On Inverse Optimal Control Problems of Human Locomotion: Stability and Robustness of the Minimizers
- 126 Downloads
In recent papers, models of human locomotion by means of optimal control problems have been proposed. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem whose cost has to be determined. The purpose of the present paper is to analyze the class of optimal control problems defined in this way. We prove strong convergence results for their solutions, on the one hand, for perturbations of the initial and final points (stability), and, on the other hand, for perturbations of the cost (robustness).
KeywordsOptimal Control Problem Uniform Convergence Linear Matrix Inequality Optimal Trajectory Humanoid Robot
Unable to display preview. Download preview PDF.
- 1.A. A. Agrachev and Yu. L. Sachkov, “Control theory from the geometric viewpoint,” in: Encyclopaedia of Mathematical Sciences, 87, Springer-Verlag, Berlin (2004).Google Scholar
- 2.G. Arechavaleta, J.-P. Laumond, H. Hicheur, and A. Berthoz, “Optimizing principles underlying the shape of trajectories in goal oriented locomotion for humans,” in: IEEE/RAS International Conference on Humanoid Robots, Genoa (2006).Google Scholar
- 6.T. Bayen, Y. Chitour, F. Jean, and P. Mason, “Asymptotic analysis of an optimal control problem connected to the human locomotion,” in: Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai (2009).Google Scholar
- 8.B. Bonnard and M. Chyba, “Singular trajectories and their role in control theory,” in: Math. Appl., 40, Springer-Verlag, Berlin (2003).Google Scholar
- 12.C. Darlot, J.-P. Gauthier, F. Jean, C. Papaxanthis, and T. Pozzo, “The inactivation principle: Mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements,” PLoS Comput. Biol., 4, No. 10 (2008).Google Scholar
- 15.A. Y. Ng and S. Russell, “Algorithms for inverse reinforcement learning,” in: Proc. 17th International Conf. on Machine Learning, Morgan Kaufmann, San Francisco (2000), pp. 663–670.Google Scholar
- 17.E. Todorov, “Optimal control theory,” in: Bayesian Brain: Probabilistic Approaches to Neural Coding (K. Doya et al., eds.), MIT Press, Cambridge (2006), pp. 269–298.Google Scholar