发表机构
Massachusetts Institute of Technology; University of California Santa Barbara（麻省理工学院; 加州大学圣巴巴拉分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种双凸优化方法，用于凸障碍物周围的最小时间运动规划，可保证收敛、支持任意阶导数约束，实验表明其轨迹质量高、鲁棒性强且计算效率与现有方法相当。
AI 中文摘要
我们提出了一种用于凸障碍物周围最小时间运动规划的双凸方法，该方法保证收敛、具备任意时间性，并支持任意阶导数约束。我们通过变量变换联合凸化最小时间目标和所有导数约束，通过时变分离平面处理避障，将问题简化为双凸规划。该规划通过交替计算最大间隔分离平面和优化轨迹来求解。仅为当前迭代发生碰撞的障碍物添加平面，可使轨迹绕障碍物跳转并逃离局部极小值。该方法从简单的无碰撞多边形曲线开始即可保证收敛。在无人机导航和双臂料箱卸载的实验中，我们发现所提方法能可靠生成高质量轨迹，计算时间与最先进的基于分解的运动规划器相当，同时能处理更大类别的问题，且对不良初始化的鲁棒性显著更高。项目页面：this https URL
英文摘要
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/
Comments18 pages, 9 figures, 4 tables. Submitted to IEEE Transactions on Robotics. Project page: https://wernerpe.github.io/bmtp-website/ Code: https://github.com/wernerpe/pybmtp
