Variational Collision Integrators and Optimal Control

Pekarek, D. and J. E. Marsden

Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS), (2008)


This paper presents a methodology for generating locally optimal control policies for mechanical systems that undergo collisions at point contacts. Principles of nonsmooth mechanics for rigid bodies are used in both continuous and discrete time, and provide impact models for a variety of collision behaviors. The discrete Euler-Lagrange (DEL) equations that follow from the discrete time analyses yield variational integration schemes for the different impact models. These DEL equations play a pivotal role in the method of Discrete Mechanics and Optimal Control (DMOC), which generates locally optimal control policies as the solution to equality constrained nonlinear optimization problems. The DMOC method is demonstrated on a 4-link planar walking robot model, generating locally optimal periodic walking gaits.