Research Papers

Evolution of Multi-Agent Systems as Continua

[+] Author and Article Information
Hossein Rastgoftar

Department of Mechanical
Engineering and Mechanics,
Drexel University,
3141 Chestnut Street,
Philadelphia, PA 19104
e-mail: hossein.rastgoftar@mail.drexel.edu

Suhada Jayasuriya

Department of Mechanical
Engineering and Mechanics,
Drexel University,
3141 Chestnut Street,
Philadelphia, PA 19104
e-mail: sjayasuriya@coe.drexel.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 6, 2013; final manuscript received February 2, 2014; published online April 8, 2014. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 136(4), 041014 (Apr 08, 2014) (9 pages) Paper No: DS-13-1305; doi: 10.1115/1.4026659 History: Received August 06, 2013; Revised February 02, 2014

In this paper, a new framework for evolution of multi-agent systems (MAS) based on principles of continuum mechanics is developed. Agents are treated as mass particles of a continuum whose evolution (both translation and deformation) is modeled as a homeomorphism from a reference to the current configuration. Such a mapping assures that no two mass particles of the continuum occupy the same location at any given time, thus guaranteeing that inter-agent collision is avoided during motion. We show that a special class of mappings whose Jacobian is only time varying and not spatially varying has some desirable properties that are advantageous in studying swarms. Two specific scenarios are studied where the evolution of a swarm from one configuration to another occurs with no inter-agent collisions while avoiding obstacles, under (i) zero inter-agent communication and (ii) local inter-agent communication. In the first case, a desired map is computed by each agent all knowing the positions of a few leader agents in a reference and the desired configurations. In the second case, paths of n + 1 leader agents evolving in an n-D space are known only to the leaders, while positions of follower agents evolve through updates that are based on positions of n + 1 adjacent agent through local communication with them. The latter is based on a set of weights of communication of follower agents that are predicated on certain distance ratios assigned on the basis of the initial formation of the MAS. Properties of homogeneous maps are exploited to characterize the necessary communication protocol.

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Fig. 1

Kinematics of a deforming body

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Fig. 2

Homogenous transformation of a planar deformable body specified by three leader agents

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Fig. 3

Typical path plan for a MAS in the plane

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Fig. 4

Sample communication topology for a 2D swarm

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Fig. 5

Seven subregions based on the signs of weights of communication

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Fig. 6

Planar motion field; initial and desired (final) configurations of MAS

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Fig. 7

Paths of leader agents 1, 2, and 3

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Fig. 8

Final distribution of follower agents

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Fig. 9

Elements of Jacobian matrix Q(t)

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Fig. 10

Elements of rigid body displacement vector D(t)

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Fig. 11

Eigenvalues of the Jacobian matrix Q(t)

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Fig. 12

MAS configurations at five sample times t = 0 s, t = 10 s, t = 20 s, t = 25 s, and t = 30 s

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Fig. 13

x and y coordinates of r18(t) and r18HT(t) of follower 18

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Fig. 14

Configuration of agents at t = 5 s

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Fig. 15

Configuration of agents at t = 10 s

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Fig. 16

Configuration of agents at t = 15 s

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Fig. 17

Configuration of agents at t = 20 s

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Fig. 18

Configuration of agents at t = 25 s




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