaging 10 runs for each of the algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.3 Comparison of learning multi-DOF movements (2,10, and 50 DOFs) with planar robot arms passing through a via-point G. a,c,e) illustrate the learning curves for different RL algorithms, while b,d,f) illustrate the end-effector movement after learning for all algorithms. Additionally, b,d,f) also show the initial end-effector movement, before learning to pass through G, and a “stroboscopic” visualization of the arm movement for the final result of PI2 (the movements proceed in time starting at the very right and ending by (almost) touching the y axis). . . . . . . . . . . . . . . . . 200 6.4 Reinforcement learning of optimizing to jump over a gap with a robot dog. The improvement in cost corresponds to about 15 cm improvement in jump distance, which changed the robot’s behavior from an initial barely successful jump to jump that completely traversed the gap with entire body. This learned behavior allowed the robot to traverse a gap at much higher speed in a competition on learning locomotion. . . . . . . . . . . . 202 x |
