A Complete Set of Connectivity-aware Local Topology Manipulation Operations for Robot Swarms

TL;DR

This paper introduces a comprehensive set of local topology manipulation operations for robot swarms, enabling transformation of network structures using only local information, which enhances control and flexibility.

Contribution

It proves the existence of a complete set of local operations for topology transformation, allowing any initial spanning tree to be converted into any other connected tree.

Findings

Any tree-to-tree transformation can be achieved through a sequence of local operations.

Sequences of operations can form specific topologies like lines or stars from any initial spanning tree.

The method provides a local information-based framework comparable to global network control.

Abstract

The topology of a robotic swarm affects the convergence speed of consensus and the mobility of the robots. In this paper, we prove the existence of a complete set of local topology manipulation operations that allow the transformation of a swarm topology. The set is complete in the sense that any other possible set of manipulation operations can be performed by a sequence of operations from our set. The operations are local as they depend only on the first and second hop neighbors' information to transform any initial spanning tree of the network's graph to any other connected tree with the same number of nodes. The flexibility provided by our method is similar to global methods that require full knowledge of the swarm network. We prove the existence of a sequence of transformations for any tree-to-tree transformation, and derive sequences of operations to form a line or star from any initial spanning tree. Our work provides a theoretical and practical framework for topological control of a swarm, establishing global properties using only local information.