Certification of Bottleneck Task Assignment with Shortest Path Criteria

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge shortest length paths between all and goal destinations. Determining exact in an environment obstacles is NP-hard however. In this paper, we investigate when polynomial-time approximations path search are sufficient to determine optimal assignment goals. particular, propose algorithm which accuracy planning iteratively increased. The approach provides certificate uncertainties on estimates become small enough guarantee optimality assignment. To end, apply results from sensitivity assuming upper lower bounds paths. We then provide methods find such by applying sampling-based planning. given feasible paths, obtained expanding sample set leveraging dispersion. demonstrate application proposed method multi-robot path-planning case study.