On Hand-Eye Calibration via On-Manifold Gauss-Newton Optimization

Perception of autonomous robotic systems is highly dependent on accurate data fusion of multiple heterogeneous sensors. However, to maximally exploit the advantages of such setups, sensor data fusion necessitates accurate extrinsic calibration. In this paper, we propose a novel derivation of the Gauss-Newton based iterative on-manifold batch solution to the hand-eye calibration problem. By adopting a special Euclidean group formulation of the objective function, we derive exact and approximate solutions and validate them via synthetic and real-world experiments. The results show that the accuracy of the proposed approximate solutions is on par with the exact solution and alternative on-manifold iterative solutions. Moreover, due to the near commutativity of the hand-eye problem in low noise scenarios, the proposed 0th order approximation achieves up to 4 times faster execution time, thus opening up practical possibilities of utilization in more complex optimization techniques.