Limit cycle walker push recovery based on a receding horizon control scheme

The capability of limit cycle walking in external disturbance rejection is still a relatively unexplored field of study in comparison with zero moment point based walking, whereas the motions achievable by limit cycle walkers are highly efficient and natural looking. In this paper, a balance recovery controller is implemented for a limit cycle walker subjected to an impulsive push based on a receding horizon control scheme. The biped robot model is considered as an under-actuated hybrid planar system with five degrees of freedom having two actuators, which experiences an impulsive push event on its torso. The main idea of push recovery consists in the choice of particular trajectories for the directly controlled degrees of freedom, for which the dynamics of the indirectly controlled degrees of freedom (un-actuated coordinates) of the system tracks a desired trajectory. Particular trajectories are chosen based on a low dimensional online constrained optimization. A discrete-time feedback controller is implemented to track the obtained trajectory and control the whole system to sustain its stable cyclic walking after push. Several simulations have been done considering disturbances exerted during the walking. The results demonstrate the effectiveness of the scheme in recovery of small and large pushes occurring in single and double support phases of walking.