An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such tasks arise naturally in many robotic motion planning problems, particularly in exploration, surveillance and reconnaissance, and classical TSP algorithms on graphs are typically inapplicable in this setting. An important question about such problems is: if the target points are random, what is the length of the tour (either in expectation or as a concentration bound) as n grows? This problem is the Dynamic Stochastic TSP (DSTSP), and has been studied both for specific important vehicle models and for general dynamic systems; however, in general only the order of growth is known. In this work, we explore the connection between the distribution from which the targets are drawn and the dynamics of the system, yielding a more precise lower bound on tour length as well as a matching upper bound for the case of symmetric (or driftless) systems. We then extend the symmetric dynamics results to the case when the points are selected by a (non-random) adversary whose goal is to maximize the length, thus showing worst-case bounds on the tour length.

翻译：经典旅行商问题（TSP）的一个重要变体是动态TSP，其中受动态约束的系统需在最短时间内访问n个目标位置（顺序不限）。此类问题自然出现在许多机器人运动规划场景中，尤其是勘探、监视与侦察任务，而图上的经典TSP算法通常不适用于该场景。这类问题的核心在于：若目标点随机分布，当n增大时，路径长度（期望值或集中界）如何变化？这便是动态随机TSP问题（DSTSP），已有研究针对特定重要车辆模型及一般动态系统展开；然而，通常仅知其增长阶数。本文探索了目标分布与系统动态之间的关联，不仅得到了路径长度更精确的下界，还针对对称（或无漂移）系统给出了匹配的上界。随后，我们将对称动态系统的结论推广至目标点由（非随机）对抗选择器选取（其目标为最大化路径长度）的情形，从而展示了路径长度的最坏情况界。