Local Stability Analysis for Tensegrity-Based Multi-Agent Formations

This paper discusses the local stability property of a multi-agent system using a tensegrity framework. Given a desired multi-agent configuration in general positions with its corresponding stress matrix, we propose a new type of virtual tensegrity frameworks consisting of cables and struts, with which the designed controllers locally stabilize the formation at the desired shape. The center manifold theorem is used for the proof of local exponential stability of the target set since linearization fails at any given equilibria. The local stability analysis sheds new light on the understanding of both the pre-stressed equilibrium and those controllers derived from more general distance-based functions.