Heterogeneous Multi-Robot Graph Coverage with Proximity and Movement Constraints

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 parameters ∥F ∥, d and ω - 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 ε produces a tour that is within a 1 + ε . error(∥F ∥, d)) of the optimal one, and the computation runs in time poly(n) . h(¹_ε, ∥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(ε), independent of d.