Constrained Orientation Control of a Spherical Parallel Manipulator via Online Convex Optimization

This paper introduces a new framework for the closed-loop orientation control of spherical parallel manipulators (SPMs) based on the online solution of a convex optimization problem. The aim of solving a constrained optimization problem is to define a reference position for the SPM that remains as close as possible to the ideal reference (i.e., the one for which the top mobile platform has the desired orientation), at the same time keeping the SPM within the set of configurations in which collisions between links and singular configurations are avoided (the so-called feasible workspace). The proposed approach relies on a recently introduced method for obtaining unique inverse kinematics for SPMs and a newly proposed method for generating an approximation of the feasible workspace suitable for fast online optimization. The proposed control scheme is experimentally tested on an Agile Wrist SPM prototype, confirming the performance expected from the theoretical formulation.