Decentralized Formation Control with A Quadratic Lyapunov Function

TL;DR

This paper introduces a decentralized formation control approach utilizing a quadratic Lyapunov function, ensuring convergence to a target configuration and addressing multiple equilibria through simulated annealing, with promising simulation results.

Contribution

It presents a novel decentralized formation control method with a quadratic Lyapunov function and applies simulated annealing to ensure convergence to the desired formation.

Findings

Quadratic Lyapunov function guarantees convergence to target formation.

Simulated annealing effectively guides agents to the desired configuration.

Simulation results confirm the method's practical effectiveness.

Abstract

In this paper, we investigate a decentralized formation control algorithm for an undirected formation control model. Unlike other formation control problems where only the shape of a configuration counts, we emphasize here also its Euclidean embedding. By following this decentralized formation control law, the agents will converge to certain equilibrium of the control system. In particular, we show that there is a quadratic Lyapunov function associated with the formation control system whose unique local (global) minimum point is the target configuration. In view of the fact that there exist multiple equilibria (in fact, a continuum of equilibria) of the formation control system, and hence there are solutions of the system which converge to some equilibria other than the target configuration, we apply simulated annealing, as a heuristic method, to the formation control law to fix this problem. Simulation results show that sample paths of the modified stochastic system approach the target configuration.