Control of the Passive-Dynamic Locomotion of the Compass-Gait Biped Robot

This paper discusses a stabilization method for the passive dynamic walking (PDW) of the compass-gait biped robot using an explicit analytical classical expression of the controlled Poincaré map in order to control its passive gaits. A linearization method is used to cast the problem from the impulsive hybrid nonlinear dynamics into the linear dynamics around a desired one-periodic hybrid limit cycle of the PDW. Thus, using the first-order Taylor approximation, we design an explicit expression of the controlled Poincaré map. In order to control the passive gaits, we develop first the linearized Poincaré map obtained around the period-one fixed point. We adopt a state-feedback control law using the LMI approach to stabilize this fixed point. We present finally some simulation results to reveal the efficiency of the designed control law in the control of the passive-dynamic locomotion of the compass-gait biped robot.