arXiv:2409.09852cs.RO2024-09中稿 · WAFR 2024被引 6

提出首个完整算法,解决带障碍物的移动目标旅行商问题。

A Complete Algorithm for a Moving Target Traveling Salesman Problem with Obstacles

  • 构建时空轨迹树,枚举目标拦截序列与时间窗组合。
  • 引入移动目标可视图,高效求解点到移动目标的路径规划。
  • 在30个目标场景下,计算效率最高提升38倍,优于基线方法。

带障碍物的移动目标旅行商问题(MT-TSP-O)是旅行商问题的推广,其中目标在移动。解是一个轨迹,在特定时间窗口内访问每个移动目标,且避开静态障碍物。假设目标在各时间窗口内以恒定速度移动,代理有速度上限,且不低于任一目标速度。本文提出首个可完全求解MT-TSP-O的算法。算法构建一棵树,节点为按唯一顺序访问目标及其时间窗口的代理轨迹。通过扩展父节点轨迹,逐个添加新目标拦截,每条子路径对应不同目标和时间窗口选择。扩展过程需规划从父轨迹终点到移动目标的路径,为此我们提出一种新型可视图——移动目标可视图(MTVG)。整体算法称为MTVG-TSP。在最多含30个目标的570个实例上验证该算法。对比基于已有特例研究的基线方法(将目标轨迹采样为点),MTVG-TSP在所有基线可行的案例中均找到解;当目标时间窗总长度进入临界范围时,计算时间最多减少至基线的1/38。

原文摘要 · Abstract (English)

The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits each moving target during a certain time window(s), and this trajectory avoids stationary obstacles. We assume each target moves at a constant velocity during each of its time windows. The agent has a speed limit, and this speed limit is no smaller than any target's speed. This paper presents the first complete algorithm for finding feasible solutions to the MT-TSP-O. Our algorithm builds a tree where the nodes are agent trajectories intercepting a unique sequence of targets within a unique sequence of time windows. We generate each of a parent node's children by extending the parent's trajectory to intercept one additional target, each child corresponding to a different choice of target and time window. This extension consists of planning a trajectory from the parent trajectory's final point in space-time to a moving target. To solve this point-to-moving-target subproblem, we define a novel generalization of a visibility graph called a moving target visibility graph (MTVG). Our overall algorithm is called MTVG-TSP. To validate MTVG-TSP, we test it on 570 instances with up to 30 targets. We implement a baseline method that samples trajectories of targets into points, based on prior work on special cases of the MT-TSP-O. MTVG-TSP finds feasible solutions in all cases where the baseline does, and when the sum of the targets' time window lengths enters a critical range, MTVG-TSP finds a feasible solution with up to 38 times less computation time.

路径规划优化算法移动目标可见图

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