TripleSolver: A Separate-Simultaneous-Separate Solving Framework for Dual-Robot Calibration

Calibrating unknown transformation relationships is crucial for achieving coordinated motion in dual-robot systems. This calibration process can be formulated by solving the transformation matrix equation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {AXB=YCZ}$</tex-math></inline-formula>. Existing separate approaches handle the rotation and translation components of this equation sequentially, which may suffer from error propagation. In contrast, simultaneous approaches optimize both components together but often encounter instability due to challenges in balancing their weights. To tackle these issues, this paper introduces <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TripleSolver</i>, a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">separate-simultaneous-separate</i> solving framework to address <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {AXB = YCZ}$</tex-math></inline-formula> through a three-stage process. First, the rotation and translation components are solved separately, yielding two sets of estimates. Second, the shared rotation parameters from these estimates are refined using simultaneous optimization with automatically calculated weights. Last, the remaining parameters are determined based on the refined rotation parameters. Comparative results against state-of-the-art methods indicate that the proposed framework offers efficient calibration with improved accuracy and robustness. Its implementation is available as open-source at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">http://github.com/MatthewJin001/SSS</uri>.