Symmetric Walking Control: Invariance and Global Stability

This paper first presents a novel control strategy for periodic motion control based on a Hamiltonian system. According to the strategy, hybrid symmetric orbits (ideal walking gaits) are explored using reversal symmetry of the Hamiltonian system. Then, an invariance controller, a Symmetric Walking Controller, is derived systematically to distribute the symmetric orbits densely throughout the entire phase space. Finally, a new robust walking speed controller is formulated based on the passivity of the controlled system. Consequently, solutions starting from any point globally converge to a stable limit cycle having a desired energy level. The controller has strong passivity and robustness, thereby rendering it capable of using external disturbances as energy for walking propulsion. It requires no model parameters and can be implemented in a very small program size. Furthermore, it is applicable to any biped robot without major modification. In this report, the effectiveness of this controller is proved mathematically, validated numerically, and confirmed experimentally.