Geometric Analysis of the Formation Problem for Autonomous Robots

TL;DR

This paper uses differential geometry to analyze the global stability of formation control in autonomous robots, proving the target formation's stability and the instability of other invariant sets.

Contribution

It introduces a differential geometric approach for global stability analysis in formation control, extending beyond local linearization methods.

Findings

Target formation is globally stable.

Other invariant sets are proven unstable.

Method applies to cyclic triangular formations.

Abstract

In the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. It is well known that there are various other undesired invariant sets of the robots' closed-loop dynamics. This paper addresses a global stability analysis by a differential geometric approach considering invariant manifolds and their local stability properties. The theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation.