Distributed Multi-task Formation Control under Parametric Communication Uncertainties

TL;DR

This paper develops a robust distributed formation control method for multi-agent systems with uncertain communication links, ensuring desired formations, collision avoidance, and connectivity preservation despite uncertainties.

Contribution

It introduces a novel LMI-based condition for maintaining connectivity under uncertainties and designs a gradient-based controller using Lyapunov-like barrier functions.

Findings

The proposed method effectively maintains formation and connectivity in uncertain environments.

Numerical examples demonstrate the controller's robustness and effectiveness.

The approach ensures collision avoidance while preserving network topology.

Abstract

Formation control is a key problem in the coordination of multiple agents. It arises new challenges to traditional formation control strategy when the communication among agents is affected by uncertainties. This paper considers the robust multi-task formation control problem of multiple non-point agents whose communications are disturbed by uncertain parameters. The control objectives include 1. achieving the desired configuration; 2. avoiding collisions; 3. preserving the connectedness of uncertain topology. To achieve these objectives, firstly, a condition of Linear Matrix Inequalities (LMIs) is proposed for checking the connectedness of an uncertain communication topology. Then, by preserving the initial topological connectedness, a gradient-based distributed controller is designed via Lyapunov-like barrier functions. Two numerical examples illustrate the effectiveness of the proposed method.