用双凸优化求解绕凸障碍物的最短时间轨迹，可保证收敛且鲁棒性好。
Biconvex Optimization for Smooth Minimum-Time Trajectories around Convex Obstacles
- 通过变量变换将目标与约束凸化，结合时变分离平面处理碰撞避免
- 在无人机和双臂机械臂任务中计算速度接近顶尖分解法，且更稳定
- 支持任意阶导数约束，对初始值不敏感，适合复杂动态规划场景
本文提出一种双凸优化方法，用于在凸障碍物周围规划最短时间运动轨迹，该方法保证收敛、具备即时求解能力，并支持任意阶导数约束。通过变量变换联合凸化最小时间目标与所有导数约束，利用时变分离平面处理碰撞规避，将问题转化为双凸规划。通过交替求解最大间隔分离平面与轨迹优化实现求解。仅对当前迭代中发生碰撞的障碍物添加平面，使轨迹能跳过障碍物并逃离局部极小值。方法从一个简单的无碰撞多边形曲线出发即可保证收敛。在无人机导航与双臂装箱任务的实验中，所提方法能可靠生成高质量轨迹，计算时间与最先进的分解式规划器相当，同时能处理更广泛的问题类型，且对不良初始化具有显著更强的鲁棒性。
原文摘要 · Abstract (English)
We present a biconvex approach for minimum-time motion planning around convex obstacles that is guaranteed to converge, is anytime, and supports derivative constraints to arbitrary order. We jointly convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. This program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape local minima. The method is guaranteed to converge starting from a simple collision-free polygonal curve. In our experiments on drone navigation and dual-arm bin unloading, we find that the proposed method reliably produces high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a larger class of problems and being substantially more robust to bad initialization. Project page:https://wernerpe.github.io/bmtp-website/
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