{"ID":2852973,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.18063","arxiv_id":"2510.18063","title":"MOFM-Nav: On-Manifold Ordering-Flexible Multi-Robot Navigation","abstract":"This paper addresses the problem of multi-robot navigation where robots maneuver on a desired \\(m\\)-dimensional (i.e., \\(m\\)-D) manifold in the $n$-dimensional Euclidean space, and maintain a {\\it flexible spatial ordering}. We consider $ m\\geq 2$, and the multi-robot coordination is achieved via non-Euclidean metrics. However, since the $m$-D manifold can be characterized by the zero-level sets of $n$ implicit functions, the last $m$ entries of the GVF propagation term become {\\it strongly coupled} with the partial derivatives of these functions if the auxiliary vectors are not appropriately chosen. These couplings not only influence the on-manifold maneuvering of robots, but also pose significant challenges to the further design of the ordering-flexible coordination via non-Euclidean metrics. To tackle this issue, we first identify a feasible solution of auxiliary vectors such that the last $m$ entries of the propagation term are effectively decoupled to be the same constant. Then, we redesign the coordinated GVF (CGVF) algorithm to {\\it boost} the advantages of singularities elimination and global convergence by treating $m$ manifold parameters as additional $m$ virtual coordinates. Furthermore, we enable the on-manifold ordering-flexible motion coordination by allowing each robot to share $m$ virtual coordinates with its time-varying neighbors and a virtual target robot, which {\\it circumvents} the possible complex calculation if Euclidean metrics were used instead. Finally, we showcase the proposed algorithm's flexibility, adaptability, and robustness through extensive simulations with different initial positions, higher-dimensional manifolds, and robot breakdown, respectively.","short_abstract":"This paper addresses the problem of multi-robot navigation where robots maneuver on a desired \\(m\\)-dimensional (i.e., \\(m\\)-D) manifold in the $n$-dimensional Euclidean space, and maintain a {\\it flexible spatial ordering}. We consider $ m\\geq 2$, and the multi-robot coordination is achieved via non-Euclidean metrics....","url_abs":"https://arxiv.org/abs/2510.18063","url_pdf":"https://arxiv.org/pdf/2510.18063v1","authors":"[\"Bin-Bin Hu\",\"Weijia Yao\",\"Ming Cao\"]","published":"2025-10-20T19:56:02Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}