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A General Solution to the Formation Control Problem Without Collisions for First-Order Multi-Agent Systems

Published online by Cambridge University Press:  22 August 2019

J. F. Flores-Resendiz Open the ORCID record for J. F. Flores-Resendiz [Opens in a new window]  and
E. Aranda-Bricaire
J. F. Flores-Resendiz*
Affiliation:
Universidad Autónoma de Baja California, Facultad de Ingeniería y Negocios Tecate, 21460 Tecate, Baja California, México
E. Aranda-Bricaire
Affiliation:
CINVESTAV, Electrical Engineering Department, Mechatronics Section, AP 14-740, 07000 México City, México
*
*Corresponding author. E-mail: francisco.flores32@uabc.edu.mx
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Summary

In this paper, a general solution to the formation control problem without collisions for first-order multi-agent systems is proposed. The case of an arbitrary number of mobile agents on a plane with saturated input velocity is analysed. Besides, conditions on the communication graph among agents are relaxed to the only requirement of containing a directed spanning tree. This general approach is an extended result from the simpler case of combinations of cyclic pursuit communication graphs. The proposed solution to this problem is designed in two steps. First, the asymptotic convergence in the absence of collisions is ensured. After this, the non-collision problem is faced by analysing the most general possible geometrical scenario which can lead to collision among agents. Discontinuous vector fields with unstable counterclockwise focus behaviour are applied by every agent in order to repel each other. Numerical simulations illustrate the performance of the proposed scheme.

Keywords

Multi-agent systemsFormation controlCollision avoidanceDiscontinuous vector field
Type
Articles
Information
Robotica , Volume 38 , Issue 6 , June 2020 , pp. 1123 - 1137
Copyright
© Cambridge University Press 2019

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