An Alignment Strategy for Evolution of Multi-Agent Systems

Dyn. Sys., Meas., Control, 137(2), 021009 (2014) (10 pages).

Hossein Rastgoftar ,  Suhada Jayasuriya.

Department of Mechanical Engineering and Mechanics, Drexel University, 3141 Chestnut Street 115 B, Randall Hall Philadelphia, PA 19104-2884.

 

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 mlines 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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Significance statement

The key idea of this paper is inspired by the hypothesis natural biological swarms do not perform peer-to-peer communication to sustain their group behavior as a collective. Biological swarms evolve based on individual agents’ perception. However, most, if not all, of engineering based techniques rely on peer-to-peer communication that requires each individual agent to know the exact state information of its neighbors. Therefore sensors with high accuracy are required to be applied by individual agents in order to measure exact state information of the neighboring agents. In this paper, mobile robots can be treated as particles of continuum (deformable body) deforming under a homogenous transformation where the desired homogenous mapping is learned by them through preserving alignment. This is because of the unique feature of homogenous transformations that maps two crossing lines in the initial configuration into two different crossing lines in the current configuration. Notice that preserving alignment only requires the direction information and not the exact locations. Hence, agents that were initially aligned, can acquire a desired homogenous deformation through preserving alignment where (i) every follower agent updates its position based only on its perception of the positions of some local agents, and not their exact positions, (ii) avoidance of inter-agent collision is properly addressed, and (iii) the region occupied by the MAS can be largely expanded and contracted.

An Alignment Strategy for Evolution of Multi-Agent Systems. Advances In Engineering

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