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 fixed walking rate for a planar, biped robot with one degree of underactuation. This note provides two additional control features: 1) the ability to compose such controllers to obtain walking at several discrete walking rates with guaranteed stability during the transitions; and 2) the ability to regulate the average walking rate to a continuum of values.