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Cone invariance and rendezvous of multiple agents

Bhattacharya, R. and Tiwari, A. and Fung, J. and Murray, R. M. (2009) Cone invariance and rendezvous of multiple agents. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 223 (6). pp. 779-789. ISSN 0954-4100. https://resolver.caltech.edu/CaltechAUTHORS:20091106-154852106

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Abstract

In this article is presented a dynamical systems framework for analysing multi-agent rendezvous problems and characterize the dynamical behaviour of the collective system. Recently, the problem of rendezvous has been addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of the problem. The proposed approach is based on the set invariance theory and focusses on how to generate feedback between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions of the agents and the dynamics is modelled as linear first-order systems. These algorithms have also been applied to non-linear first-order systems. The rendezvous problem in the framework of cooperative and competitive dynamical systems is analysed that has had some remarkable applications to biological sciences. Cooperative and competitive dynamical systems are shown to generate monotone flows by the classical Muller–Kamke theorem, which is analysed using the set invariance theory. In this article, equivalence between the rendezvous problem and invariance of an appropriately defined cone is established. The problem of rendezvous is cast as a stabilization problem, with a the set of constraints on the trajectories of the agents defined on the phase plane. The n-agent rendezvous problem is formulated as an ellipsoidal cone invariance problem in the n-dimensional phase space. Theoretical results based on set invariance theory and monotone dynamical systems are developed. The necessary and sufficient conditions for rendezvous of linear systems are presented in the form of linear matrix inequalities. These conditions are also interpreted in the Lyapunov framework using multiple Lyapunov functions. Numerical examples that demonstrate application are also presented.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1243/09544100JAERO443DOIUNSPECIFIED
http://journals.pepublishing.com/content/y04282511wr7wl3v/?p=c71b13307fd94753af9e417373cc9e1e&pi=16PublisherUNSPECIFIED
ORCID:
AuthorORCID
Murray, R. M.0000-0002-5785-7481
Additional Information:© 2009 Professional Engineering Publishing. The manuscript was received on 12 August 2008 and was accepted after revision for publication on 6 April 2009.
Subject Keywords:cooperative control; Muller–Kamke theorem; rendezvous; multi-agent coordination; self-assembly
Issue or Number:6
Record Number:CaltechAUTHORS:20091106-154852106
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20091106-154852106
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16611
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:13 Nov 2009 23:04
Last Modified:03 Oct 2019 01:14

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