Finite time distributed distance‐constrained shape stabilization and flocking control for d‐dimensional undirected rigid formations. (12th November 2015)

• Record Type: Journal Article
• Authors: Sun, Zhiyong; Mou, Shaoshuai; Deghat, Mohammad; Anderson, Brian D. O.
• Is Part Of: International journal of robust and nonlinear control. Volume 26:Number 13(2016)
• Page Start: 2824
• Page End: 2844
• Publication Date: 2015-11-12
• Subjects: shape stabilization -- finite time stability -- graph rigidity -- flocking control; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3477
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: Most of the existing results on distributed distance‐constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non‐collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. Copyright © 2015 John Wiley & Sons, Ltd.