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arXiv · 2504.18978

A biconvex method for minimum-time motion planning through sequences of convex sets

Tobia Marcucci·Mathew Halm·Will Yang·Dongchan Lee·Andrew D. Marchese
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Abstract

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.

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Tobia Marcucci, Mathew Halm, Will Yang, Dongchan Lee, Andrew D. Marchese. 2025-04-26. A biconvex method for minimum-time motion planning through sequences of convex sets. https://arxiv.org/abs/2504.18978

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