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

arXiv: https://arxiv.org/abs/2504.18978 · HTML: https://mlsanity.com/paper/2504.18978/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2025.

## Built on by (most cited first, 2 of 2)

- [Search-Based Spatiotemporal and Multi-Robot Motion Planning on Graphs of Space-Time Convex Sets](https://mlsanity.com/paper/2607.00444/) (2026)
- [Multi Graph Search for High-Dimensional Robot Motion Planning](https://mlsanity.com/paper/2602.12096/) (2026)

## Abstract (arXiv)

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.