Generation of the optimal trajectory for the biped robot

This paper proposes the methods of generation of the energy-efficient trajectory and the centroid trajectory for the biped robot. Based on the function approximation method, the energy-efficient trajectory between the initial state and the terminal state is generated by converting minimization of energy consuming to minimization of input torques. Reducing the biped robot to an inverted pendulum, the relationship between the energy and the centroid motion for the simplified model is analyzed. And the switch conditions for the stance leg are analyzed too. Then the continuous centriod trajectory can be obtained to avoid the forward or backward falling. Simulation results show that the methods proposed in this paper are valid.