Controlled Recurrence of a Biped with Torso

We have recently used a symbolic reachability method for controlling the stability of special hybrid systems called 'sampled switched systems'. We show here how the method can be extended in order to control the stability of more general hybrid systems with guard conditions and state resets. We illustrate the method through the example of a biped robot with 6 state variables, using a proportional-derivative (PD) controller. More specifically, we isolate a state region R such that, starting from a state located in R just after a footstep, the PD-control makes the robot state return to R at the end of the following footstep.