Controlled Recurrence of a Biped with Torso
This work addresses stability control for hybrid systems like biped robots, but the method is an extension of prior work and the demonstration is on a simplified model.
The authors extend a symbolic reachability method to control stability in hybrid systems with guard conditions and state resets, and demonstrate it on a 6-state biped robot with a PD controller, ensuring the robot's state returns to a region R after each footstep.
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.