Planar bipedal locomotion control based on state discretization

In this paper, a new control method for a planar bipedal robot, which we call Graph-based Model Predictive Control, is proposed. This method makes use of a directed graph constructed on the state space of the robot. The vertices of the directed graph are called waypoints, and they serve as intermediate target states to compose complex motions of the robot. By simply tracing the directed edges of the graph, one can achieve Model Predictive Control over the waypoint set. Such a directed graph is pre-designed and stored into the controller’s memory to significantly reduce the computational effort required in real time. In addition, by constructing multiple directed graphs based on different objective functions, one can design multiple motions and switching trajectories among them in a uniform way. The proposed method is applied to variable-speed walking control of a bipedal walker on a two-dimensional plane, and its effectiveness is verified by numerical simulations.