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

J F Flores-Resendiz,J Santiaguillo-Salinas,E Aranda-Bricaire,J González-Sierra

doi:10.1155/2015/948086

Abstract

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.

Highlights

During the last years, formation control in multiagent systems has received much attention due to the wide range of applications in which they can be used as exploration, rescue tasks, toxic residues cleaning, and so forth, [1, 2]
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
In one hand we undertake the design of attractive vector fields based on the well known cyclic pursuit algorithm but, unlike the results reported in the literature [7], we focus our analysis on normalized vector fields

Summary

Introduction

Formation control in multiagent systems has received much attention due to the wide range of applications in which they can be used as exploration, rescue tasks, toxic residues cleaning, and so forth, [1, 2]. One main drawback is the fact that the combination of gradients of attractive and repulsive potential functions could result in the appearance of undesired equilibrium points, leading the agents to get stuck at an undesired formation Attending this problem, a solution has been proposed with the requirement of having totally centralized schemes [11]. A new strategy for designing the repulsive vector fields has been proposed [16] This approach differs from the classical one on the use of scaled unstable focus structures centred at the position of others agents.

Preliminaries

Problem Statement

Control Design

Numerical Simulation Results

Real-Time Experiments

Conclusions