Preservation of Giant Component Size After Robot Failure for Robustness of Multi-robot Network

This paper approaches a network topology control method for networked multi-robot systems. Although robustness of network connectivity against robot failures is a matter of concern for the multi-robot control, the robustification impedes the motion of robots because of limitations of the wireless communication. For mitigating the impediments, we focus our attention on the giant connected component size after a single robot fails, and aim to control such component size. A modified algebraic connectivity is introduced here as an indicator of the component size: a threshold for the algebraic connectivity is analyzed to preserve the component size. Theoretical properties and numerical examples are shown to demonstrate our control method.