Hybrid Dynamical Modeling and Control of an Under-Actuated Limit Cycle Walker Subjected to Impulsive External Disturbances

The motions which are achievable by Limit Cycle Walkers are energetically efficient and natural looking. But their capability in external disturbance rejection is still an unexplored field of study in comparison with ZMP based walkers. In this paper a planar, under-actuated and hybrid Limit Cycle Walker with seven degrees of freedom (DOF) is considered. During walking, it is assumed that the robot is subjected to an impulsive external disturbance. First, some maps have been obtained to relate the states of the system just before and just after the impact events. Then, the control is done based on the determination of holonomic constraints for the event-based feedback controller. Several simulations have been done considering disturbances exerted during walking. The results showed the performance of the method in recovery of disturbances occurring in the sagittal plane in both anterior and posterior directions. Moreover, the results showed that the simulated motions can be characterized in terms of strategies observed in human for balance recovery against perturbations during walking.