Trajectory Planning and Control of a Limit Cycle Walker Based on a Receding Horizon Control Scheme

Investigation of the aspects of Limit Cycle Walking (LCW) is still a relatively unexplored field of study in comparison whit ZMP based walking robots. In this paper, for a limit cycle walker, a receding horizon based controller is implemented. The biped robot model is considered an under-actuated hybrid planar system with five degrees of freedom having two actuators. The model is hybrid because of the impacts of the foot with ground. So, there is a discontinuity (jumps) in the states of the robot and controller should tackle this problem. The main idea of control design consists in the choice of particular trajectories for the directly controlled degree of freedoms (using receding horizon scheme) for which the dynamics of indirectly controlled DOF (un-actuated coordinate) of the system tracks a desired trajectory. The controller is implemented to control the whole system to sustain its stable cyclic walking. This approach avoids the need to use Poincare-like argumentation in the proof of stability of limit cycles. Simulation results demonstrate the effectiveness of the method.