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with sliding and surface constraints (Blemker & Delp 2005.). Several advances also allow
representing muscles as volumetric en- tities with data extracted from imaging studies
(Blemker & Delp 2005.) ,(S. S. Blemker & Delp 2007), and defining tendon paths as
wrapping in a piecewise linear way around ellipses defining joint locations (R. Davoodi &
Loeb 2003), (Delp & Loan 2007). The path of the musculotendon in these cases is defined
based on knowledge of the anatomy. Sometimes, it may not be necessary to model the
musculotendon paths but obtaining a mathematical expression for the moment arm (r)
could suffice. The moment arm is often a function of joint angle and can be obtained by
recording incremental tendon excursions (*s) and corresponding joint angle changes (*")
in cadaveric specimens.
7.5 Discussion
The use of stochastic optimal control theory as conceptual tool towards understanding
neuromuscular behavior was proposed in, for example, (He, Levine & Loeb 1991), (Harris
& Wolpert 1998), (Todorov 2004). In that work, a stochastic optimal control framework
for systems with linear dynamics and control-dependent noise was used to understand
the variability profiles of reaching movements. The influential work by (Todorov 2004)
established the minimal intervention principle in the context of optimal control. The
minimal interven- tion principle was developed based on the characteristics of stochastic
optimal controllers for systems with multiplicative noise in the control signals.
The LQR and LQG optimal control methods have been mostly tested on linear dynam-ical
systems for modeling sen- sorimotor behavior; e.g, in reaching tasks, linear models
232
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 246 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | with sliding and surface constraints (Blemker & Delp 2005.). Several advances also allow representing muscles as volumetric en- tities with data extracted from imaging studies (Blemker & Delp 2005.) ,(S. S. Blemker & Delp 2007), and defining tendon paths as wrapping in a piecewise linear way around ellipses defining joint locations (R. Davoodi & Loeb 2003), (Delp & Loan 2007). The path of the musculotendon in these cases is defined based on knowledge of the anatomy. Sometimes, it may not be necessary to model the musculotendon paths but obtaining a mathematical expression for the moment arm (r) could suffice. The moment arm is often a function of joint angle and can be obtained by recording incremental tendon excursions (*s) and corresponding joint angle changes (*") in cadaveric specimens. 7.5 Discussion The use of stochastic optimal control theory as conceptual tool towards understanding neuromuscular behavior was proposed in, for example, (He, Levine & Loeb 1991), (Harris & Wolpert 1998), (Todorov 2004). In that work, a stochastic optimal control framework for systems with linear dynamics and control-dependent noise was used to understand the variability profiles of reaching movements. The influential work by (Todorov 2004) established the minimal intervention principle in the context of optimal control. The minimal interven- tion principle was developed based on the characteristics of stochastic optimal controllers for systems with multiplicative noise in the control signals. The LQR and LQG optimal control methods have been mostly tested on linear dynam-ical systems for modeling sen- sorimotor behavior; e.g, in reaching tasks, linear models 232 |
