Distributed assignment with limited communication for multi-robot multi-target tracking


We study the problem of tracking multiple moving targets using a team of mobile robots. Each robot has a set of motion primitives to choose from in order to collectively maximize the number of targets tracked or the total quality of tracking. Our focus is on scenarios where communication is limited and the robots have limited time to share information with their neighbors. As a result, we seek distributed algorithms that can find solutions in a bounded amount of time. We present two algorithms: (1) a greedy algorithm that is guaranteed to find a 2-approximation to the optimal (centralized) solution but requiring |R| communication rounds in the worst case, where |R| denotes the number of robots, and (2) a local algorithm that finds a \(\mathcal {O}\left( (1+\epsilon )(1+1/h)\right) \)—approximation algorithm in \(\mathcal {O}(h\log 1/\epsilon )\) communication rounds. Here, h and \(\epsilon \) are parameters that allow the user to trade-off the solution quality with communication time. In addition to theoretical results, we present empirical evaluation including comparisons with centralized optimal solutions.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17


  1. 1.

    An algorithm is called a \(\mathcal {O}(x)\) approximation to a maximization problem if it guarantees a solution whose value is at least \(\frac{c}{x}\) of the optimal value, where c is some constant.

  2. 2.

    After these assumptions, we omit the time index (i.e., k) for notational convenience.

  3. 3.

    If all \(x_{m}^{i}=0\) for a robot i, then it can choose any motion primitives since the objective value will remain the same.

  4. 4.

    Note that Problem 2 can also be converted into a simpler Mixed Integer Linear Programming (MILP) by linearizing the product of the binary variables in Eq. (4), which is not covered in this paper.

  5. 5.

    Although we model linear motion for the targets, more sophisticated models for the prediction of target states can also be employed.


  1. Ahmad, A., Lawless, G., & Lima, P. (2017). An online scalable approach to unified multirobot cooperative localization and object tracking. IEEE Transactions on Robotics, 33(5), 1184–1199.

    Google Scholar 

  2. Angluin, D. (1980) Local and global properties in networks of processors. In Proceedings of the twelfth annual ACM symposium on theory of computing. ACM, (pp. 82–93).

  3. Åstrand, M., & Suomela, J. (2010) Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks. In Proceedings of the twenty-second annual ACM symposium on parallelism in algorithms and architectures. ACM, (pp. 294–302).

  4. Åstrand, M., Floréen, P., Polishchuk, V., Rybicki, J., Suomela, J., & Uitto, J. (2009) A local 2-approximation algorithm for the vertex cover problem. In International symposium on distributed computing. Springer (pp. 191–205).

  5. Bandyopadhyay, S., Chung, S.-J., & Hadaegh, F. Y. (2017). Probabilistic and distributed control of a large-scale swarm of autonomous agents. IEEE Transactions on Robotics, 33(5), 1103–1123.

    Google Scholar 

  6. Banfi, J., Guzzi, J., Amigoni, F., Flushing, E. F., Giusti, A., Gambardella, L., & Di Caro, G. A. (2018) An integer linear programming model for fair multitarget tracking in cooperative multirobot systems. Autonomous Robots, pp. 1–16.

  7. Best, G., Forrai, M., Mettu, R. R., & Fitch, R. (2018). Planning-aware communication for decentralised multi-robot coordination. In Proceedings of the international conference on robotics and automation, Brisbane, Australia, (Vol. 21).

  8. 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.

    Google Scholar 

  9. Charrow, B., Kumar, V., & Michael, N. (2014). Approximate representations for multi-robot control policies that maximize mutual information. Autonomous Robots, 37(4), 383–400.

    Google Scholar 

  10. Choi, H.-L., Brunet, L., & How, J. P. (2009). Consensus-based decentralized auctions for robust task allocation. IEEE Transactions on Robotics, 25(4), 912–926.

    Google Scholar 

  11. Chung, S.-J., Paranjape, A., Dames, P., Shen, S., & Kumar, V. (2018). A Survey on Aerial Swarm Robotics. IEEE Transactions on Robotics.

  12. Dimarogonas, D. V., Frazzoli, E., & Johansson, K. H. (2012). Distributed event-triggered control for multi-agent systems. IEEE Transactions on Automatic Control, 57(5), 1291–1297.

    MathSciNet  MATH  Google Scholar 

  13. Floréen, P., Hassinen, M., Kaasinen, J., Kaski, P., Musto, T., & Suomela, J. (2011). Local approximability of max-min and min-max linear programs. Theory of Computing Systems, 49(4), 672–697.

    MathSciNet  MATH  Google Scholar 

  14. Ge, X., & Han, Q.-L. (2017). Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism. IEEE Transactions on Industrial Electronics, 64(10), 8118–8127.

    Google Scholar 

  15. Gerkey, B. P., & Matarić, M. J. (2004). A formal analysis and taxonomy of task allocation in multi-robot systems. The International Journal of Robotics Research, 23(9), 939–954.

    Google Scholar 

  16. Ge, X., Yang, F., & Han, Q.-L. (2017). Distributed networked control systems: A brief overview. Information Sciences, 380, 117–131.

    Google Scholar 

  17. Gharesifard, B. & Smith, S. L. (2017). Distributed submodular maximization with limited information. In IEEE transactions on control of network systems.

  18. Guo, M., & Zavlanos, M. M. (2018). Multirobot data gathering under buffer constraints and intermittent communication. IEEE transactions on robotics.

  19. Hanckowiak, M., Karonski, M., & Panconesi, A. (2001). On the distributed complexity of computing maximal matchings. SIAM Journal on Discrete Mathematics, 15(1), 41–57.

    MathSciNet  MATH  Google Scholar 

  20. Hönig, W., & Ayanian, N. (2016) Dynamic multi-target coverage with robotic cameras. In IEEE RSJ International conference on intelligent robots and systems (IROS) (pp. 1871–1878).

  21. Howard, T., Pivtoraiko, M., Knepper, R. A., & Kelly, A. (2014). Model-predictive motion planning: Several key developments for autonomous mobile robots. IEEE Robotics and Automation Magazine, 21(1), 64–73.

    Google Scholar 

  22. Kanakia, A., Touri, B., & Correll, N. (2016). Modeling multi-robot task allocation with limited information as global game. Swarm Intelligence, 10(2), 147–160.

    Google Scholar 

  23. Kantaros, Y., Thanou, M., & Tzes, A. (2015). Distributed coverage control for concave areas by a heterogeneous robot-swarm with visibility sensing constraints. Automatica, 53, 195–207.

    MathSciNet  MATH  Google Scholar 

  24. Kantaros, Y., & Zavlanos, M. M. (2016). Global planning for multi-robot communication networks in complex environments. IEEE Transactions on Robotics, 32(5), 1045–1061.

    Google Scholar 

  25. Kantaros, Y., & Zavlanos, M. M. (2017). Distributed intermittent connectivity control of mobile robot networks. IEEE Transactions on Automatic Control, 62(7), 3109–3121.

    MathSciNet  MATH  Google Scholar 

  26. Kassir, A., Fitch, R., & Sukkarieh, S. (2016) Communication-efficient motion coordination and data fusion in information gathering teams. In 2016 IEEE/RSJ international conference on intelligent robots and systems (IROS). IEEE, (pp. 5258–5265).

  27. Khan, A., Rinner, B., & Cavallaro, A. (2016) Cooperative robots to observe moving targets: Review, IEEE transactions on cybernetics.

  28. 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.

    Google Scholar 

  29. Korsah, G. A., Stentz, A., & Dias, M. B. (2013). A comprehensive taxonomy for multi-robot task allocation. The International Journal of Robotics Research, 32(12), 1495–1512.

    Google Scholar 

  30. Kuhn, F., Moscibroda, T., & Wattenhofer, R. (2006) The price of being near-sighted. In Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm. Society for Industrial and Applied Mathematics, (pp. 980–989).

  31. Le Ny, J., Ribeiro, A., & Pappas, G. J. (2012). Adaptive communication-constrained deployment of unmanned vehicle systems. IEEE Journal on Selected Areas in Communications, 30(5), 923–934.

    Google Scholar 

  32. Lenzen, C., & Wattenhofer, R. (2010) Minimum dominating set approximation in graphs of bounded arboricity. In International symposium on distributed computing. Springer, (pp. 510–524).

  33. Li, H., Chen, G., Huang, T., & Dong, Z. (2017). High-performance consensus control in networked systems with limited bandwidth communication and time-varying directed topologies. IEEE Transactions on Neural Networks and Learning Systems, 28(5), 1043–1054.

    Google Scholar 

  34. Linial, N. (1992). Locality in distributed graph algorithms. SIAM Journal on Computing, 21(1), 193–201.

    MathSciNet  MATH  Google Scholar 

  35. Liu, L., & Shell, D. A. (2011). Assessing optimal assignment under uncertainty: An interval-based algorithm. The International Journal of Robotics Research, 30(7), 936–953.

    Google Scholar 

  36. Luo, L., Chakraborty, N., & Sycara, K. (2015). Distributed algorithms for multirobot task assignment with task deadline constraints. IEEE Transactions on Automation Science and Engineering, 12(3), 876–888.

    Google Scholar 

  37. Morgan, D., Subramanian, G. P., Chung, S.-J., & Hadaegh, F. Y. (2016). Swarm assignment and trajectory optimization using variable-swarm, distributed auction assignment and sequential convex programming. The International Journal of Robotics Research, 35(10), 1261–1285.

    Google Scholar 

  38. Naor, M., & Stockmeyer, L. (1995). What can be computed locally? SIAM Journal on Computing, 24(6), 1259–1277.

    MathSciNet  MATH  Google Scholar 

  39. Nemhauser, G. L., Wolsey, L. A., & Fisher, M. L. (1978). An analysis of approximations for maximizing submodular set functions–1. Mathematical programming, 14(1), 265–294.

    MathSciNet  MATH  Google Scholar 

  40. Niehsen, W. (2002) Information fusion based on fast covariance intersection filtering. In Proceedings of the fifth international conference on information fusion, 2002, vol. 2. IEEE, (pp. 901–904).

  41. Otte, M., & Correll, N. (2013). Any-com multi-robot path-planning: Maximizing collaboration for variable bandwidth. In A. Martinoli, F. Mondada, N. Correll, G. Mermoud, M. Egerstedt, M. A. Hsieh, L. E. Parker, & K. Støy (Eds.), Distributed autonomous robotic systems (pp. 161–173), Springer.

  42. Otte, M., Kuhlman, M., & Sofge, D. (2017) Multi-robot task allocation with auctions in harsh communication environments. In International symposium on multi-robot and multi-agent systems (MRS) 2017. IEEE, (pp. 32–39).

  43. Otte, M., & Correll, N. (2018). Dynamic teams of robots as ad hoc distributed computers: Reducing the complexity of multi-robot motion planning via subspace selection. Autonomous Robots, 42(8), 1691–1713.

    Google Scholar 

  44. Parker, L.E., & Emmons, B. A. (1997) Cooperative multi-robot observation of multiple moving targets. In Proceedings IEEE International conference on robotics and automation, vol. 3 (pp. 2082–2089).

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

    MATH  Google Scholar 

  46. Pimenta, L. C., Schwager, M., Lindsey, Q., Kumar, V., Rus, D., Mesquita, R. C., & Pereira, G. A. (2009). Simultaneous coverage and tracking (scat) of moving targets with robot networks. In G. S. Chirikjian, H. Choset, M. Morales, & T. Murphey (Eds.), Algorithmic foundation of robotics VIII (pp. 85–99). Springer.

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

    Google Scholar 

  48. Sung, Y., Budhiraja, A. K., Williams, R. K., & Tokekar, P. (2018) Distributed simultaneous action and target assignment for multi-robot multi-target tracking. In 2018 IEEE International conference on robotics and automation (ICRA) (pp. 1–9).

  49. Suomela, J. (2013). Survey of local algorithms. ACM Computing Surveys (CSUR), 45(2), 24.

    MATH  Google Scholar 

  50. Tokekar, P., Isler, V., & Franchi, A. (2014) Multi-target visual tracking with aerial robots. In 2014 IEEE RSJ International conference on intelligent robots and systems (pp. 3067–3072).

  51. Tomlab: Optimization environment large-scale optimization in matlab. http://tomopt.com/docs/quickguide/quickguide006.php, Accessed 3 Jan 2017.

  52. Touzet, C. F. (2000). Robot awareness in cooperative mobile robot learning. Autonomous Robots, 8(1), 87–97.

    Google Scholar 

  53. Turpin, M., Michael, N., & Kumar, V. (2014). Capt: Concurrent assignment and planning of trajectories for multiple robots. The International Journal of Robotics Research, 33(1), 98–112.

    Google Scholar 

  54. Vander Hook, J., Tokekar, P., & Isler, V. (2015). Algorithms for cooperative active localization of static targets with mobile bearing sensors under communication constraints. IEEE Transactions on Robotics, 31(4), 864–876.

    Google Scholar 

  55. Vazirani, V. (2001). Approximation algorithms. Berlin: Springer.

    Google Scholar 

  56. Williams, R. K., Gasparri, A., Sukhatme, G. S., & Ulivi, G. (2015) Global connectivity control for spatially interacting multi-robot systems with unicycle kinematics. In 2015 IEEE international conference on robotics and automation (ICRA). IEEE, (pp. 1255–1261).

  57. Williams, R. K., & Sukhatme, G. S. (2013). Constrained interaction and coordination in proximity-limited multiagent systems. IEEE Transactions on Robotics, 29(4), 930–944.

    Google Scholar 

  58. Xu, Z., Fitch, R., Underwood, J., & Sukkarieh, S. (2013). Decentralized coordinated tracking with mixed discrete-continuous decisions. Journal of Field Robotics, 30(5), 717–740.

    Google Scholar 

  59. Yan, Z., Jouandeau, N., & Cherif, A. A. (2013). A survey and analysis of multi-robot coordination. International Journal of Advanced Robotic Systems, 10(12), 399.

    Google Scholar 

  60. Young, N. E. (2001) Sequential and parallel algorithms for mixed packing and covering. In Proceedings 42nd IEEE symposium on foundations of computer science (pp. 538–546).

  61. Yu, H., Meier, K., Argyle, M., & Beard, R. W. (2015). Cooperative path planning for target tracking in urban environments using unmanned air and ground vehicles. IEEE/ASME Transactions on Mechatronics, 20(2), 541–552.

    Google Scholar 

  62. Zavlanos, M. M., Egerstedt, M. B., & Pappas, G. J. (2011). Graph-theoretic connectivity control of mobile robot networks. Proceedings of the IEEE, 99(9), 1525–1540.

    Google Scholar 

  63. Zhou, K., Roumeliotis, S. I., et al. (2011). Multirobot active target tracking with combinations of relative observations. IEEE Transactions on Robotics, 27(4), 678–695.

    Google Scholar 

  64. Zhou, L., & Tokekar, P. (2018). Active target tracking with self-triggered communications in multi-robot teams. IEEE Transactions on Automation Science and Engineering, 99, 1–12.

    Google Scholar 

Download references


The authors would like to thank Dr. Jukka Suomela from Aalto University for fruitful discussion.

Author information



Corresponding author

Correspondence to Yoonchang Sung.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This material is based upon work supported by the National Science Foundation under Grant No. 1637915.

This is one of the several papers published in Autonomous Robots comprising Special Issue on Robot Communication Challenges: Real-World Problems, Systems, and Methods.


Proof of lemma 1

Equation (5) of a max-min linear program is equivalent to the following max-min problem if the scalar variable w which represents the inner minimization is eliminated:

$$\begin{aligned} \begin{aligned} \max _{x_{m}^{i}}\min _{j\in T}\,&\left( \sum _{i\in R}\sum _{m\in P^i}c_{i,m}^jx_{m}^{i}\right) \\ \text{ subject } \text{ to }\ \ \,&\sum _{m\in {P^i}}x_{m}^{i}\le {1}\ \ \forall {i\in {R}} \\&\ \ \ \ \ \ \ \ x_{m}^{i}\ge {0}\ \ \forall {m\in {P^i}}. \end{aligned} \end{aligned}$$

From Eqs. (5) and (7), the following relationship is satisfied:

$$\begin{aligned} w^*=\min _{j\in T}\left( \sum _{i\in R}\sum _{m\in P^i}c_{i,m}^j{x_{m}^{i}}^*\right) . \end{aligned}$$

Since Eq. (2) does not require \(x_{m}^{i}\) to be a linear value, Eq. (2) is equivalent to Eq. (5) with additional integer constraints.

Proof of lemma 2

Considering \(c_{i,m}^j\), which is a weight between m-th motion primitive of i-th robot and j-th target on graph \(\mathcal {G}_S\), a quality of tracking (\(w(\mathbf t _j)\)) for j-th target can be defined as follows:

$$\begin{aligned} w(\mathbf t _j)\triangleq \max \{c_{i,m}^j\big |x_m^i=1,\ \forall i\in R, m\in P^i\}. \end{aligned}$$

Therefore, the sum of quality of tracking over all targets is:

$$\begin{aligned} \begin{aligned} \sum _{j\in T} w(\mathbf t _j)&=\sum _{j\in T}\max \{c_{i,m}^j\big |x_m^i=1,\ \forall i\in R, m\in P^i\} \\&=\sum _{j\in T}\Big (\sum _{i\in R}y_{i}^{j}\Big (\sum _{m\in P^i}c_{i,m}^jx_{m}^{i}\Big )\Big ). \end{aligned} \end{aligned}$$

Equation (10) is obtained by taking into account the conditional term of the first equation explicitly. The last equation follows from the property that \(y_i^j\) chooses the maximum value of \(\sum _{m\in P^i}c_{i,m}^jx_{m}^{i}\) among all robots, which is shown in lines 10–14 of Algorithm 2. Therefore, the last equation is equal to the inner term of Eq. (4).

Greedy performs poorly for the Bottleneck variant

We present an example of instance that shows an arbitrary poor performance of the greedy algorithm when applied to the Bottleneck variant. Consider the following case where there are two robots (\(\mathbf r _i\)) having two motion primitives (\(\mathbf p _m^i\)) for each and two targets. The realization of the communication and sensing graphs are as in the following table. The tracking quality in this example corresponds to the number of targets being tracked.

 \(\mathbf p _1^1\), \(\mathbf p _1^2\)\(\mathbf p _2^1\), \(\mathbf p _2^2\)
\(\mathbf r _1\)\(\mathbf t _1\)\(\varnothing \)
\(\mathbf r _2\)\(\varnothing \)\(\mathbf t _2\)

Let’s apply the Bottleneck version of greedy algorithm to this case. Since the objective of the Bottleneck variant is to maximize the minimum tracking quality, the robot 1 (\(\mathbf r _1\)) chooses motion primitive 2 (\(\mathbf p _2^1\)) because choosing motion primitive 1 (\(\mathbf p _1^1\)) gives the value of 1 while choosing motion primitive 2 (\(\mathbf p _2^1\)) gives the value of 0. For the same reason, the robot 2 (\(\mathbf r _2\)) chooses motion primitive 1 (\(\mathbf p _1^2\)). This gives the total value of 0, whereas the optimal solution is 2 as the first robot and second robot choose motion primitive 1 (\(\mathbf p _1^1\)) and motion primitive 2 (\(\mathbf p _2^2\)), respectively. The similar case is reproducible with a larger number of robots, motion primitives, and targets. Thus, the simple greedy performs arbitrarily badly for the Bottleneck variant.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sung, Y., Budhiraja, A.K., Williams, R.K. et al. Distributed assignment with limited communication for multi-robot multi-target tracking. Auton Robot 44, 57–73 (2020). https://doi.org/10.1007/s10514-019-09856-1

Download citation


  • Multi-robot system
  • Task assignment
  • Distributed algorithm