Heterogeneous Multi-Robot Graph Coverage with Proximity and Movement Constraints

TL;DR

This work introduces Multi-Robot Formation Graph Coverage (MRFGC), a centralized framework for planning coverage with heterogeneous robots under proximity and movement constraints on a graph ${G=(V,E)}$. It formalizes formations and transpositions, enabling a precise model of how robots must spatially organize and move while ensuring connectivity or proximity requirements. The authors develop an ${\textsf{FPT}}$-time algorithm based on a nice tree decomposition to compute optimal traversals, leveraging a bounded sequence length via the Z-Lemma and dynamic-programming over bags with signatures and condensed sequences; the overall runtime scales as ${O}(n\cdot h(||{\mathcal{F}}||,d,tw))$ and is ${\textsf{FPT}}$ in ${||{\mathcal{F}}||}$, the maximum degree ${d}$, and treewidth ${tw}$. For tree graphs, they prove a ${\textsf{PTAS}}$ under collapsible formations, achieving near-optimal traversals with runtime independent of ${d}$; additionally, a ${\textsf{PTAS}}$ for the special case of three robots with connected formations yields a multiplicative $(1+O(\varepsilon))$-approximation independent of ${d}$. These results enable centralized planning for complex multi-robot teams in safety-critical and large-scale applications, such as search-and-rescue, cleaning, and maintenance, particularly when the underlying graph has bounded treewidth.

Abstract

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.

Figures (1)

• Figure 1: Traversal $\mathcal{Z}$. The repeated configurations are highlighted in red, flipped transitions are colored in gray.

Theorems & Definitions (6)

• Lemma 1
• proof
• Definition 2
• Lemma 3
• Lemma 4
• proof