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The learning curve for this problem is depicted in Figure 6.9. The trajectory of the
end-effector after 30 and 100 updates is depicted in Figure 6.10. The intermediate goal
at t = 0.5 is visualized by circles. Finally, Figure 6.11 shows the gain schedules after 30
and 100 updates for the 6 joints of the Kuka robot.
Figure 6.10: Initial (red, dotted), intermediate (green, dashed), and final (blue, solid)
end-effector trajectories of the Kuka robot.
From these graphs, we draw the following conclusions:
• PI2 has adapted joint trajectories such that the end-effector passes through the
intermediate subgoal at the right time. It learns to do so after only 30 updates
(Figure 6.7).
• After 100 updates the peaks of most gains occur just before the end-effector passes
through the intermediate goal (Figure 6.11), and in many cases decrease to the
minimum gain directly afterwards. As with the phantom robot we observe high
impedance when the task requires accuracy, and more compliance when the task is
relatively unconstrained.
211
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 225 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | The learning curve for this problem is depicted in Figure 6.9. The trajectory of the end-effector after 30 and 100 updates is depicted in Figure 6.10. The intermediate goal at t = 0.5 is visualized by circles. Finally, Figure 6.11 shows the gain schedules after 30 and 100 updates for the 6 joints of the Kuka robot. Figure 6.10: Initial (red, dotted), intermediate (green, dashed), and final (blue, solid) end-effector trajectories of the Kuka robot. From these graphs, we draw the following conclusions: • PI2 has adapted joint trajectories such that the end-effector passes through the intermediate subgoal at the right time. It learns to do so after only 30 updates (Figure 6.7). • After 100 updates the peaks of most gains occur just before the end-effector passes through the intermediate goal (Figure 6.11), and in many cases decrease to the minimum gain directly afterwards. As with the phantom robot we observe high impedance when the task requires accuracy, and more compliance when the task is relatively unconstrained. 211 |
