提出快速求解凸集序列最短时轨迹规划的新方法。
A biconvex method for minimum-time motion planning through sequences of convex sets
- 交替求解两个凸子问题，迭代优化轨迹
- 比现有非凸优化求解器快数倍，且保证可行
- 适合实时运动规划，优于传统航点规划
本文研究在满足速度与加速度约束下，通过一系列凸集的光滑轨迹最小时间规划问题。该问题自然表述为非凸优化。为此，我们提出一种双凸方法，能快速生成初始轨迹，并通过交替求解两个凸子问题迭代优化。该方法保证收敛，即使提前停止也能返回可行轨迹，无需选择线搜索或信赖域参数。大量实验表明，本方法在远低于现有非凸优化求解器耗时的情况下，获得高质量轨迹；同时运行时间接近工业标准航点规划器，却始终生成比现有优化式规划器更短时长的轨迹。
原文摘要 · Abstract (English)
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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