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The Inverse Kinematics (IK) problem is to nd robot control parameters tobring it into the desired position under the kinematics and collisionconstraints. We present a global solution to the optimal IK problem for ageneral serial 7DOF manipulator with revolute joints and a quadratic polynomialobjective function. We show that the kinematic constraints due to rotations canall be generated by second-degree polynomials. This is important since itsignicantly simplies further step where we nd the optimal solution by Lasserrerelaxations of non-convex polynomial systems. We demonstrate that the secondrelaxation is sucient to solve the 7DOF IK problem. Our approach is certiablyglobally optimal. We demonstrate the method on the 7DOF KUKA LBR IIWAmanipulator and show that we are able to compute the optimal IK or certifyin-feasibility in 99 % tested poses.

Globally Optimal Solution to Inverse Kinematics of 7DOF Serial Manipulator