Dynamic Optimization of Pointing Trajectories Exploiting the Redundancy of Parallel Wrists

Abstract

In this paper the functional redundancy of a spherical parallel manipulator performing a pointing task is exploited to optimize its posture upon minimizing dynamic index. A general method to derive the inertia matrix reduced to the mobile platform via screw theory is presented. This matrix encases geometrical and inertial information of all the bodies and it allows a simple computation of dynamic indices due to its feature of being dependent only on the pose of the robot. The indices are used to compute the objective function of the optimization problem, while the orientation of the pointing task constitutes the constraint equations. The posture-optimization is used as a redundancy-resolution and it is extended to any pointing direction. Optimal postural maps are obtained and then used to drive the optimal planning of pointing trajectories by using Bézier curves. To this aim, a higher level optimization problem than previous one is solved and inverse dynamic simulations are conducted to verify the results.