Effect of ZMP relaxation on time optimal problem of a walking biped

Human walking is a complex locomotion that benefits from falling like attribute to perform forward movement. "Zero Moment Point" method (ZMP) is one of the most simple and practical criteria in the field of bipedal walking to assure the dynamic balance. However, this method is highly conservative and bipedal walking according to this criterion is not optimal in comparison with actual human walking. Hence, in this paper, the necessity of considering ZMP criterion in a time optimal problem of walking (which considers natural pattern of human motion for solving the problem), is investigated by relaxation of ZMP. It is assumed that the supporting polygon to encircle the ZMP is expanded virtually step by step. The necessity of enforcing the ZMP criterion to solve such a problem is strongly questioned because of the behavior of the system under relaxation of ZMP and the significant effect of relaxation on the highest achievable speed of walking.