Trajectory planning of a parallel manipulator based on kinematic transmission property

In order to obtain smooth trajectory and real-time performance of micro-manipulation for micro-motion parallel manipulator, this paper presents a new smooth trajectory planning based on the kinematic transmission property. Under the requirement of high tracking precision, seven-degree B-spline is adopted to interpolate poses of the micro-motion parallel manipulator in Cartesian space, which will make the velocities, accelerations and jerks bounded and continuous. Moreover, the start-end velocities, the start-end accelerations and the start-end jerks are configurable based on the seven-degree B-spline. In order to ensure that the planned trajectory is the optimal, an objective function containing accumulated jerk based on the kinematic transmission property is considered. Then, sequential quadratic programming method is adopted to obtain the optimal smooth trajectory based on the good kinematic transmission property, which can meet the kinematic constraints. Simulations and experiments show that the planning trajectories based on the proposed method have the advantages of continuous and small accumulated jerk. Furthermore, the proposed method can decrease tracking errors of the trajectories more effectively than the cubic spline.