Formation Control with Triangulated Laman Graphs

TL;DR

This paper introduces a class of rigid graphs and control laws in formation control that ensure all stable equilibria correspond to desired target configurations, addressing a key challenge in decentralized multi-agent systems.

Contribution

The paper proposes a novel class of rigid graphs and control laws that guarantee all stable equilibria are target configurations in formation control.

Findings

All stable equilibria are target configurations for the proposed class.

The approach addresses the problem of undesired stable equilibria in formation control.

Provides a partial solution to stabilizing desired formations in decentralized systems.

Abstract

Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration that satisfies the inter-agent distance conditions a target configuration. It is well known that when the distance conditions are defined via a rigid graph, there is a finite number of target configurations modulo rotations and translations. We can thus recast the objective of formation control as stabilizing one or many of the target configurations. A major issue is that such control laws will also have equilibria corresponding to configurations which do not meet the desired inter-agent distance conditions; we refer to these as undesired equilibria. The undesired equilibria become problematic if they are also stable. Designing decentralized control laws whose stable equilibria are all target configurations in the case of a general rigid graph is still an open problem. We propose here a partial solution to this problem by exhibiting a class of rigid graphs and control laws for which all stable equilibria are target configurations.