Switching and PI Control of Walking Motions of Planar Biped Walkers

A companion paper has addressed the problem of designing controllers that induce exponentially stable, periodic walking motions at a given fixed walking rate for a planar, biped robot with one degree of underactuation in single support. This note provides two additional control features: (i) the ability to compose such controllers in order to obtain walking at several discrete walking rates with guaranteed stability during the transitions; (ii) the ability to regulate the robot's average walking rate to a continuum of values. Taken together, these two features a#ord the construction of a feedback controller that takes the robot from a standing position, through a range of walking rates, and back to a standing position, while providing local stabilization and disturbance rejection. The key technical tool is the hybrid zero dynamics of the robot model