ハミルトン力学系の対称軌道族と2足歩行の大域的歩容生成への応用

抄録

This paper proposes a novel walking gait generation for a double-pendulum-like biped walking model based on the family of the symmetric orbits. By introducing an involution R associated with the leg switching map, the flow of the saddle-center dynamics of the uncontrolled pendulum possesses the time-reversal symmetry with respect to R, and the conjunction of the flow and R forms a family of symmetric orbits parameterized by the orbital energy and the stride bound. The invariant manifold of the family of symmetric orbits is obtained numerically or approximately using a perturbation method. By constraining the solution onto the invariant manifold using the control inputs, stable walking gaits are generated in a semi-global manner. Based on the passivity of the closed-loop system, a robust speed-controlled walking is achieved in a very simple way.