Research Papers

Three-Dimensional Dynamic Formation Control of Multi-Agent Systems Using Rigid Graphs

[+] Author and Article Information
Pengpeng Zhang

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
Baton Rouge, LA 70803

Marcio de Queiroz

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: mdeque1@lsu.edu

Xiaoyu Cai

R&D Laser Tracker,
FARO Technologies,
Exton, PA 19341

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 21, 2015; final manuscript received June 5, 2015; published online August 13, 2015. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 137(11), 111006 (Aug 13, 2015) (7 pages) Paper No: DS-15-1034; doi: 10.1115/1.4030973 History: Received January 21, 2015

In this paper, we consider the problem of formation control of multi-agent systems in three-dimensional (3D) space, where the desired formation is dynamic. This is motivated by applications where the formation size and/or geometric shape needs to vary in time. Using a single-integrator model and rigid graph theory, we propose a new control law that exponentially stabilizes the origin of the nonlinear, interagent distance error dynamics and ensures tracking of the desired, 3D time-varying formation. Extensions to the formation maneuvering problem and double-integrator model are also discussed. The formation control is illustrated with a simulation of eight agents forming a dynamic cube.

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Gazi, V. , and Passino, K. M. , 2011, Swarm Stability and Optimization, Springer-Verlag, Berlin. [CrossRef]
Ren, W. , and Beard, R. W. , 2008, Distributed Consensus in Multi-Vehicle Cooperative Control, Springer-Verlag, London. [CrossRef]
Ren, W. , and Cao, Y. , 2011, Distributed Coordination of Multi-Agent Networks: Emergent Problems, Models, and Issues, Springer-Verlag, London. [CrossRef]
Summers, T. H. , Yu, C. , Dasgupta, S. , and Anderson, B. D. O. , 2011, “Control of Minimally Persistent Leader-Remote-Follower and Coleader Formations in the Plane,” IEEE Trans. Autom. Control, 56(12), pp. 2778–2792. [CrossRef]
Anderson, B. D. O. , Yu, C. , Fidan, B. , and Hendrickx, J. M. , 2008, “Rigid Graph Control Architectures for Autonomous Formations,” IEEE Control Syst. Mag., 28(6), pp. 48–63. [CrossRef]
Cai, X. , and de Queiroz, M. , 2012, “On the Stabilization of Planar Multi-Agent Formations,” ASME Paper No. DSCC2012-MOVIC2012-8534. [CrossRef]
Cao, M. , Morse, A. S. , Yu, C. , Anderson, B. D. O. , and Dasgupta, S. , 2011, “Maintaining a Directed, Triangular Formation of Mobile Autonomous Agents,” Commun. Inf. Syst., 11(1), pp. 1–16. [CrossRef]
Dörfler, F. , and Francis, B. , 2010, “Geometric Analysis of the Formation Problem for Autonomous Robots,” IEEE Trans. Autom. Control, 55(10), pp. 2379–2384. [CrossRef]
Krick, L. , Broucke, M. E. , and Francis, B. A. , 2009, “Stabilization of Infinitesimally Rigid Formations of Multi-Robot Networks,” Int. J. Control, 82(3), pp. 423–439. [CrossRef]
Oh, K.-K. , and Ahn, H.-S. , 2011, “Formation Control of Mobile Agents Based on Inter-Agent Distance Dynamics,” Automatica, 47(10), pp. 2306–2312. [CrossRef]
Cai, X. , and de Queiroz, M. , 2014, “Rigidity-Based Stabilization of Multi-Agent Formations,” ASME J. Dyn. Syst., Meas., Control, 136(1), p. 014502. [CrossRef]
Oh, K.-K. , and Ahn, H.-S. , 2014, “Distance-Based Undirected Formations of Single-Integrator and Double-Integrator Modeled Agents in n-Dimensional Space,” Int. J. Robust Nonlinear Control, 24(12), pp. 1809–1820. [CrossRef]
Kang, S.-M. , Park, M.-C. , Lee, B.-H. , and Ahn, H.-S. , 2014, “Distance-Based Formation Control With a Single Moving Leader,” American Control Conference (ACC), Portland, OR, June 4–6, pp. 305–310. [CrossRef]
Oh, K.-K. , and Ahn, H.-S. , 2011, “Distance-Based Control of Cycle-Free Persistent Formations,” IEEE International Symposium on Intelligent Control (ISIC), Denver, CO, Sept. 28–30, pp. 816–821. [CrossRef]
Cai, X. , and de Queiroz, M. , 2013, “Multi-Agent Formation Maintenance and Target Tracking,” American Control Conference (ACC), Washington, DC, June 17–19, pp. 2537–2532.
Cai, X. , and de Queiroz, M. , 2015, “Formation Maneuvering and Target Interception for Multi-Agent Systems Via Rigid Graphs,” Asian J. Control, 17(6), pp. 1–13. [CrossRef]
Asimow, L. , and Roth, B. , 1979, “The Rigidity of Graphs, II,” J. Math. Anal. Appl., 68(1), pp. 171–190. [CrossRef]
Izmestiev, I. , 2009, Infinitesimal Rigidity of Frameworks and Surfaces (Lectures on Infinitesimal Rigidity), Kyushu University, Fukuoka, Japan.
Roth, B. , 1981, “Rigid and Flexible Frameworks,” Am. Math. Monthly, 88(1), pp. 6–21. [CrossRef]
Jackson, B. , 2007, “Notes on the Rigidity of Graphs,” Levico Conference Notes, Levico Terme, Italy, Oct. 22–26.
Connelly, R. , 2005, “Generic Global Rigidity,” Discrete Comput. Geom., 33(4), pp. 549–563. [CrossRef]
Aspnes, J. , Egen, T. , Goldenberg, D. K. , Morse, A. S. , Whiteley, W. , Yang, Y. R. , Anderson, B. D. O. , and Belhumeur, P. N. , 2006, “A Theory of Network Localization,” IEEE Trans. Mobile Comput., 5(12), pp. 1663–1678. [CrossRef]
Ben-Israel, A. , and Greville, T. N. E. , 2003, Generalized Inverses: Theory and Applications, Springer-Verlag, New York.
Khalil, H. K. , 2002, Nonlinear Systems, Prentice Hall, Englewood Cliffs, NJ.
Krstic, M. , Kanellakopoulos, I. , and Kokotovic, P. , 1995, Nonlinear and Adaptive Control Design, Wiley, New York.


Grahic Jump Location
Fig. 1

Desired formation F*(t) at t = 0

Grahic Jump Location
Fig. 2

Single-integrator: agent trajectories from an arbitrary initial formation

Grahic Jump Location
Fig. 3

Single-integrator: interagent distance errors for i,j ∈ V*

Grahic Jump Location
Fig. 4

Single-integrator: control inputs along x (top plot), y (middle plot), and z (bottom plot) directions for i = 1,…,8 during the transient phase (left plots) and steady-state phase (right plots)

Grahic Jump Location
Fig. 5

Double-integrator: agent trajectories from an arbitrary initial formation

Grahic Jump Location
Fig. 6

Double-integrator: interagent distance error for i,j ∈ V*

Grahic Jump Location
Fig. 7

Double-integrator: variable s along x (top plot), y (middle plot), and z (bottom plot) directions for i = 1,…,8

Grahic Jump Location
Fig. 8

Double-integrator: control inputs along x (top plots), y (middle plots), and z (bottom plots) directions for i = 1,…,8 during the transient phase (left plots) and steady-state phase (right plots)




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