Biped Gait Generation and Control Based on Mechanical Energy Constraint

Realization of natural and energy-efficient dynamic walking has come to be one of the main subjects in the research area of robotic biped locomotion. Recently, many approaches considering the efficiency of gait have been proposed and McGeer’s passive dynamic walking (McGeer, 1990) has been attracted as a clue to elucidate the mechanism of efficient dynamic walking. Passive dynamic walkers can walk down a gentle slope without any external actuation. Although the robot's mechanical energy is dissipated by heel-strike at the stance-leg exchange instant, the gravity potential automatically restores it during the single-support phase in the case of passive dynamic walking on a slope and thus the dynamic walking is continued. If we regard the passive dynamic walking as an active one on a level, it is found that the robot is propelled by the small gravity in the walking direction and the mechanical energy is monotonically restored by the virtual control inputs representing the small gravity effect. Restoration of the mechanical energy dissipated by heel-strike is a necessary condition common to dynamic gait generations from the mathematical point of view, and efficient active dynamic walking should be realized by reproducing this mechanism on a level. Mechanical systems satisfy a relation between the control inputs and the mechanical energy, the power-input for the system is equal to the time-derivative of mechanical energy, and we introduce a constraint condition so that the time-change rate of mechanical energy is kept positive constant. The dynamic gait generation is then specified by a simple redundant equation including the control inputs as the indeterminate variables and yields a problem of how to solve the equation in real-time. The ankle and the hip joint torques are determined according to the phases of cycle based on the pre-planned priority. The zero moment point (Vukobuatovi & Stepanenko, 1972) can be easily manipulated by adjusting the anklejoint torque, and the hip-joint torque in this case is secondly determined to satisfy the desired energy constraint condition with the pre-determined ankle-joint torque. Several solutions considering the zero moment point condition are proposed, and it is shown that a stable dynamic gait is easily generated without using any pre-designed desired trajectories. The typical gait is analyzed by numerical simulations, and an experimental case study using a simple machine is performed to show the validity of the proposed method.