Model Predictive Control and Stability Analysis of a Standing Biped with Toe-Joint

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. To assess stability of system and to find domain of attraction of the fixed point, concept of Lyapunov exponents is utilized. Using the proposed control and stability analysis, we studied the effect of toe-joint in improving the stability of the biped and in decreasing actuator demand, necessary for stabilizing the system. In addition, effect of toe-joint is studied in improving domain of attraction of the stabilized fixed pint.