Determining the robot-to-robot 3D relative pose using combinations of range and bearing measurements: 14 Minimal problems and closed-form solutions to three of them

In this paper, we address the problem of motion-induced 3D extrinsic calibration based on different combinations of inter-robot measurements (i.e., distance and/or bearing observations from either or both of the two robots, recorded across multiple time steps) and ego-motion estimates. In particular, we focus on solving minimal problems where the unknown 6-degree-of-freedom transformation between the two robots is determined based on the minimum number of measurements necessary for finding a discrete set of, in general, multiple solutions. In order to address the very large number of possible combinations of inter-robot observations, we identify symmetries in these problems and use them to prove that any of the possible extrinsic robot-to-robot calibration problems can be solved based on the solution of only 14 (base) minimal problems. Finally, we derive analytical solutions to three of these base problems, and evaluate their performance through extensive simulations.