Constrained-optimal balance regulation of a biped with toe-joint using model predictive control

In this paper standing balance control of a biped with toe-joint is presented. The model consists of an inverted pendulum as the upper body and the foot contains toe-joint. The biped is actuated by two torques at ankle-joint and toe-joint to regulate the upper body in upright position. To model the interaction between foot and the ground, configuration constraints are defined and utilized. To stabilize the biped around upright position model predictive control (MPC) is implemented by which the constraints can be incorporate to the optimal control algorithm properly. Simulations show that the controller has a good capability of stabilization. In addition by comparison with a similar flat foot bipedal model without toe-joint in literature, the present model displays better performance and enhances the actuator demand.