Optimal Motion Planning for Fast Pointing Tasks With Spherical Parallel Manipulators

摘要

Spherical parallel manipulators can be effectively used for the execution of pointing tasks provided that their functional redundancy is well exploited. The present letter shows how the dynamic behavior of parallel wrists can be enhanced by optimizing their posture through suitable performance indexes; the indexes used in this letter are based on the manipulator inertia matrix reduced to the mobile platform, which can be readily worked out from the total kinetic energy of the wrist. First, the redundancy is solved by finding, for each pointing direction, the posture leading to the best dynamic manipulation capacity. Then, a path is planned on the surface of a sphere by means of Bézier curves; in this case, the performance function of the optimization problem drives the platform through the spherical attitudes that grant the maximum angular accelerations along a useful direction. The theoretical results are verified in simulation for the three-CPU manipulator by means of inverse dynamic analyses performed in a multibody software environment; however, the developed methodology is of general use and this letter is aimed at showing how it can be applied to a whole class of spherical parallel robots.