Generating optimal trajectory of humanoid arm that minimizes torque variation using differential dynamic programming

This paper proposes an optimal control method to generate a minimum-torque change trajectory of humanoid arm by using a differential dynamic programming (DDP). Since DDP is a locally optimal feedback controller, the convergence is not guaranteed unless DDP starts with a good reference trajectory for high-dimensional nonlinear dynamical systems. The reference trajectory is generated by using the minimum-jerk trajectory method, and then the corresponding torque profile is obtained by using the computed-torque method. This reference trajectory is not optimal because it is solely based on the kinematics of the system. In the proposed method, the rate of torque change is used as control input in DDP to generate the optimal trajectory, which concurrently minimizes the torque variations and considers the dynamics of the system. The effectiveness of the proposed method is verified by computer simulations for generating the optimal trajectory of a 7 degrees-of-freedom (DOF) MyBot humanoid arm in Webots simulator.