A biconvex method for minimum-time motion planning through sequences of convex sets
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913810060673024 |
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| author | Marcucci, Tobia Halm, Mathew Yang, Will Lee, Dongchan Marchese, Andrew D. |
| author_facet | Marcucci, Tobia Halm, Mathew Yang, Will Lee, Dongchan Marchese, Andrew D. |
| contents | We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A biconvex method for minimum-time motion planning through sequences of convex sets Marcucci, Tobia Halm, Mathew Yang, Will Lee, Dongchan Marchese, Andrew D. Robotics We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners. |
| title | A biconvex method for minimum-time motion planning through sequences of convex sets |
| topic | Robotics |
| url | https://arxiv.org/abs/2504.18978 |