Trajectory Planning Method for Fracture Reduction of Parallel Robots Based on DMP and APF

The operation of tibial fracture reduction is complex and may involve risks of iatrogenic injuries due to fatigue or insufficient experience of the surgeon. Therefore, this paper proposes a tibial fracture reduction trajectory planning method based on dynamic movement primitives (DMP) and artificial potential fields (APF) to avoid the collision between the distal and proximal fracture fragments during the reduction process and to achieve safe tibial fracture reduction. First, DMP is used to learn the motion characteristics from the orientation demonstration trajectory, generating a new orientation trajectory for the distal fracture fragment. Second, DMP with an obstacle avoidance mechanism based on APF is used to learn the motion characteristics from the position demonstration trajectory, generating a position trajectory for the distal fracture fragment with obstacle avoidance capability. Then, the position trajectory and the orientation trajectory are combined synchronously to form the reduction trajectory. Finally the aforementioned trajectory is optimized to minimize both the the sum of squared velocities and the the sum of squared accelerations of all branch chains under specific constraints, enabling the robot to perform a smooth fracture reduction. Simulations and experiments are conducted, and the results demonstrate that the proposed method can effectively perform trajectory planning for tibial fracture reduction. The proposed method can provide technical references for the trajectory planning and obstacle avoidance problems of orthopedic robots in unstructured environments.