A fast online gait planning method is proposed. Based on an approximate dynamical biped model whose mass is concentrated to COG, general solution of the equation of motion is analytically obtained. Dynamical constraint on the external reaction force due to the underactuation is resolved by boundary condition relaxation, namely, by admitting some error between the desired and actually reached state. It potentially creates responsive motion which requires strong instantaneous acceleration by accepting discontinuity of ZMP trajectory, which is designed as an exponential function. A semi-automatic continuous gait planning is also presented. It generates physically feasible referential trajectory of the whole-body only from the next desired foot placement. The validity of proposed is ensured through both simulations and experiments with a small anthropomorphic robot.
Sugihara et al. (Wed,) studied this question.