Mixed Logic Dynamical Modeling and On Line Optimal Control of Biped Robot

Abstract

In this study, we proposed a MLD modeling and MPC approach for the on line optimization of biped motion. Such modeling approach possesses advantage that it describes both the continuous dynamics and the impact event within one framework, consequently it provides a unified approach for mathematical, numerical and control investigations. This MLD model allows model predictive control (MPC) and subsequent stability from the numerical analysis viewpoints, by powerful MIQP solver. Hence the biped robot can be on line controlled without pre-defined trajectory. The optimal solution corresponds to the optimal gait for current environment and control requirement. The feasibility of the MLD model based predictive control is shown by simulations. How to effectively decrease the computation time in order to realize the real time implementation is an important research topic left to future. Finally, we mention that a human uses his predictive function based on an internal model together with his feedback function for motion, which is considered as a motor control model of a cerebellum (Kawato, 1999). Stimulated by this, a general theoretical study for motion control of hybrid systems is reported in (Yin & Hosoe, 2004) which is based on the MLD model of a hybrid system. We are further developing this theory to help the biped motion synthesis and control. It will be also useful for the realization of complex motion of other bio-mimetic robots.