Well-Connected Set and Its Application to Multi-Robot Path Planning
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914684896018432 |
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| author | Guo, Teng Yu, Jingjin |
| author_facet | Guo, Teng Yu, Jingjin |
| contents | Parking lots and autonomous warehouses for accommodating many vehicles/robots adopt designs in which the underlying graphs are \emph{well-connected} to simplify planning and reduce congestion. In this study, we formulate and delve into the \emph{largest well-connected set} (LWCS) problem and explore its applications in layout design for multi-robot path planning. Roughly speaking, a well-connected set over a connected graph is a set of vertices such that there is a path on the graph connecting any pair of vertices in the set without passing through any additional vertices of the set. Identifying an LWCS has many potential high-utility applications, e.g., for determining parking garage layout and capacity, as prioritized planning can be shown to be complete when start/goal configurations belong to an LWCS. In this work, we establish that computing an LWCS is NP-complete. We further develop optimal and near-optimal LWCS algorithms, with the near-optimal algorithm targeting large maps. A complete prioritized planning method is given for planning paths for multiple robots residing on an LWCS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-Connected Set and Its Application to Multi-Robot Path Planning Guo, Teng Yu, Jingjin Robotics Parking lots and autonomous warehouses for accommodating many vehicles/robots adopt designs in which the underlying graphs are \emph{well-connected} to simplify planning and reduce congestion. In this study, we formulate and delve into the \emph{largest well-connected set} (LWCS) problem and explore its applications in layout design for multi-robot path planning. Roughly speaking, a well-connected set over a connected graph is a set of vertices such that there is a path on the graph connecting any pair of vertices in the set without passing through any additional vertices of the set. Identifying an LWCS has many potential high-utility applications, e.g., for determining parking garage layout and capacity, as prioritized planning can be shown to be complete when start/goal configurations belong to an LWCS. In this work, we establish that computing an LWCS is NP-complete. We further develop optimal and near-optimal LWCS algorithms, with the near-optimal algorithm targeting large maps. A complete prioritized planning method is given for planning paths for multiple robots residing on an LWCS. |
| title | Well-Connected Set and Its Application to Multi-Robot Path Planning |
| topic | Robotics |
| url | https://arxiv.org/abs/2402.11766 |