Journal of Intelligent and Robotic Systems

, Volume 56, Issue 1–2, pp 47–67 | Cite as

An Optimal Approach to Collaborative Target Tracking with Performance Guarantees

Article

Abstract

In this paper, we present a discrete-time optimization framework for target tracking with multi-agent systems. The “target tracking” problem is formulated as a generic semidefinite program (SDP) that when paired with an appropriate objective yields an optimal robot configuration over a given time step. The framework affords impressive performance guarantees to include full target coverage (i.e. each target is tracked by at least a single team member) as well as maintenance of network connectivity across the formation. Key to this work is the result from spectral graph theory that states the second-smallest eigenvalue—λ2—of a weighted graph’s Laplacian (i.e. its inter-connectivity matrix) is a measure of connectivity for the associated graph. Our approach allows us to articulate agent-target coverage and inter-agent communication constraints as linear-matrix inequalities (LMIs). Additionally, we present two key extensions to the framework by considering alternate tracking problem formulations. The first allows us to guarantee k-coverage of targets, where each target is tracked by k or more agents. In the second, we consider a relaxed formulation for the case when network connectivity constraints are superfluous. The problem is modeled as a second-order cone program (SOCP) that can be solved significantly more efficiently than its SDP counterpart—making it suitable for large-scale teams (e.g. 100’s of nodes in real-time). Methods for enforcing inter-agent proximity constraints for collision avoidance are also presented as well as simulation results for multi-agent systems tracking mobile targets in both ℝ2 and ℝ3.

Keywords

Optimal target tracking Convex optimization Semidefinite programming Second-order cone programming Multi-agent systems 

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References

  1. 1.
    Spletzer, J., Taylor, C.: Dynamic sensor planning and control for optimally tracking targets. Int. J. Rob. Res. 22(1), 7–20 (2003)CrossRefGoogle Scholar
  2. 2.
    Kim, Y., Mesbahi, M.: On maximizing the second smallest eigenvalue of a state-dependent graph laplacian. IEEE Trans. Automat. Contr. 51, 116–120 (2006)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Winfield, A.F.T.: Distributed sensing and data collection via broken ad hoc wireless connected network of mobile robots. In: Parker, G.B.L.E., Barhen, J. (eds.) Distributed Autonomous Robotic Systems, vol. 4, pp. 273–282. Springer, New York (2000)Google Scholar
  4. 4.
    Arkin, R., Diaz, J.: Line-of-sight constrained eploration for reactive multiagent robotic teams. In: AMC 7th International Workshop on Advanced Motion Control, Maribor, 3–5 July 2002Google Scholar
  5. 5.
    Sweeney, J., Brunette, T.J., Yang, Y., Grupen, R.A.: Coordinated teams of reactive mobile platforms. In: Proceedings of the International Conference on Robotics and Automation (ICRA), pp. 99–304. Washington, DC (May 2002)Google Scholar
  6. 6.
    Pereira, G.A.S., Das, A.K., Kumar, V., Campos, M.F.M.: Decentralized motion planning for multiple robots subject to sensing and communication constraints. In: Proceedings of the Second Multi-Robot Systems Workshop, pp. 267–278. Washington, DC (March 2003)Google Scholar
  7. 7.
    Wagner, A.R., Arkin, R.C.: Communication-sensitive multi-robot reconnaissance. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 2480–2487. IEEE, Piscataway (2004)Google Scholar
  8. 8.
    Sweeney, J.D., Grupen, R.A., Shenoy, P.: Active qos flow maintenance in controlled mobile networks. In: Proceedings of the Fourth International Symposium on Robotics and Automation (ISRA). IEEE, Queretaro (2004)Google Scholar
  9. 9.
    Powers, M., Balch, T.: Value-based communication preservation for mobile robots. In: 7th International Symposium on Distributed Autonomous Robotic Systems, Toulouse, 23–25 (June 2004)Google Scholar
  10. 10.
    Hsieh, M.A., Cowley, A., Kumar, V., Taylor, C.J.: Towards the deployment of a mobile robot network with end-to-end performance guarantees. In: International Conference on Robotics and Automation (ICRA) 2006, Orlando (April 2006)Google Scholar
  11. 11.
    LaValle, S., Gonzalez-Banos, H., Becker, C., Latombe, J.: Motion strategies for maintaining visibility of a moving target. In: Proceeding of the IEEE Int. Conference on Robotics and Automation. pp. 731–736, Albuquerque (April 1997)Google Scholar
  12. 12.
    Stamos, I., Allen, P.: Interactive sensor planning. In: Computer Vision and Pattern Recognition Conference, pp. 489–495. Santa Barbara (June 1998)Google Scholar
  13. 13.
    Fabiani, P., Gonzalez-Banos, H., Latombe, J., Lin, D.: Tracking a partially predictable object with uncertainties and visibility constraints. J. Auton. Robots 38(1), 31–48 (2001)CrossRefGoogle Scholar
  14. 14.
    Liu, Z., Ang Jr. M.H., Seah, W.K.G.: A potential field based approach for multi-robot tracking of multiple moving targets. In: Proc. 1st International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management, Manila (March 2003)Google Scholar
  15. 15.
    Jung, B.: Cooperative target tracking using mobile robots. Ph.D. dissertation, University of Southern California, Los Angeles (2005)Google Scholar
  16. 16.
    Krishna, K.M., Hexmoor, H., Sogani, S.: A t-step ahead constrained optimal target detection algorithm for a multi sensor surveillance system. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robot and Systems, pp. 1840–1845. Edmonton (October–November 2005)Google Scholar
  17. 17.
    Mirzaei, F.M., Mourikis, A.I., Roumeliotis, S.I.: On the performance of multi-robot target tracking. In: Accepted to IEEE International Conference on Robotics and Automation (ICRA) 2007, Rome (April 2007)Google Scholar
  18. 18.
    Shucker, B., Bennett, J.K.: Target tracking with distributed robotic macrosensors. In: Proceedings of MILCOM 2005, Atlantic City (October 2005)Google Scholar
  19. 19.
    Stroupe, A., Balch, T.: Value-based observation with robot teams (vbort) for dynamic targets. In: Proceedings of IROS 2003, Las Vegas (September 2003)Google Scholar
  20. 20.
    Gennaro, M.D., Jadbabaie, A.: Decentralized control of connectivity in multi-agent systems. In: Proc. IEEE Conf. on Decision and Control, San Diego (December 2006)Google Scholar
  21. 21.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge Unviersity Press, Cambridge (2004)MATHGoogle Scholar
  22. 22.
    Isler, V., Khanna, S., Spletzer, J., Taylor, C.: Target tracking with distributed sensors: the focus of attention problem. J. Comput. Vis. Image Underst. 100, 225–247 (1988) (Special Issue on Attention and Performance in Computer Vision)CrossRefGoogle Scholar
  23. 23.
    Mourikis, A.I., Roumeliotis, S.I.: Optimal sensing strategies for mobile robot formations: resource-constrained localization. In: Proceedings of Robotics: Science and Systems, Cambridge (June 2005)Google Scholar
  24. 24.
    Advanced Optimization Laboratory: Addendum to the SeDuMi User Guide Version 1.1 Advanced Optimization Laboratory. McMaster University. http://sedumi.mcmaster.ca/ (2006)
  25. 25.
    Lofberg, J.: Yalmip: a toolbox for modeling and optimization in matlab. In: Proceedings of the CACSD Conference. Taipei, Taiwan. http://control.ee.ethz.ch/ joloef/yalmip.php (2004)
  26. 26.
    The MOSEK Optimization Tools Version 3.2 (Revision 8) User’s Manual and Reference. MOSEK ApS. http://www.mosek.com (2008)

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Computer Science and EngineeringLehigh UniversityBethlehemUSA
  2. 2.Mechanical Engineering and MechanicsDrexel UniversityPhiladelphiaUSA

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