Synthesis of biped locomotion from view point of hybrid systems

The objective of this study is to analyze and synthesize a hybrid system for the systematic generation of biped locomotion. The structure, the manifold of initial state, and the selection of parameters of the hybrid system are addressed. The output of the hybrid system corresponds to the periodic trajectory of joint positions of the biped robot, which can be designed piecewise arbitrary smoothly. Comparing with the traditional numerical methods for gait planning, where the joint trajectory is approximated by polynomial, our proposal is systematic and analytic. The variation of the trajectory caused by perturbation of the initial state of the reference generator can be predicted. Then according to the nonlinear output regulation theory, the biped robot can be controlled to asymptotically track the periodic gait generated by the hybrid external system.