2025/04/26 by Tobia Marcucci, Marcucci, Tobia, Mathew Halm +6 · 1 citation
Computer Science · Engineering · #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Robotic Mechanisms and Dynamics #Robotic Path Planning Algorithms #Robotics (cs.RO)
paper · pdf · doi:10.48550/arxiv.2504.18978
openalex publication_date 2025/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.