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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.20974 |
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| _version_ | 1866916663475044352 |
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| author | Parkinson, Christian Baca, Adan |
| author_facet | Parkinson, Christian Baca, Adan |
| contents | We present an algorithm for a multi-agent path planning problem with pattern coordination based on dynamic programming and a Hamilton-Jacobi-Bellman equation. This falls broadly into the class of partial differential equation (PDE) based optimal path planning methods, which give a black-box-free alternative to machine learning hierarchies. Due to the high-dimensional state space of multi-agent planning problems, grid-based methods for PDE which suffer from the curse of dimensionality are infeasible, so we instead develop grid-free numerical methods based on variational Hopf-Lax type representations of solutions to Hamilton-Jacobi Equations. Our formulation is amenable to nonlinear dynamics and heterogeneous agents. We apply our method to synthetic examples wherein agents navigate around obstacles while attempting to maintain a prespecified formation, though with small changes it is likely applicable to much larger classes of problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hopf-Lax Type Formula for Multi-Agent Path Planning with Pattern Coordination Parkinson, Christian Baca, Adan Optimization and Control We present an algorithm for a multi-agent path planning problem with pattern coordination based on dynamic programming and a Hamilton-Jacobi-Bellman equation. This falls broadly into the class of partial differential equation (PDE) based optimal path planning methods, which give a black-box-free alternative to machine learning hierarchies. Due to the high-dimensional state space of multi-agent planning problems, grid-based methods for PDE which suffer from the curse of dimensionality are infeasible, so we instead develop grid-free numerical methods based on variational Hopf-Lax type representations of solutions to Hamilton-Jacobi Equations. Our formulation is amenable to nonlinear dynamics and heterogeneous agents. We apply our method to synthetic examples wherein agents navigate around obstacles while attempting to maintain a prespecified formation, though with small changes it is likely applicable to much larger classes of problems. |
| title | A Hopf-Lax Type Formula for Multi-Agent Path Planning with Pattern Coordination |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.20974 |