A necessary and sufficient condition for conservation of angular momentum at foot strike during passive dynamic walking

Legged robots can walk stably down slopes without any actuation or control. The locomotion is called passive dynamic walking. Its dynamics at foot strike are governed by impact forces. The impulsive dynamics have been modelled in several approaches, where all the approaches assume that the stance leg instantaneously loses contact with the ground at foot strike. The loss-of-contact assumption has been introduced so as to guarantee conservation of angular momentum at foot strike; however, it is shown in this paper that the loss-of-contact assumption is neither necessary nor sufficient for that purpose. This paper provides a necessary and sufficient condition for conservation of angular momentum at foot strike in a modelling framework for multibody dynamics with impact. A compass-like biped robot is considered in this paper. Its impulsive dynamics are modelled by the relationship between impact forces and change of momentum with constraints. A necessary and sufficient condition for conservation of angular momentum is derived by examining the validity of foot velocities and impact forces in the impulsive model.