Minimum-Jerk Trajectory Planning of a 3-DOF Translational Parallel Manipulator

Since jerk-limiting is universally recognized to possess the advantages of reducing residual vibration and improving accuracy, this paper utilizes a minimum-jerk trajectory planning algorithm in trajectory planning of a three degree-of-freedom 3-Prismatic-Universal-Universal (3PUU) translational parallel manipulator. The trajectory execution time is set to fixed time duration. The sequence of joint positions are derived by a series of predefined via-points in Cartesian space through kinematic inversion. In order to generate a trajectory featuring great continuity and fine smoothness, a piecewise fifth-order polynomial is used to interpolate the joint position series and generate a smooth trajectory characterized by continuous velocity, acceleration, and jerk. The minimum jerk trajectory planning algorithm, which minimizes the maximum of the absolute value of joints’ jerk, is actually a constrained minimax optimization problem. Subjecting to the specified limitations of kinematic constraints, this multi-variables constrained optimization problem is solved by the sequential quadratic programming (SQP) strategy. The simulated results demonstrate that this trajectory planning algorithm for the designed parallel manipulator is effective and feasible.