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Mathematical Problems in Engineering
Volume 2015, Article ID 948086, 17 pages
Research Article

Finite-Time Formation Control without Collisions for Multiagent Systems with Communication Graphs Composed of Cyclic Paths

CINVESTAV, Electrical Engineering Department, Mechatronics Section, AP 14-740, 07000 México, DF, Mexico

Received 26 November 2014; Accepted 20 January 2015

Academic Editor: Luis Rodolfo Garcia Carrillo

Copyright © 2015 J. F. Flores-Resendiz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses the formation control problem without collisions for multiagent systems. A general solution is proposed for the case of any number of agents moving on a plane subject to communication graph composed of cyclic paths. The control law is designed attending separately the convergence to the desired formation and the noncollision problems. First, a normalized version of the directed cyclic pursuit algorithm is proposed. After this, the algorithm is generalized to a more general class of topologies, including all the balanced formation graphs. Once the finite-time convergence problem is solved we focus on the noncollision complementary requirement adding a repulsive vector field to the previous control law. The repulsive vector fields display an unstable focus structure suitably scaled and centered at the position of the rest of agents in a certain radius. The proposed control law ensures that the agents reach the desired geometric pattern in finite time and that they stay at a distance greater than or equal to some prescribed lower bound for all times. Moreover, the closed-loop system does not exhibit undesired equilibria. Numerical simulations and real-time experiments illustrate the good performance of the proposed solution.