Tight displacement-based formation control under bounded disturbances. A set-theoretic perspective

TL;DR

This paper introduces a set-theoretic, deterministic approach to designing controllers for displacement-based formation control that are robust against bounded disturbances like measurement noise, ensuring tight formations in complex environments.

Contribution

It develops a novel set-theoretic framework for controller synthesis in formation control, providing deterministic guarantees under bounded disturbances, unlike traditional stochastic methods.

Findings

Successfully maintains tight formations amidst obstacles.

Provides a rigorous set-invariance based analysis.

Optimizes control parameters for guaranteed performance.

Abstract

This paper investigates the synthesis of controllers for displacement-based formation control in the presence of bounded disturbances, specifically focusing on uncertainties originating from measurement noise. While the literature frequently addresses such problems using stochastic frameworks, this work proposes a deterministic methodology grounded in set-theoretic concepts. By leveraging the principles of set invariance, we adapt the theory of ultimate boundedness to the specific dynamics of displacement-based formations. This approach provides a rigorous method for analyzing the system's behavior under persistent disturbances. Furthermore, this set-theoretic framework allows for the optimized selection of the proposed control law parameters to guarantee pre-specified performance bounds. The efficacy of the synthesized controller is demonstrated in the challenging application of maintaining tight formations in a multi-obstacles environment.