Posture Optimization of a Functionally Redundant Parallel Robot

The use of parallel-kinematics machines (PKM) for manufacturing operations is attractive because of the high accuracy they can ensure. These robots might perform a task that requires less degrees of freedom than those offered by the robot. This is the case of a robot facing a functional redundancy, which can be exploited to further increase the accuracy of the task, e.g. upon minimizing the condition number of the Jacobian matrix. A practical case study of a spherical manipulator performing a pointing task are reported, to show how posture-optimization can be used as a redundancy-resolution means for functionally redundant PKMs. The kinematics of the machine and the orientation of the pointing task is used to build, respectively, the objective function and the constraint equations. Sequential Quadratic Programming is conducted to solve the nonlinear constrained optimization problem and to find the end-effector pose corresponding to the robot posture of minimum condition number for every direction of a given pointing path. Lastly, the constrained problem is rewritten as one of unconstrained optimization of one objective function in one design variable.