Minimal Energy Control of a Biped Robot with Numerical Methods and a Recursive Symbolic Dynamic Model

The problem of constructing a nonlinear controller for a biped robot optimal with respect to a minimal energy performance criteria is considered. The solution of this diicult, highly nonlinear problem is facilitated by the conjunction of several new developments in numerical optimal control and constrained recursive dynamic models for robotic systems. A 5-link biped model is used with the full dynamics and a uniform distribution of mass at each link. Contacts are modeled as inelastic, and the full dynamics together with the contact and collision forces are calculated eeciently using a recursive symbolic representation of the dynamics. The exibility and modularity of our dynamics algorithms allows one to construct reduced unconstrained models which do not suuer from integration diicul-ties. The numerical optimal control software used is powerful and quick enough to handle high dimensional nonlinear systems. The result of our experiment is a walking controller which is optimal with respect to a type of minimum energy performance.