Control of a Four-Link Biped in a Back Somersault Maneuver

A back somersault maneuver is studied for a four-link planar biped by a digital computer simulation. The maneuver consists of the following. 1) The takeoff phase: the system is in contact with the ground, and the ground reaction forces are instrumental in propelling the system in the air with appropriate position angles and angular velocities. 2) The flight phase: this is the airborne phase of motion for the system. The motion in this phase is governed by the trajectory of the center of gravity and the conservation of angular momentum. 3) The landing phase: in this phase the biped reestablishes a point of contact with the ground. The contact is such that impulsive forces are minimum. The kinetic energy of the system is dissipated, and a final vertical standing stance is achieved. Two control strategies are proposed. In the takeoff and landing phases a feedback strategy is needed. The airborne phase is ballistic, and an open-loop control strategy is sufficient. In all three phases of motion the biped model follows a set of desired trajectories which are approximations of a gymnast's performance. Digital computer simulations are presented to illustrate the motions and the effectiveness of the control strategies.