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

• Published in: IEEE robotics and automation letters Vol. 9; no. 6; pp. 5998 - 6003
• Main Authors: Votroubek, Tomas, Kroupa, Tomas
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01-06-2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Convergence; Design parameters; End effectors; Inverse kinematics; Kinematics; Manipulators; Optimization; optimization and optimal control; Polynomials; Quadratic programming; redundant robots; Weight measurement
• ISSN: 2377-3766; 2377-3766
• DOI: 10.1109/LRA.2024.3398433

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.