Optimal gait generation for a one-legged robot based on variational symmetry of Hamiltonian systems

This paper proposes a novel framework to generate an optimal gait trajectory with respect to the energy consumption for a planar one-legged robot via iterative learning control. The proposed method is based on the symmetric property of the variational systems of Hamiltonian systems called variational symmetry. This technique allows one to obtain solutions of a class of optimal control problems without using precise knowledge of the plant system. Furthermore, its application to the robot produces a passive gait trajectory with zero control input. Some numerical examples demonstrate the effectiveness of the proposed method.