Stability of biped robotic walking with frictional constraints

Tipping-over and slipping, which are related to zero moment point (ZMP) and frictional constraint respectively, are the two most common instability forms of biped robotic walking. Conventional criterion of stability is not sufficient in some cases, since it neglects frictional constraint or considers translational friction only. The goal of this paper is to fully address frictional constraints in biped walking and develop corresponding stability criteria. Frictional constraints for biped locomotion are first analyzed and then the method to obtain the closed-form solutions of the frictional force and moment for a biped robot with rectangular and circular feet is presented. The maximum frictional force and moment are calculated in the case of ZMP at the center of contact area. Experiments with a 6-degree of freedom active walking biped robot are conducted to verify the effectiveness of the stability analysis.