A real-time optimal energy-saving walking pattern generator based on gradient descent method and linear quadratic control

Many recent approaches have successfully generated a stable walking pattern for biped robots, but discussions about its optimization are relatively few. In this paper, a Center of Gravity (COG) trajectory optimization method is proposed to minimize the cost function of joint torque, joint limit, and joint speed limit. The linear quadratic control-based inverted pendulum controller optimizes the COG trajectories in sagittal and lateral directions with the COG height trajectory. The COG height trajectory is optimized by finding the derivative of the cost function with respect to the COG height offline. Then the proposed walking pattern generator builds the COG height trajectory database of different walking steps for online connection of a walking pattern. The walking pattern generator is verified by experiments and simulations of different step cycles with our humanoid robot, NINO, and it can clearly reduce the required joint torque of the robot while walking. In addition, compared with the fixed COG height trajectory, the energy consumption is reduced by 14% from the experimental results. Thus, the method succeeds in generating a more energy-saving walking pattern.