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Jinha, A., Ait-Haddou, R., Binding, P. & Herzog, W. (2006), ‘Antagonistic activity of
one-joint muscles in three-dimensions using non-linear optimisation’, Mathematical
Biosciences 202(1), 57 – 70.
Kalman, R. (1964), ‘When is a linear control system optimal?’, ASME Transactions,
Journal of Basic Engineering 86, 51–60.
Kappen, H. J. (2005a), ‘Linear theory for control of nonlinear stochastic systems’, Phys.
Rev. Lett. 95, 200201.
Kappen, H. J. (2005b), ‘Path integrals and symmetry breaking for optimal control theory’,
Journal of Statistical Mechanics: Theory and Experiment (11), P11011.
Kappen, H. J. (2007), An introduction to stochastic control theory, path integrals and
reinforcement learning, in J. Marro, P. L. Garrido & J. J. Torres, eds, ‘Cooperative
Behavior in Neural Systems’, Vol. 887 of American Institute of Physics Conference
Series, pp. 149–181.
Karatzas, I. & Shreve, S. E. (1991), Brownian Motion and Stochastic Calculus (Graduate
Texts in Mathematics), 2nd edn, Springer.
Kober, J. & Peters, J. (2009), Learning motor primitives in robotics, in D. Schuurmans,
J. Benigio & D. Koller, eds, ‘Advances in Neural Information Processing Systems
21’, Cambridge, MA: MIT Press, Vancouver, BC, Dec. 8-11.
Lau, A. W. C. & Lubensky, T. C. (2007), ‘State-dependent diffusion: thermodynamic
consistency and its path integral formulation’.
URL: http://arxiv.org/abs/0707.2234
Leitmann, G. (1981), The Calculus Of Variations and Optimal Control, Plenum Press,
New York.
Li, W. & Todorov, E. (2004), Iterative linear quadratic regulator design for nonlinear
biological movement systems, in ‘ICINCO (1)’, pp. 222–229.
Li, W. & Todorov, E. (2006), An iterative optimal control and estimation design for
nonlinear stochastic system, in ‘Decision and Control, 2006 45th IEEE Conference
on’, pp. 3242 –3247.
Morimoto, J. & Atkeson, C. (2002), Minimax differential dynamic programming: An ap-plication
to robust biped walking, in ‘In Advances in Neural Information Processing
Systems 15’, MIT Press, Cambridge, MA.
Morimoto, J. & Doya, K. (2005), ‘Robust reinforcement learning’, Neural Comput. 17(2).
Murray, R. M., Li, Z. & Sastry, S. S. (1994), A Mathematical Introduction to Robotic
Manipulation, 1 edn, CRC.
Mussa-Ivaldi, A., Hogan, N. & Bizzi, E. (1982), ‘Neural, mechanical, and geometric
factors subserving arm posture in humans’, Journal of Neuroscience 5, 331–348.
271
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 285 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | Jinha, A., Ait-Haddou, R., Binding, P. & Herzog, W. (2006), ‘Antagonistic activity of one-joint muscles in three-dimensions using non-linear optimisation’, Mathematical Biosciences 202(1), 57 – 70. Kalman, R. (1964), ‘When is a linear control system optimal?’, ASME Transactions, Journal of Basic Engineering 86, 51–60. Kappen, H. J. (2005a), ‘Linear theory for control of nonlinear stochastic systems’, Phys. Rev. Lett. 95, 200201. Kappen, H. J. (2005b), ‘Path integrals and symmetry breaking for optimal control theory’, Journal of Statistical Mechanics: Theory and Experiment (11), P11011. Kappen, H. J. (2007), An introduction to stochastic control theory, path integrals and reinforcement learning, in J. Marro, P. L. Garrido & J. J. Torres, eds, ‘Cooperative Behavior in Neural Systems’, Vol. 887 of American Institute of Physics Conference Series, pp. 149–181. Karatzas, I. & Shreve, S. E. (1991), Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics), 2nd edn, Springer. Kober, J. & Peters, J. (2009), Learning motor primitives in robotics, in D. Schuurmans, J. Benigio & D. Koller, eds, ‘Advances in Neural Information Processing Systems 21’, Cambridge, MA: MIT Press, Vancouver, BC, Dec. 8-11. Lau, A. W. C. & Lubensky, T. C. (2007), ‘State-dependent diffusion: thermodynamic consistency and its path integral formulation’. URL: http://arxiv.org/abs/0707.2234 Leitmann, G. (1981), The Calculus Of Variations and Optimal Control, Plenum Press, New York. Li, W. & Todorov, E. (2004), Iterative linear quadratic regulator design for nonlinear biological movement systems, in ‘ICINCO (1)’, pp. 222–229. Li, W. & Todorov, E. (2006), An iterative optimal control and estimation design for nonlinear stochastic system, in ‘Decision and Control, 2006 45th IEEE Conference on’, pp. 3242 –3247. Morimoto, J. & Atkeson, C. (2002), Minimax differential dynamic programming: An ap-plication to robust biped walking, in ‘In Advances in Neural Information Processing Systems 15’, MIT Press, Cambridge, MA. Morimoto, J. & Doya, K. (2005), ‘Robust reinforcement learning’, Neural Comput. 17(2). Murray, R. M., Li, Z. & Sastry, S. S. (1994), A Mathematical Introduction to Robotic Manipulation, 1 edn, CRC. Mussa-Ivaldi, A., Hogan, N. & Bizzi, E. (1982), ‘Neural, mechanical, and geometric factors subserving arm posture in humans’, Journal of Neuroscience 5, 331–348. 271 |
