On the stability of biped with point foot-ground contact

Abstract

Exploiting recent results based on differential geometric control theory, it is shown in the paper that, by suitable choice of generalized coordinates, the biped dynamics may be represented by an almost linear model. This representation enables efficient use of the well known classical control methodology to define stable control. This approach is based on a complete 2-DOF and 3-DOF nonlinear model representation of robot dynamics over operative envelope without additional approximation. In this presentation, extensive use of mathematical terminology is avoided and physical interpretations of variables is proposed.