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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Murray, R. M., 2007, “Recent Research in Cooperative Control of Multivehicle System,” ASME J. Dyn. Syst., Meas., Control, 129, pp. 571–583. [CrossRef]
Consolinia, L., Morbidib, F., Prattichizzob, D., and Tosques, M., 2008, “Leader–Follower Formation Control of Nonholonomic Mobile Robots With Input Constraints,” Automatica, 44, pp. 1343–1349. [CrossRef]
Vidal, R., Shakernia, O., and Sastry, S., 2004, “Distributed Formation Control With Omnidirectional Vision-Based Motion Segmentation and Visual Servoing,” IEEE Rob. Autom. Mag., 11, pp. 1–13. [CrossRef]
Mariottini, G. L., Morbidi, F., Prattichizzo, D., Vander Valk, N., Michael, N., Pappas, G., and Daniilidis, K., 2009, “Vision-Based Localization for Leader–Follower Formation Control,” IEEE Trans. Rob., 25(6), pp. 1431–1438. [CrossRef]
Gamage, G. W., Mann, G. K. I., and Gosine, R. G., 2010, “Leader Follower Based Formation Control Strategies for Nonholonomic Mobile Robots: Design, Implementation and Experimental Validation,” American Control Conference Marriott Waterfront, Baltimore, MD.
Mehrjerdi, H., Ghommamb, J., and Saad, M., 2011, “Nonlinear Coordination Control for a Group of Mobile Robots Using a Virtual Structure,” Mechatronics, 21, pp. 1147–1155. [CrossRef]
Wang, Sh., and Schuab, H., 2011, “Nonlinear Feedback Control of a Spinning Two-Spacecraft Coulomb Virtual Structure,” IEEE Trans. Aerosp. Electron. Syst., 47(3), pp. 2055–2067. [CrossRef]
Xin, M., Balakrishnan, S. N., and Pernicka, H. J., 2007, “Multiple Spacecraft Formation Control With O-D Method,” IET Control Theory Appl., 1(2), pp. 485–493. [CrossRef]
Li, Q., and Jiang, Zh. P., 2008, “Formation Tracking Control of Unicycle Teams With Collision Avoidance,” Proceedings of the 47th IEEE Conference on Decision and Control Cancun, Mexico.
Balch, T., and Arkin, R. C., 1998, “Behavior-Based Formation Control for Multirobot Teams,” IEEE Trans. Rob. Autom., 14(6), pp. 156–160. [CrossRef]
Antonelli, G., Arrichiello, F., and Chiaverini, S., 2009, “Experiments of Formation Control With Multirobot Systems Using the Null-Space-Based Behavioral Control,” IEEE Trans. Control Syst. Technol., 17(5), pp. 1173–1182. [CrossRef]
Roussos, G., and Kyriakopoulos, K. J., 2010, “Completely Decentralised Navigation of Multiple Unicycle Agents With Prioritisation and Fault Tolerance,” 49th IEEE Conference on Decision and Control Hilton Atlanta Hotel, Atlanta, GA.
Gerdes, J. C., and Rossetter, E. J., 2001, “A Unified Approach to Driver Assistance Systems Based on Artificial Potential Fields,” ASME J. Dyn. Syst., Meas., Control, 123(3), pp. 431–438. [CrossRef]
Gazi, V., and Passino, K. M., 2011, Swarm Stability and Optimization, Springer, New York.
Kang, Y. H., Lee, M. Ch., Kim, Ch. Y., Yoon, S. M., and Noh, Ch. B., 2011, “A Study of Cluster Robots Line Formatted Navigation Using Potential Field Method,” Proceedings of the IEEE International Conference on Mechatronics and Automation, Beijing.
Ghods, N., and Krstic, M., 2012, “Multi-Agent Deployment Over a Source,” IEEE Trans. Control Syst. Technol., 20(1), pp. 277–285. [CrossRef]
Frihauf, P., and Krstic, M., 2011, “Leader-Enabled Deployment onto Planar Curves: A PDE-Based Approach,” IEEE Trans. Autom. Control, 56(8), pp. 1791–1806. [CrossRef]
Frihauf, P., and Krstic, M., 2010, “Multi-Agent Deployment to a Family of Planar Arcs,” American Control Conference Marriott Waterfront, Baltimore, MD.
Kim, J., Kim, K. D., Natarajan, V., Kelly, S. D., and Bentsman, J., 2008, “PdE-Based Model Reference Adaptive Control of Uncertain Heterogeneous Multi-Agent Networks,” Nonlinear Anal.: Hybrid Syst., 2, pp. 1152–1167. [CrossRef]
Rastgoftar, H., 2013, “Planning and Control of Swarm Motion as Continua,” M.S. thesis, University of Central Florida, Orlando, FL, http://ucf.catalog.fcla.edu/cf.jsp?st=rastgoftar&ix=kw&S=0311390934586915&fl=bo
Rastgoftar, H., and Jayasuriya, S., 2013, “Distributed Control of Swarm Motions as Continua Using Homogeneous Maps and Agent Triangulation,” European Control Conference, Zurich, Switzerland.
Rastgoftar, H., and Jayasuriya, S., 2013, “Preserving Stability Under Communication Delays in Multi-Agent Systems,” ASME Dynamic Systems and Control Conference, Palo Alto, CA, Oct. 21–23.
Qu, Z., 2009, Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles, Springer, London.


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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. 1

Kinematics of a deforming body

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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. 8

Final distribution of follower agents

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Fig. 18

Configuration of agents at t = 25 s

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Fig. 6

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

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Fig. 9

Elements of Jacobian matrix Q(t)

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Fig. 7

Paths of leader agents 1, 2, and 3

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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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