Multi-Robot Coverage problems have been extensively studied in robotics, planning and multi-agent systems. In this work, we consider the coverage problem when there are constraints on the proximity (e.g., maximum distance between the agents, or a blue agent must be adjacent to a red agent) and the movement (e.g., terrain traversability and material load capacity) of the robots. Such constraints naturally arise in many real-world applications, e.g. in search-and-rescue and maintenance operations. Given such a setting, the goal is to compute a covering tour of the graph with a minimum number of steps, and that adheres to the proximity and movement constraints. For this problem, our contributions are four: (i) a formal formulation of the problem, (ii) an exact algorithm that is FPT in F, d and tw, the set of robot formations that encode the proximity constraints, the maximum nodes degree, and the tree-width of the graph, respectively, (iii) for the case that the graph is a tree: a PTAS approximation scheme, that given an approximation parameter epsilon, produces a tour that is within a epsilon times error(||F||, d) of the optimal one, and the computation runs in time poly(n) times h(1/epsilon,||F||). (iv) for the case that the graph is a tree, with $k=3$ robots, and the constraint is that all agents are connected: a PTAS scheme with multiplicative approximation error of 1+O(epsilon), independent of the maximal degree d.

翻译：多机器人覆盖问题在机器人学、规划与多智能体系统中已被广泛研究。本文探讨存在邻近约束（例如智能体间最大距离，或蓝色智能体必须与红色智能体相邻）与运动约束（例如地形可通行性与物资负载能力）的覆盖问题。此类约束自然存在于许多现实应用中，例如搜救与维护作业。在此设定下，目标是在满足邻近与运动约束的前提下，计算图的最小步数覆盖路径。针对该问题，本文贡献包含四个方面：（i）问题的形式化表述；（ii）精确算法，其固定参数可解性参数为F、d与tw，分别表示编码邻近约束的机器人编队集合、图的最大节点度与树宽；（iii）针对树状图情形：提出PTAS近似方案，给定近似参数epsilon，可生成路径长度在最优解epsilon倍误差(||F||, d)范围内，且计算时间复杂度为poly(n)乘以h(1/epsilon,||F||)；（iv）针对树状图、$k=3$个机器人且约束为全智能体连通的情形：提出具有1+O(epsilon)乘性近似误差的PTAS方案，其误差与最大度d无关。