Optimal control models of goal-oriented human locomotion

SIAM Journal on Control and Optimization

Volumn 50, Issue 1, 2012, Pages 147-170

  Chitour, Yacine ^a   Jean, Frédéric ^b   Mason, Paolo ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b ENSTA PARISTECH   (France)

Author keywords

Human locomotion; Inverse optimal control; Pontryagin maximum principle; Stable manifold theorem

Indexed keywords

ASYMPTOTIC BEHAVIORS; GOAL-ORIENTED; HUMAN LOCOMOTIONS; INVERSE OPTIMAL CONTROL; OPTIMAL CONTROL MODEL; OPTIMAL CONTROL PROBLEM; OPTIMAL SYNTHESIS; OPTIMAL TRAJECTORIES; STABLE MANIFOLD THEOREM; TARGET POINT;

ASYMPTOTIC ANALYSIS; DYNAMICAL SYSTEMS; MAXIMUM PRINCIPLE; OPTIMAL CONTROL SYSTEMS;

OPTIMIZATION;

EID: 84858633134     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/100799344     Document Type: Article

References (16)

1. G. Arechavaleta, J.-P. Laumond, H. Hicheur, and A. Berthoz, Optimizing principles underlying the shape of trajectories in goal oriented locomotion for humans, in Proceedings of the 6th IEEE-RAS International Conference on Humanoid Robots, (Genoa, Italy), IEEE Press, Piscataway, NJ, 2006, pp. 131-136.
2. G. Arechavaleta, J.-P. Laumond, H. Hicheur, and A. Berthoz, On the nonholonomic nature of human locomotion, Autonomous Robots, 25 (2008), pp. 25-35.
3. G. Arechavaleta, J.-P. Laumond, H. Hicheur, and A. Berthoz, An optimality principle governing human walking, IEEE Trans. Robotics, 24 (2008), pp. 5-14. (Pubitemid 351411193)
4. A. V. Arutyunov and R. B. Vinter, A simple "finite approximations" proof of the Pontryagin maximum principle under reduced differentiability hypotheses, Set-Valued Anal., 12 (2004), pp. 5-24. (Pubitemid 39051050)
5. T. Bayen, Y Chitour, F. Jean, and P. Mason, Asymptotic analysis of an optimal control problem connected to the human locomotion, in Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (Shanghai), IEEE Press, Piscataway, NJ, 2009, pp. 2248-2253.
6. B. Berret, C. Darlot, F. Jean, T. Pozzo, C. Papaxanthis, and J.-P. Gauthier, The inactivation principle: Mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements, PLoS Comput. Biol., 4 (2008), e1000194.
7. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Stud. Appl. Math. 15, SIAM, Philadelphia, 1994.
8. H. Brezis, Analyse fonctionnelle, Collec. Math. Appl. Maîtrise, Masson, Paris, 1983.
9. J.-P. Gauthier, B. Berret, and F. Jean, A biomechanical inactivation principle, Proc. Steklov Inst. Math., 268 (2010), pp. 93-116.
10. R. Kalman, When is a linear control system optimal?, Trans. ASME, J. Basic Engrg., 86 (1964), pp. 51-60.
11. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia Math. Appl. 54, Cambridge University Press, Cambridge, UK, 1995.
12. E. B. Lee and L. Markus, Foundations of Optimal Control Theory, John Wiley & Sons, New York, 1967.
13. A. Y. Ng and S. Russell, Algorithms for inverse reinforcement learning, in Proceedings of the 17th International Conference on Machine Learning, Morgan Kaufmann, San Francisco, 2000, pp. 663-670.
14. L. Pontryagin, V. Boltyanskii, R. Gamkrelidze, and E. Mischenko, The Mathematical Theory of Optimal Processes, Wiley Interscience, New York, 1962.
15. E. Todorov, Optimal control theory, in Bayesian Brain: Probabilistic Approaches to Neural Coding, K. Doya et al. ed., MIT Press, Cambridge, MA, 2006, pp. 269-298.
16. E. Trélat, Contrôle optimal. Théorie and applications, Mathématiques Concr. Vuibert, Paris, 2005.