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variables of the underlying dynamics and the strength of control gains that are incorpo-rated
in the control policy. Essentially, the goal for the robot is to be able to perform the
task with as lower gains as possible.
6.6 Way-point experiments
We start our evaluations with way -point experiments in two simulated robots, the 3DOF
Phantom robot and the 6DOF Kuka robot. For both robots, the immediate reward at
time step t is given as:
r(t) = wgain
>
i
KiP
,t + wacc||¨x|| + wsubgoalC(t) (6.38)
Here,
C
i KiP
,t is the sum over the proportional gains over all joints. The reasoning
behind penalizing the gains is that low gains lead to several desirable properties of the
system such as compliant behavior (safety and/or robustness (Buchli, Kalakrishnan, Mis-try,
Pastor & Schaal 2009)), lowered energy consumption, and less wear and tear. The
term ||¨x|| is magnitude of the accelerations of the end-effector. This quantity is penalized
to avoid high-jerk end-effector motion. This penalty is low in comparison to the gain
penalty.
The robot’s primary task is to pass through an intermediate goal, either in joint
space or end-effector space – such scenarios occur in tasks like playing tennis or table
tennis. The component of the cost function C(t) that represents this primary task will
be described individually for each robot in the next sections. Gains and accelerations are
penalized at each time step, but C(t) only leads to a cost at specific time steps along
205
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 219 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | variables of the underlying dynamics and the strength of control gains that are incorpo-rated in the control policy. Essentially, the goal for the robot is to be able to perform the task with as lower gains as possible. 6.6 Way-point experiments We start our evaluations with way -point experiments in two simulated robots, the 3DOF Phantom robot and the 6DOF Kuka robot. For both robots, the immediate reward at time step t is given as: r(t) = wgain > i KiP ,t + wacc||¨x|| + wsubgoalC(t) (6.38) Here, C i KiP ,t is the sum over the proportional gains over all joints. The reasoning behind penalizing the gains is that low gains lead to several desirable properties of the system such as compliant behavior (safety and/or robustness (Buchli, Kalakrishnan, Mis-try, Pastor & Schaal 2009)), lowered energy consumption, and less wear and tear. The term ||¨x|| is magnitude of the accelerations of the end-effector. This quantity is penalized to avoid high-jerk end-effector motion. This penalty is low in comparison to the gain penalty. The robot’s primary task is to pass through an intermediate goal, either in joint space or end-effector space – such scenarios occur in tasks like playing tennis or table tennis. The component of the cost function C(t) that represents this primary task will be described individually for each robot in the next sections. Gains and accelerations are penalized at each time step, but C(t) only leads to a cost at specific time steps along 205 |
