Collisionless Multi-Agent Path Planning in the Hamilton-Jacobi Formulation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915900923314176 |
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| author | Parkinson, Christian Baca, Adan Nguyen, Huy |
| author_facet | Parkinson, Christian Baca, Adan Nguyen, Huy |
| contents | We present a method for collisionless multi-agent path planning using the Hamilton-Jacobi-Bellman equation. Because the method is rooted in optimal control theory and partial differential equations, it avoids the need for hierarchical planners and is black-box free. Our model can account for heterogeneous agents and realistic, high-dimensional dynamics. We develop a grid-free numerical method based on a variational formulation of the solution of the Hamilton-Jacobi-Bellman equation which can resolve optimal trajectories even in high-dimensional problems, and include some practical implementation notes. In particular, we resolve the solution using a primal-dual hybrid gradient optimization scheme. We demonstrate the method's efficacy on path planning problems involving simple cars and quadcopter drones. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28993 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Collisionless Multi-Agent Path Planning in the Hamilton-Jacobi Formulation Parkinson, Christian Baca, Adan Nguyen, Huy Optimization and Control We present a method for collisionless multi-agent path planning using the Hamilton-Jacobi-Bellman equation. Because the method is rooted in optimal control theory and partial differential equations, it avoids the need for hierarchical planners and is black-box free. Our model can account for heterogeneous agents and realistic, high-dimensional dynamics. We develop a grid-free numerical method based on a variational formulation of the solution of the Hamilton-Jacobi-Bellman equation which can resolve optimal trajectories even in high-dimensional problems, and include some practical implementation notes. In particular, we resolve the solution using a primal-dual hybrid gradient optimization scheme. We demonstrate the method's efficacy on path planning problems involving simple cars and quadcopter drones. |
| title | Collisionless Multi-Agent Path Planning in the Hamilton-Jacobi Formulation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.28993 |