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rroll =
&''''(
'''')
100 & (|rollt| − 0.3)2, if (|rollt| > 0.3)
0, otherwise
(6.35)
ryaw =
&''''(
'''')
100 & (|yawt| − 0.1)2, if (|yawt| > 0.1)
0, otherwise
(6.36)
&tN = 50000(goal − xnose)2 (6.37)
where roll, yaw are the roll and yaw angles of the robot’s body, and xnose is the position
of the front tip (the “nose”) of the robot in the forward direction, which is the direc-tion
towards the goal. The multipliers for each reward component were tuned to have
a balanced influence of all terms. Ten learning trials were performed initially for the
first parameter update. The best 5 trials were kept, and five additional new trials were
performed for the second and all subsequent updates. Essentially, this method performs
importance sampling, as the rewards for the 5 trials in memory were re-computed with
the latest parameter vectors. A total of 100 trials was performed per run, and ten runs
were collected for computing mean and standard deviations of learning curves.
(i.e., 5 updates), the performance of the robot was converged and significantly im-proved,
such that after the jump, almost the entire body was lying on the other side of
the gap. Figure 6.4 captures the temporal performance in a sequence of snapshots of the
robot. It should be noted that applying PI2 was algorithmically very simple, and manual
tuning only focused on generated a good cost function, which is a different research topic
beyond the scope of this paper.
203
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 217 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | rroll = &''''( '''') 100 & (|rollt| − 0.3)2, if (|rollt| > 0.3) 0, otherwise (6.35) ryaw = &''''( '''') 100 & (|yawt| − 0.1)2, if (|yawt| > 0.1) 0, otherwise (6.36) &tN = 50000(goal − xnose)2 (6.37) where roll, yaw are the roll and yaw angles of the robot’s body, and xnose is the position of the front tip (the “nose”) of the robot in the forward direction, which is the direc-tion towards the goal. The multipliers for each reward component were tuned to have a balanced influence of all terms. Ten learning trials were performed initially for the first parameter update. The best 5 trials were kept, and five additional new trials were performed for the second and all subsequent updates. Essentially, this method performs importance sampling, as the rewards for the 5 trials in memory were re-computed with the latest parameter vectors. A total of 100 trials was performed per run, and ten runs were collected for computing mean and standard deviations of learning curves. (i.e., 5 updates), the performance of the robot was converged and significantly im-proved, such that after the jump, almost the entire body was lying on the other side of the gap. Figure 6.4 captures the temporal performance in a sequence of snapshots of the robot. It should be noted that applying PI2 was algorithmically very simple, and manual tuning only focused on generated a good cost function, which is a different research topic beyond the scope of this paper. 203 |
