Trajectory Optimization and Force Control with Modified Dynamic Movement Primitives under Curved Surface Constraints*

Dynamic Movement Primitives (DMPs) have been used extensively for trajectory planning due to robust against perturbations and excellent generalization performance. However, canonical discrete DMP could not generate right trajectories in three cases: the goal point is same as the start point, the goal point is close to the start point, and the goal point is changing across the start point. Moreover, when the original trajectory is on a curved surface, it is difficult to ensure that the generalized trajectory remains on this surface. In this paper, we propose a modified DMP method with the scaling factor and acceleration coupling term to solve the policy of the above learning problems using redundant robots. First, we introduce the adjusted cosine similarity as the performance index of the generalized curve. The cosine similarity is optimized to get the scaling factor. Then, by adding the acceleration coupling term to the original DMP, trajectory planning and force control are achieved on the curved surface. Finally, some simulations and experiments demonstrate the performance of our proposed method.