Formation Control of Rigid Graphs with a Flex Node Addition

TL;DR

This paper analyzes the stability of formation control with a rigid graph plus a flex node, showing that desired formations are almost globally stable in specific cases where undesired equilibria are unstable.

Contribution

It provides new stability analysis results for formation control with a flex node added to rigid graphs, especially for triangle and tetrahedral configurations.

Findings

Desired equilibrium set is locally asymptotically stable.

Undesired equilibria are unstable in specific cases.

Desired formations are almost globally asymptotically stable.

Abstract

This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but there exist undesired equilibria. Specifically, we further consider two cases where the rigid graph is a triangle in 2-D and a tetrahedral in 3-D, and prove that any undesired equilibrium point in these cases is unstable. Thus in these cases, the desired formations are almost globally asymptotically stable.