A Family of Symmetric Orbits of Hamiltonian Dynamical Systems and Its Application to Global Gait Generation for Biped Locomotion

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  • 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
  • ハミルトン リキガクケイ ノ タイショウ キドウゾク ト 2ソク ホコウ ノ タイイキテキ ホヨウ セイセイ エノ オウヨウ

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Abstract

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.

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