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Research Papers

# An Alignment Strategy for Evolution of Multi-Agent Systems

[+] Author and Article Information
Hossein Rastgoftar

Department of Mechanical
Engineering and Mechanics,
Drexel University,
3141 Chestnut Street 115 B,
e-mail: hossein.rastgoftar@drexel.edu

Department of Mechanical Engineering
and Mechanics,
Drexel University,
3141 Chestnut Street 115 B,

1Corresponding author.

2Deceased.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 5, 2013; final manuscript received July 3, 2014; published online September 11, 2014. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 137(2), 021009 (Sep 11, 2014) (10 pages) Paper No: DS-13-1488; doi: 10.1115/1.4028147 History: Received December 05, 2013; Revised July 03, 2014

## Abstract

Developed in this paper is the notion that the collective behavior of swarms can be achieved without explicit peer-to-peer communication among agents. It is based on a recently proposed continuum framework for studying swarms where homogeneous maps are the key. The paper focuses on 2D evolution of a multi-agent system (MAS) that consists of N agents with $Nl$ leaders at the two ends of $m$ lines called leading segments, that are on the boundary of a moving convex domain $Ωt$. Rest of the ($N-Nl$) agents, the followers, are distributed along the m leading segments while lying inside the convex domain $Ωt$. Every follower $i$ is initially located at the intersection of two line segments whose end points define four agents that are adjacent to $i$. Under this setup if the domain $Ωt$ is transformed under a homogenous mapping and if every follower agent moves in such a way to reach the point of intersection of the two line segments connecting the adjacent agents, then the final formation of the MAS will satisfy the same homogenous map. This alignment strategy has the distinct advantage that the followers do not need the exact positions of the adjacent local agents to stay aligned.

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## Figures

Fig. 1

A convex domain Ωt0 with some interior points resulting from intersection of some lines passing through Ωt0

Fig. 2

Schematic of a homeomorhic mapping between two convex curves

Fig. 3

An schematic of MAS transformation when adjacency among the agents is changed

Fig. 4

Schematic of alignment strategy for MAS evolution

Fig. 5

A triangular domain Ωt0 with interior points defined by intersection of straight-lines lying in Ωt0

Fig. 6

Plane of motion divided into seven subregions based the signs of αi,iks

Fig. 7

Fig. 8

Elements of Q

Fig. 9

Elements of D

Fig. 10

Variations of hdi,1,2 and hdi,3,4 versus time for the follower 32

Fig. 11

MAS configurations at four sample times t = 5 s, t = 12 s, t = 17 s, and t = 20 s

Fig. 12

Variations of hdi,1,2 and hdi,3,4 versus time for follower 32

Fig. 13

MAS configurations at four sample times t = 5 s, t = 12 s, t = 17 s, and t = 20 s

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