Globally Optimal Inverse Kinematics as a Non-Convex Quadratically Constrained Quadratic Program

We show how to compute globally optimal solutions to inverse kinematics by formulating the problem as a non-convex quadratically constrained quadratic program. Our approach makes solving inverse kinematics instances of generic redundant manipulators feasible. We demonstrate the performance on randomly generated designs and real-world robots with up to ten revolute joints. The same technique can be used for manipulator design by introducing kinematic parameters as variables.