A Certifably Correct Algorithm for Generalized Robot-World and Hand-Eye Calibration
This work provides a reliable, general-purpose solution for automatic extrinsic sensor calibration, a fundamental problem in multi-sensor platforms, with theoretical guarantees and practical efficiency.
The paper introduces a fast and certifiably globally optimal algorithm for generalized robot-world and hand-eye calibration, supporting multiple sensors and monocular cameras without scale. It demonstrates superior performance over existing methods in simulations and real experiments, and provides identifiability criteria and global optimality guarantees.
Automatic extrinsic sensor calibration is a fundamental problem for multi-sensor platforms. Reliable and general-purpose solutions should be computationally efficient, require few assumptions about the structure of the sensing environment, and demand little effort from human operators. In this work, we introduce a fast and certifiably globally optimal algorithm for solving a generalized formulation of the robot-world and hand-eye calibration (RWHEC) problem. The formulation of RWHEC presented is "generalized" in that it supports the simultaneous estimation of multiple sensor and target poses, and permits the use of monocular cameras that, alone, are unable to measure the scale of their environments. In addition to demonstrating our method's superior performance over existing solutions through extensive simulated and real experiments, we derive novel identifiability criteria and establish a priori guarantees of global optimality for problem instances with bounded measurement errors. As part of our analysis, we propose a new constraint qualification for nonlinear programs with redundant constraints; this constraint qualification is of independent interest for establishing the exactness of SDP relaxations of QCQPs that have been tightened through the addition of redundant constraints. Finally, we provide a free and open-source implementation of our algorithms and experiments.