Constraint augmented differential dynamic programming for humanoid robot automatic falling recovery

The complex mechanical structure and multiple degrees of freedom (DoF) make the humanoid robot system unstable and nonlinear. The humanoid robot may fall accidentally while performing tasks due to these inherent properties. For this reason, research on the automatic falling recovery of humanoid robots is a very useful project. Fall recovery motion planning for humanoid robots is a complex, whole-body, multiple-contact and nonlinear optimization problem. To address this challenge, the constraint augmented differential dynamic programming (CA-DDP) algorithm is proposed in our work to enable the humanoid robot to recover from arbitrary fall posture. Firstly, the collision dynamics constraint based on the Karush–Kuhn–Tucker (KKT) condition is formulated to satisfy the robot's dynamics constraint and absolute static stability requirement of contact points. Then, an improved derivation process is developed to modify the action-value function and its gradient and Hessian matrices during the backward pass of CA-DDP algorithm. Through CA-DDP iterations, the optimal control torque and joint trajectories are obtained with a faster convergence speed. Finally, the effectiveness of the proposed CA-DDP is verified through simulation and real-world experiments on a BHR-FCR humanoid robot automatically falling recovery. With various arbitrary initial falling postures and CA-DDP iterations, the optimal solutions enable the BHR-FCR robot to achieve the desired recovery state with over 95% recovery accuracy and computation time under 50 s. Moreover, the BHR-FCR robot successfully achieves state recovery on a flat floor, grass ground and soft cushion in real-world experiments.