An integer linear programming model for fair multitarget tracking in cooperative multirobot systems


Cooperative Multi-Robot Observation of Multiple Moving Targets (CMOMMT) denotes a class of problems in which a set of autonomous mobile robots equipped with limited-range sensors keep under observation a (possibly larger) set of mobile targets. In the existing literature, it is common to let the robots cooperatively plan their motion in order to maximize the average targets’ detection rate, defined as the percentage of mission steps in which a target is observed by at least one robot. We present a novel optimization model for CMOMMT scenarios which features fairness of observation among different targets as an additional objective. The proposed integer linear formulation exploits available knowledge about the expected motion patterns of the targets, represented as a probabilistic occupancy maps estimated in a Bayesian framework. An empirical analysis of the model is performed in simulation, considering multiple scenarios to study the effects of the amount of robots and of the prediction accuracy for the mobility of the targets. Both centralized and distributed implementations are presented and compared to each other evaluating the impact of multi-hop communications and limited information sharing. The proposed solutions are also compared to two algorithms selected from the literature. The model is finally validated on a real team of ground robots in a limited set of scenarios.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2

Image taken from Banfi et al. (2015)

Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. 1.

    While in the literature the term “tracking” is mostly used in this context, here we will usually employ the term “monitoring” since it refers to a more general action of intermittently keeping a target under observation.

  2. 2.

    In the following, we will often use the index t to refer to a generic time step in \(\{\tau ,\ldots ,\tau +h\}\).


  1. Banfi, J., Basilico, N., & Amigoni, F. (2017). Intractability of time-optimal multirobot path planning on 2D grid graphs with holes. IEEE Robotics and Automation Letters, 2(4), 1941–1947.

    Article  Google Scholar 

  2. Banfi, J., Guzzi, J., Giusti, A., Gambardella, L., & Di Caro, G. (2015). Fair multi-target tracking in cooperative multi-robot systems. In Proceedings of ICRA (pp. 5411–5418).

  3. Bertuccelli, L. F., & How, J. P. (2005). Robust UAV search for environments with imprecise probability maps. In Proceedings of CDC (pp. 5680–5685).

  4. Bertuccelli, L. F., & How, J. P. (2006). Search for dynamic targets with uncertain probability maps. In Proceedings of ACC (pp. 737–742).

  5. Bertuccelli, L. F., & How, J. P. (2011). Active exploration in robust unmanned vehicle task assignment. Journal of Aerospace Computing, Information, and Communication, 8, 250–268.

    Article  Google Scholar 

  6. Branke, J., Deb, K., Miettinen, K., & Słowiński, R. (2008). Multiobjective optimization. Berlin: Springer.

    Google Scholar 

  7. Capitan, J., Spaan, M. T., Merino, L., & Ollero, A. (2013). Decentralized multi-robot cooperation with auctioned POMDPs. The International Journal of Robotics Research, 32(6), 650–671.

    Article  Google Scholar 

  8. Ding, Y., Zhu, M., He, Y., & Jiang, J. (2006). P-CMOMMT algorithm for the cooperative multi-robot observation of multiple moving targets. In Proceedings of WCICA (pp. 9267–9271).

  9. Elmogy, A. M., Khamis, A. M., & Karray, F. O. (2012). Market-based approach to mobile surveillance systems. Journal of Robotics, 2012, 841291.

  10. Gurobi Optimization. (2014). Gurobi optimizer reference manual. Accessed 12 Apr 2018.

  11. Guzzi, J., Giusti, A., Gambardella, L., & Di Caro, G. A. (2013). Human-friendly robot navigation in dynamic environments. In Proceedings of ICRA (pp 423–430).

  12. Hu, J., Xie, L., Lum, K. Y., & Xu, J. (2013). Multiagent information fusion and cooperative control in target search. IEEE Transactions on Control Systems, 21(4), 1223–1235.

    Article  Google Scholar 

  13. Jung, B., & Sukhatme, G. S. (2006). Cooperative multi-robot target tracking. In Proceedings of DARS (pp. 81–90).

  14. Khan, A., Rinner, B., & Cavallaro, A. (2016). Cooperative robots to observe moving targets: Review. IEEE Transactions on Cybernetics, PP(99), 1–12. (Available online).

    Google Scholar 

  15. Kolling, A., & Carpin, S. (2006). Multirobot cooperation for surveillance of multiple moving targets-a new behavioral approach. In Proceedings of ICRA (pp. 1311–1316).

  16. Kolling, A., & Carpin, S. (2007). Cooperative observation of multiple moving targets: An algorithm and its formalization. The International Journal of Robotics Research, 26(9), 935–953.

    Article  Google Scholar 

  17. Luke, S., Sullivan, K., Panait, L., & Balan, G. (2005). Tunably decentralized algorithms for cooperative target observation. In Proceedings of AAMAS (pp. 911–917).

  18. Mercier, L., & Van Hentenryck, P. (2007). Performance analysis of online anticipatory algorithms for large multistage stochastic integer programs. In Proceedings of IJCAI (pp. 1979–1984).

  19. Parker, L. E. (2002). Distributed algorithms for multi-robot observation of multiple moving targets. Autonomous Robots, 12(3), 231–255.

    Article  MATH  Google Scholar 

  20. Parker, L. E., & Emmons, B. A. (1997). Cooperative multi-robot observation of multiple moving targets. Proceeding of ICRA (Vol. 3, pp. 2082–2089).

  21. Pióro, M., & Medhi, D. (2004). Routing, flow, and capacity design in communication and computer networks. Amsterdam: Elsevier.

    Google Scholar 

  22. Robin, C., & Lacroix, S. (2016). Multi-robot target detection and tracking: Taxonomy and survey. Autonomous Robots, 40(4), 729–760.

    Article  Google Scholar 

  23. Silver, D. (2005). Cooperative pathfinding. In Proceedings of AIIDE (pp. 117–122).

  24. Standley, T., & Korf, R. (2011). Complete algorithms for cooperative pathfinding problems. In Proceedings of IJCAI (pp. 668–673).

  25. Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic robotics. Cambridge: The MIT Press.

    Google Scholar 

  26. Thunberg, J., & Ögren, P. (2011). A mixed integer linear programming approach to pursuit evasion problems with optional connectivity constraints. Autonomous Robotos, 31(4), 333–343.

    Article  Google Scholar 

  27. Vansteenwegen, P., Souffriau, W., & Oudheusden, D. V. (2011). The orienteering problem: A survey. European Journal of Operations Research, 209(1), 1–10.

    MathSciNet  Article  MATH  Google Scholar 

  28. Yu, J., & LaValle, S. (2016). Optimal multirobot path planning on graphs: Complete algorithms and effective heuristics. IEEE Transaction on Robotics, 32(5), 1163–1177.

    Article  Google Scholar 

Download references


The authors would like to thank Nicola Basilico for useful discussions about this work.

Author information



Corresponding author

Correspondence to Jacopo Banfi.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 17879 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Banfi, J., Guzzi, J., Amigoni, F. et al. An integer linear programming model for fair multitarget tracking in cooperative multirobot systems. Auton Robot 43, 665–680 (2019).

Download citation


  • Multirobot systems
  • Cooperative target tracking
  • Fair resource allocation