Orthogonal dual tensor method for solving the AX = XB sensor calibration problem

•A new approach for solving the AX = XB sensor calibration problem•Isomorphism between SE3 and the orthogonal dual tensors set SO̲3•Closed-form simultaneous solutions for data recorded from any number of displacements•The new solutions are free of coordinates and can easily be put into practice.•Implementation algorithms are presented and numerical results are discussed.

The AX = XB sensor calibration problem is very important in multiple fields such as robotics, computer vision or machine vision. In this type of problem, A and B are parameterizations of rigid body motions, while X is an unknown transformation. This research proposes a new approach for solving the AX = XB sensor calibration problem by mapping the SE3 classic formulation into an orthogonal dual tensors set SO̲3representation. Using an isomorphism between SE3 and SO̲3, together with a set of properties from SO̲3, we formulate closed-form simultaneous solutions for data recorded from any number of displacements. These solutions are free of coordinates and can easily be put into practice. Implementation algorithms are presented and numerical results are discussed in order to evaluate the performance of the proposed solutions.