A branch-and-bound based globally optimal solution to 2D multi-robot relative pose estimation problems

Abstract

The relative pose estimation problem is important for multi-robot systems when they execute a variety of tasks cooperatively, such as cooperative sensing, multi-robot search and rescue, formation control. The finding of reliable solutions to this problem is essential, however, algorithms that guarantee to provide globally optimal solutions are still in demand. In this paper, an alternative dimensionality reduced objective function is proposed for the planar ground multi-robot relative pose estimation problem, and a new branch-and-bound (BnB) based method is developed, through which initialization is not required and the globally optimal solution is guaranteed under arbitrary noise levels. We demonstrate that the globally optimal solutions obtained via the algorithm proposed in this paper are superior than that obtained by existing classic methods such as SE-Sync algorithm when noise levels are high. Moreover, the method proposed is simple and easy to implement.