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This paper proposes a fast online gait planning method with vertical oscillation of body. It uses an analytic solution of equation of motion. In previous works, the analytic solution is calculated under the condition of constant height of COG(Center of Gravity). However these works cannot treat various motions involving vertical oscillation. Our method can treat COG vertical oscillation by Dynamical 3D-Symmetrization. This method symmetrizes dynamic characteristics of vertical motion and horizontal motion by constraining the vertical COG motion with a differential equation. Using this method we can solve for the equations of motion which involve COG vertical oscillation. This can allow the generation of various gaits such as running and dancing. The validity of proposed method is demonstrated on a simulated robot.
Terada et al. (Thu,) studied this question.