Heel-strike and toe-off walking of humanoid robot using quadratic programming considering the foot contact states

Abstract

Heel-strike and toe-off (heel-toe) walking has been studied to increase step length, reduce the torque of the leg joints, or make robots walk similarly to humans. To realize heel-toe walking, it is necessary to determine the foot angle and ensure contact between the ground and the heel and toe. The foot angle for heel-toe walking can be analytically calculated considering the position of the center of mass (CoM) before the foot lands or rises. Therefore, the trajectory of the CoM of one cycle of walking must be known in advance. However, this method cannot be easily incorporated with model predictive control (MPC) to generate the trajectory of CoM in real time. This paper proposes a heel-toe walking method that can be used with the CoM trajectory generated using the MPC scheme. The CoM trajectory generation method that reduced the velocity fluctuation using MPC, which was proposed in a previous study, was used. The stability of the MPC scheme is proved in this paper. The quadratic programming is used to generate the heel-toe walking by considering the foot contact states as the constraints. The increase in step length and the decrease in singularity occurrence due to heel-toe walking were compared and analyzed in the simulation. The experiment verified the proposed heel-toe method.