Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation

This article aims to present a minimum-jerk trajectory planning approach to address the smooth trajectory generation problem of 3-prismatic-universal-universal translational parallel kinematic manipulator. First, comprehensive kinematics and dynamics characteristics of this 3-prismatic-universal-universal parallel kinematic manipulator are analyzed by virtue of the accepted link Jacobian matrices and proverbial virtual work principle. To satisfy indispensable continuity and smoothness requirements, the discretized piecewise quintic polynomials are employed to interpolate the sequence of joints' angular position knots which are transformed from these predefined via-points in Cartesian space. Furthermore, the trajectory planning problem is directly converted into a constrained nonlinear multi-variables optimization problem of which objective function is to minimize the maximum of the joints' angular jerk throughout the whole trajectory. Finally, two typical application simulations using the reliable sequential quadratic programming algorithm demonstrate that this proposed minimum-jerk trajectory planning approach is of explicit feasibility and appreciable effectiveness.