MEASUREMENT OF ROBUSTNESS FOR BIPED LOCOMOTION USING A LINEARIZED POINCARE MAP

Many studies on control of dynamic biped walking have been done in the past two decades. While the biped dynamics is highly nonlinear, the s tability analysis, if done, is usually based on a linearized model. Th e validity of the linearized model may become questionable if the walk ing involves states that are too far away from the operating point. In this paper, an approach for evaluating the robustness based on the li nearized Poincare map is suggested and examined. The Poincare map is a useful tool to investigate the periodic motion of a dynamic system. U sing the Poincare map, one can study an associated discrete time map i nstead of studying the continuous time system directly. Investigation of stability of a periodic motion can be reduced to the study of the s tability of a fixed point of the Poincare map. The computational metho d that results in a measurement for evaluating the robustness of biped locomotion is developed. Our simulation study has verified that the s uggested measurement is a good indicator.