Augmented Differential Dynamic Programming for Humanoid Robot Flipping Motion Optimization

Differential Dynamic Programming (DDP) is an efficient tool for non-linear optimal problems. And DDP shows a characteristic of fast convergence. However, the traditional DDP cannot solve the nonlinear constraints. Therefore, an augmented differential dynamic programming method is proposed in this paper for trajectory optimization of humanoid robot motion planning. The flipping motion is adopted in our work. The continuous dynamic model and collision dynamic model are constructed, in which the reset map of the collision dynamics model calculates the instantaneous velocity and acceleration change before and after the collision. Moreover, the Augmented Lagrangian (AL) method is adopted in DDP to deal with equality constraints and inequality constraints. After n times of augmented DDP iterations, the optimal flipping motion trajectory is obtained. The simulation experiments on the BHR-FCR humanoid robot show that the proposed approach has the ability to solve nonlinear constraint optimal problems.