Modeling, control and simulation of upward jump of a biped

Abstract

This paper explores the vertical upward jumping of a planar biped. The jumping process is decomposed into the crouching phase, the thrust in the knees, the flight phase, the touchdown, and the straightening up movement of the biped. A mathematical model for this kind of jump of the biped is developed. Torques are applied in the hip and knee joints. The degree of underactuation of the mechanism is equal to one in the support phase and to three in the flight phase. The control algorithm is designed to ensure the jump of the biped. This algorithm is such that the center of mass of the mechanism is always placed on the same vertical line. The biped touches the ground in the same place where it starts from. The synthesis of the jumping process is supported by simulations which give consistent results with human data from existing biomechanical literature. Furthermore, the stick diagram of the jump derived from these simulation results seems natural for the human jumping. The problem of energy recovery is considered for the jumping of the biped by using springs in the hip and knee joints. The springs have an influence to minimize the mechanical energy consumed by the drives in the hip and knee joints. The springs in the knees help to increase the lifting of the bipedal mechanism.