Further results on control of the compass gait biped

This paper continues our investigations into the passivity-based control of the compass gait biped. It was shown in [Spong, M.W., 1999] for the compass gait biped, and in [Spong, M.W., and Bullo, F., 2002] for the general case, that a passive limit cycle for a given constant slope can be made slope invariant via potential energy shaping control. In this paper we consider the application of total energy shaping to this problem. Using a control law that shapes the total energy of the biped we are able to influence both the exponential rate of convergence to the limit cycle and its basin of attraction. This increases robustness and variation in the ground slope. As illustrations we show stable walking gaits both in the presence of external disturbances and on varying slopes that do not exist without the total energy shaping control.