Research Papers

Flocking of Multi-Agent Systems Using a Unified Optimal Control Approach

[+] Author and Article Information
Jianan Wang

School of Electrical and Electronic Engineering,
University of Manchester,
Manchester M13 9PL, UK

Ming Xin

Department of Mechanical and
Aerospace Engineering,
University of Missouri,
Columbia, MO 65211
e-mail: xin618@gmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 28, 2011; final manuscript received June 25, 2013; published online August 23, 2013. Assoc. Editor: Marco P. Schoen.

J. Dyn. Sys., Meas., Control 135(6), 061005 (Aug 23, 2013) (11 pages) Paper No: DS-11-1338; doi: 10.1115/1.4024903 History: Received October 28, 2011; Revised June 25, 2013

In this paper, the multi-agent flocking problem is investigated in a unified optimal control framework. The flocking characteristics, such as velocity alignment, navigation, cohesion, and collision/obstacle avoidance, are accomplished by formulating them into respective cost function terms. The resultant nonquadratic cost function poses a challenging optimal control problem. A novel inverse optimal control strategy is adopted to derive an analytical optimal control law. The optimality and asymptotic stability are proved and the distributed feedback control law only requires local information to achieve the flocking behaviors. Various simulation scenarios are used to demonstrate the effectiveness of the optimal flocking algorithm.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Reynolds, C. W., 1987, “Flocks, Herds, and Schools: A Distributed Behavioral Model,” Comput. Graphics, 21(4), pp. 26–34.
Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I., and Shochet, O., 1995, “Novel Type of Phase Transition in a System of Self-driven Particles,” Phys. Rev. Lett., 75(6), pp. 1226–1229. [CrossRef] [PubMed]
Tanner, H. G., Jadbabaie, A., and Papps, G. J., 2007, “Flocking in Fixed and Switching Networks,” IEEE Trans. Autom. Control, 52(5), pp. 863–868. [CrossRef]
Lee, D., and Spong, M. W., 2007, “Stable Flocking of Multiple Inertial Agents on Balanced Graphs,” IEEE Trans. Autom. Control, 52(8), pp. 1469–1475. [CrossRef]
Regmi, A., Sandoval, R., Byrne, R., Tanner, H., and Abdallah, C. T., 2005, “Experimental Implementation of Flocking Algorithms in Wheeled Mobile Robots,” Proceedings of 2005 American Control Conference, Portland, OR, pp. 894–911.
Moshtagh, N., and Jadbabaie, A., 2007, “Distributed Geodesic Control Laws for Flocking of Nonholonomic Agents,” IEEE Trans. Autom. Control, 52(4), pp. 681–686. [CrossRef]
Cucker, F., and Smale, S., 2007, “Emergent Behavior in Flocks,” IEEE Trans. Autom. Control, 52(5), pp. 852–862. [CrossRef]
Dong, W. J., 2011, “Flocking of Multiple Mobile Robots Based on Backstepping,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern., 41(2), pp. 414–424. [CrossRef]
Tanner, H. G., 2004, “Flocking With Obstacle Avoidance in Switching Networks of Interconnected Vehicles,” Proceedings of 2004 IEEE International Conference on Robotics and Automation, New Orleans, LA, pp. 3006–3011.
Gu, D. B., and Hu, H. S., 2007, “Using Fuzzy Logic to Design Separation Function in Flocking Algorithms,” IEEE Trans. Fuzzy Syst., 16(4), pp. 826–838. [CrossRef]
Zavlanos, M. M., Tanner, H. G., Jadbabaie, A., and Pappas, G. J., 2009, “Hybrid Control for Connectivity Preserving Flocking,” IEEE Trans. Autom. Control, 54(12), pp. 2869–2875. [CrossRef]
Cucker, F., and Dong, J. G., 2010, “Avoiding Collisions in Flocks,” IEEE Trans. Autom. Control, 55(5), pp. 1238–1243. [CrossRef]
Zhang, H. T., Zhai, C., and Chen, Z. Y., 2011, “A General Alignment Repulsion Algorithm for Flocking of Multi-Agent Systems,” IEEE Trans. Autom. Control, 56(2), pp. 430–435. [CrossRef]
Belta, C., and Kumar, V., 2004, “Abstraction and Control for Groups of Robots,” IEEE Trans. Rob., 20(5), pp. 865–875. [CrossRef]
Olfati-Saber, R., 2006, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory,” IEEE Trans. Autom. Control, 51(3), pp. 401–419. [CrossRef]
Su, H. S., Wang, X. F., and Lin, Z. L., 2009, “Flocking of Multi-Agent With A Virtual Leader,” IEEE Trans. Autom. Control, 54(2), pp. 293–307. [CrossRef]
Gu, D. B., and Wang, Z. Y., 2009, “Leader-Follower Flocking: Algorithms and Experiments,” IEEE Trans. Control Syst. Technol., 17(5), pp. 1211–1219. [CrossRef]
Haddad, W. M., and Chellaboina, V., 2000, Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach, Princeton University Press, Princeton, NJ.
Bernstein, D. S., 1993, “Nonquadratic Cost and Nonlinear Feedback Control,” Int. J. Robust Nonlinear Control, 3(3), pp. 211–229. [CrossRef]
Ren, W., and Beard, R. W., 2008, Distributed Consensus in Multi-Vehicle Cooperative Control, Springer-Verlag, London.
Bernstein, D. S., 2005, Matrix Mathematics: Theory, Facts, and Formulas With Application to Linear Systems Theory, Princeton University Press, Princeton, NJ.
Wang, J. N., and Xin, M., 2012, “Distributed Optimal Cooperative Tracking Control of Multiple Autonomous Robots,” Rob. Auton. Syst., 60(4), pp. 572–583. [CrossRef]


Grahic Jump Location
Fig. 1

Illustration of agents and obstacles

Grahic Jump Location
Fig. 3

Scenario A: flocking demonstration with velocity alignment and navigation

Grahic Jump Location
Fig. 4

Time histories of positions and velocities in scenario A

Grahic Jump Location
Fig. 5

Scenario B: flocking demonstration with velocity alignment, navigation, and cohesion

Grahic Jump Location
Fig. 6

Time histories of positions and velocities in scenario B

Grahic Jump Location
Fig. 2

Communication topology and reference access

Grahic Jump Location
Fig. 7

Scenario C: flocking demonstration with velocity alignment, navigation, cohesion, and obstacle/collision avoidance

Grahic Jump Location
Fig. 8

Time histories of positions and velocities in scenario C

Grahic Jump Location
Fig. 9

Time histories of control inputs in scenario C



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