Edge contraction based maintenance of rigidity in multi-agent formations during agent loss

This paper proposes a systematic approach to the problem of restoring rigidity after loss of an agent, for two-dimensional rigid multi-agent formations based on a particular graph operation, the edge contraction operation. A rigidity maintenance method is proposed, for the cases where an agent is lost in an arbitrary two-dimensional rigid formation, to restore rigidity by transferring all links to which this agent was incident on to one of its neighbors. From a graph theoretical point of view, this corresponds to contraction of a certain edge incident to the vertex representing the agent being lost.