0
Research Papers

Continuum Deformation of Multi-Agent Systems Under Directed Communication Topologies

[+] Author and Article Information
Hossein Rastgoftar

Aerospace Engineering Department,
University of Michigan Ann Arbor,
Ann Arbor, MI 48109-2102
e-mail: hosseinr@umich.edu

Ella M. Atkins

Aerospace Engineering Department,
University of Michigan Ann Arbor,
Ann Arbor, MI 48109-2102
e-mail: ematkins@umich.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 9, 2015; final manuscript received June 7, 2016; published online September 9, 2016. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 139(1), 011002 (Sep 09, 2016) (11 pages) Paper No: DS-15-1312; doi: 10.1115/1.4033866 History: Received July 09, 2015; Revised June 07, 2016

A leader follower model has recently been proposed for homogeneous deformation of a multi-agent system (MAS) in n. Researchers have shown how a desired homogeneous transformation can be designed by choosing proper trajectories for n + 1 leader agents and can be learned by every follower through local communication. However, existing work requires every follower to communicate with n + 1 adjacent agents, where communication between every two adjacent followers is constrained to be bidirectional. These requirements limit the total allowable number of agents, so an arbitrary number of agents may not be able to acquire a desired homogeneous mapping by local interaction. Additionally, if followers are not allowed to communicate with more than n + 1 neighboring agents, the convergence rate of actual positions to the desired positions (defined by a homogeneous transformation) may not be sufficiently high. The system may then considerably deviate from the desired configuration during transition. The main contribution of this article is to address these two issues, where each follower is considered to be a general linear system. It will be proven that followers can acquire desired positions prescribed by a homogeneous mapping in the presence of disturbance and measurement noise by applying a new finite-time reachability model under either fixed or switching topologies, if: (i) communication among followers is defined by a directed and strongly connected subgraph, (ii) each follower applies a consensus protocol with communication weights that are consistent with the positions of the agents in the initial configuration, and (iii) every follower i is allowed to communicate with min+1 local agents. With this strategy, an MAS with an arbitrary number of agents with linear dynamics can acquire a desired homogeneous mapping in the presence of disturbance and measurement noise, where convergence rate can be enhanced by increasing the number of communication links.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Murray, R. M. , 2007, “ Recent Research in Cooperative Control of Multivehicle Systems,” ASME J. Dyn. Syst., Meas., Control, 129(5), pp. 571–583. [CrossRef]
Olfati-Saber, R. , and Murray, R. M. , 2004, “ Consensus Problems in Networks of Agents With Switching Topology and Time-Delays,” IEEE Trans. Autom. Control, 49(9), pp. 1520–1533. [CrossRef]
Olfati-Saber, R. , Fax, A. , and Murray, R. M. , 2007, “ Consensus and Cooperation in Networked Multi-Agent Systems,” Proc. IEEE, 95(1), pp. 215–233. [CrossRef]
Ren, W. , Beard, R. W. , and Atkins, E. M. , 2007, “ Information Consensus in Multivehicle Cooperative Control,” IEEE Control Syst. Mag., 2(27), pp. 71–82. [CrossRef]
Qu, Z. , 2009, Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles, Springer Science & Business Media, Springer, Heidelberg, Germany.
Chebotarev, P. , 2010, “ Comments on ‘Consensus and Cooperation in Networked Multi-Agent Systems’,” Proc. IEEE, 98(7), pp. 1353–1354. [CrossRef]
Kim, J. , Kim, K.-D. , Natarajan, V. , Kelly, S. D. , and Bentsman, J. , 2008, “ PDE-Based Model Reference Adaptive Control of Uncertain Heterogeneous Multiagent Networks,” Nonlinear Anal.: Hybrid Syst., 2(4), pp. 1152–1167. [CrossRef]
Frihauf, P. , and Krstic, M. , 2010, “ Multi-Agent Deployment to a Family of Planar Arcs,” American Control Conference (ACC), IEEE, Baltimore, MD, pp. 4109–4114.
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]
Ghods, N. , and Krstic, M. , 2012, “ Multiagent Deployment Over a Source,” IEEE Trans. Control Syst. Technol., 20(1), pp. 277–285.
Ferrari-Trecate, G. , Egerstedt, M. , Buffa, A. , and Ji, M. , 2006, “ Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control,” Hybrid Systems: Computation and Control, Springer, Heidelberg, Germany, pp. 212–226.
Ji, M. , Ferrari-Trecate, G. , Egerstedt, M. , and Buffa, A. , 2008, “ Containment Control in Mobile Networks,” IEEE Trans. Autom. Control, 53(8), pp. 1972–1975. [CrossRef]
Cao, Y. , and Ren, W. , 2009, “ Containment Control With Multiple Stationary or Dynamic Leaders Under a Directed Interaction Graph,” 48th IEEE Conference on Decision and Control, 2009 Held Jointly With the 2009 28th Chinese Control Conference, CDC/CCC 2009, IEEE, Shanghai, China, pp. 3014–3019.
Cao, Y. , Stuart, D. , Ren, W. , and Meng, Z. , 2011, “ Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments,” IEEE Trans. Control Syst. Technol., 19(4), pp. 929–938. [CrossRef]
Lin, Z. , Ding, W. , Yan, G. , Yu, C. , and Giua, A. , 2013, “ Leader–Follower Formation Via Complex Laplacian,” Automatica, 49(6), pp. 1900–1906. [CrossRef]
Rastgoftar, H. , and Jayasuriya, S. , 2015, “ Swarm Motion as Particles of a Continuum With Communication Delays,” ASME J. Dyn. Syst., Meas., Control, 137(11), p. 111008. [CrossRef]
Rastgoftar, H. , and Jayasuriya, S. , 2014, “ Continuum Evolution of a System of Agents With Finite Size,” IFAC World Congress, Cape Town, South Africa, pp. 24–29.
Ren, W. , 2007, “ Consensus Strategies for Cooperative Control of Vehicle Formations,” IET Control Theory Appl., 1(2), pp. 505–512. [CrossRef]
Attanasi, A. , Cavagna, A. , Del Castello, L. , Giardina, I. , Grigera, T. S. , Jelić, A. , Melillo, S. , Parisi, L. , Pohl, O. , Shen, E. , and Viale, M. , 2014, “ Information Transfer and Behavioural Inertia in Starling Flocks,” Nat. Phys., 10(9), pp. 691–696. [CrossRef]
Srinivasan, S. , and Ayyagari, R. , 2010, “ Consensus Algorithm for Robotic Agents Over Packet Dropping Links,” 2010 3rd International Conference on Biomedical Engineering and Informatics (BMEI), IEEE, Yantai, China, Vol. 6, pp. 2636–2640.
Nathan, D. M. , Buse, J. B. , Davidson, M. B. , Ferrannini, E. , Holman, R. R. , Sherwin, R. , and Zinman, B. , 2009, “ Medical Management of Hyperglycemia in Type 2 Diabetes: A Consensus Algorithm for the Initiation and Adjustment of Therapy a Consensus Statement of the American Diabetes Association and the European Association for the Study of Diabetes,” Diabetes Care, 32(1), pp. 193–203. [CrossRef] [PubMed]
Xu, Y. , Liu, W. , and Gong, J. , 2011, “ Stable Multi-Agent-Based Load Shedding Algorithm for Power Systems,” IEEE Trans. Power Syst., 26(4), pp. 2006–2014. [CrossRef]
Yu, W. , Zheng, W. X. , Chen, G. , Ren, W. , and Cao, J. , 2011, “ Second-Order Consensus in Multi-Agent Dynamical Systems With Sampled Position Data,” Automatica, 47(7), pp. 1496–1503. [CrossRef]
Lai, W. , Rubin, D. , and Krempl, E. , 1993, Introduction to Continuum Mechanics, Elsevier, Amsterdam.

Figures

Grahic Jump Location
Fig. 1

Leaders' paths: initial formation P and desired final configuration R

Grahic Jump Location
Fig. 2

(a) A typical bidirectional communication topology graph G3; (b) a typical graph with nonminimum interagent topology graph G1; and (c) a typical graph with minimum directed interagent topology graph G2

Grahic Jump Location
Fig. 3

MAS formations at t = 15 for topologies G1 and G3

Grahic Jump Location
Fig. 4

Parameters a10,1,a10,2, and a10,3

Grahic Jump Location
Fig. 5

MAS formations at different sample times (a) graph G1 at t = 5 s, (b) graph G1 at t = 10 s, (c) graph G2 at t = 15 s, (d) graph G2 at t = 20 s, (e) graph G3 at t = 25 s, and (f) graph G3 at t = 30 s

Grahic Jump Location
Fig. 6

(a) Position of follower ten in the presence of disturbance and measurement noise and (b) position of follower ten in the absence of disturbance and measurement noise

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In