针对机器人运动规划，提出快速预计算多组起终点最优路径的新方法。
Multi-Query Shortest-Path Problem in Graphs of Convex Sets
- 离线用半定规划求成本下界，线上增量生成可行路径
- 七关节机械臂轨迹质量更高，速度提升达两个数量级
- 适合静态环境下需快速响应的机器人运动规划场景
图中凸集的最短路径问题（SPP in GCS）是一种融合离散与连续决策的新型优化框架，可有效解决机器人避障运动规划等任务，相较现有算法能获得更低代价解和更快运行时间。本文针对机械臂在静态环境中需快速作业的需求，提出SPP in GCS的多查询扩展：高效预计算给定初始与目标状态集合间的最优路径。方法分两阶段：离线阶段利用半定规划计算问题代价到目标函数的粗糙下界；在线阶段，基于该下界通过求解短时域凸规划增量生成可行路径。对七关节机械臂实验表明，本方法生成的轨迹质量更高，速度比现有运动规划器快两个数量级。
原文摘要 · Abstract (English)
The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning, can be cast and solved as an SPP in GCS, yielding lower-cost solutions and faster runtimes than state-of-the-art algorithms. In this paper, we are motivated by motion planning of robot arms that must operate swiftly in static environments. We consider a multi-query extension of the SPP in GCS, where the goal is to efficiently precompute optimal paths between given sets of initial and target conditions. Our solution consists of two stages. Offline, we use semidefinite programming to compute a coarse lower bound on the problem's cost-to-go function. Then, online, this lower bound is used to incrementally generate feasible paths by solving short-horizon convex programs. For a robot arm with seven joints, our method designs higher quality trajectories up to two orders of magnitude faster than existing motion planners.
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