Distance-based undirected formations of single-integrator and double-integrator modeled agents in n-dimensional space

• Published in: International journal of robust and nonlinear control Vol. 24; no. 12; pp. 1809 - 1820
• Main Authors: Oh, Kwang-Kyo, Ahn, Hyo-Sung
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.08.2014; Wiley Subscription Services, Inc
• Subjects: Asymptotic properties; Control systems; Dissipation; distance-based control; Equivalence; formation control; Formations; gradient systems; graph rigidity; Hamiltonian systems; Law; Stability; Stability analysis
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.2967

SUMMARYWe study the local asymptotic stability of undirected formations of single‐integrator and double‐integrator modeled agents based on interagent distance control. First, we show that n‐dimensional undirected formations of single‐integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double‐integrator modeled agents in n‐dimensional space is achieved under a gradient‐like control law. Simulation results support the validity of the stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.