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

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