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Figure 6.5: Sequence of images from the simulated robot dog jumping over a 14cm gap.
Top: before learning. Bottom: After learning. While the two sequences look quite similar
at the first glance, it is apparent that in the 4th frame, the robot’s body is significantly
heigher in the air, such that after landing, the body of the dog made about 15cm more
forward progress as before. In particular, the entire robot’s body comes to rest on the
other side of the gap, which allows for an easy transition to walking.
6.5 Evaluations of (PI2) on planning and gain scheduling
In the next sections we evaluate the PI2 on the problems of optimal planning and gain
scheduling. In a typical planning scenario the goal is to find or to learn trajectories which
minimize some performance criterion. As we have seen in the previous sections at every
iteration of the learning algorithm, new trajectories are generated based on which the
new planing policy is computed. The new planning policy is used at the next iteration
to generated new trajectories which are again used to compute the improved planning
policy. The process continues until the convergence criterion is meet.
In this learning process main assumption is the existence of a control policy that is
adequate to steer the system such that it follows the trajectories generated at every it-eration
of the learning procedure. In this section we go one step further and apply PI2
not only to find the optimal desired trajectories but also to learn control policies that
minimize a performance criterion. This performance criterion is a function of kinematic
204
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 218 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | Figure 6.5: Sequence of images from the simulated robot dog jumping over a 14cm gap. Top: before learning. Bottom: After learning. While the two sequences look quite similar at the first glance, it is apparent that in the 4th frame, the robot’s body is significantly heigher in the air, such that after landing, the body of the dog made about 15cm more forward progress as before. In particular, the entire robot’s body comes to rest on the other side of the gap, which allows for an easy transition to walking. 6.5 Evaluations of (PI2) on planning and gain scheduling In the next sections we evaluate the PI2 on the problems of optimal planning and gain scheduling. In a typical planning scenario the goal is to find or to learn trajectories which minimize some performance criterion. As we have seen in the previous sections at every iteration of the learning algorithm, new trajectories are generated based on which the new planing policy is computed. The new planning policy is used at the next iteration to generated new trajectories which are again used to compute the improved planning policy. The process continues until the convergence criterion is meet. In this learning process main assumption is the existence of a control policy that is adequate to steer the system such that it follows the trajectories generated at every it-eration of the learning procedure. In this section we go one step further and apply PI2 not only to find the optimal desired trajectories but also to learn control policies that minimize a performance criterion. This performance criterion is a function of kinematic 204 |
