Formation Control

Many applications for cooperative multi-agent networks require the agents to arrange themselves into some spatial pattern. This can include alignment of orientations and velocities for flocking behaviors, or specific formations like spacecraft constellations for sensing or vehicle platoons for autonomous driving. The formation control problem seeks to design distributed control strategies for each agent that ensure the entire ensemble can arrange into the desired formation.

A fundamental challenge for solving the formation control problem relates to the sensing and control architecture for the multi-agent system. Our approach is to leverage results from rigidity theory. Rigidity theory studies the solution of a set of geometric constraints on a discrete configuration of points in an Euclidean space. These constraints can include distance or bearing constraints between pairs of points. Of interest in rigidity theory is to determine whether the set of polynomial equations representing these constraints (i) has a solution (independence); (ii) has locally isolated solutions (rigidity); or (iii) has exactly one solution in the given space up to isometric motions (global rigidity).

Our research explores various aspects of rigidity theory and formation control. Topics include:

  • Formation control using bearing sensing and bearing rigidity theory.
  • Alternative architectures exploiting symmetry found in formations.
  • Dynamic controllers to ensure the rigidity property is maintained in a multi-robot formation with uncertain environments.
  • Formations consisting of heterogeneous agent types with different sensing capabilities.
Bearing-only Formation Control Symmetry Forced Formations Formation Balancing

Related Publications:

  1. Z. Martinez and D. Zelazo, “Symmetry-Constrained Formation Maneuvering,” in 64th Israel Annual Conference on Aerospace Sciences, Haifa, Israel, Mar. 2025.
    Martinez2025_IACAS.slides
  2. J. Shi and D. Zelazo, “Extending the Leader-First Follower Structure for Bearing-only Formation Control on Directed Graphs,” 2025.
    Shi2025_TCNS.pdf arXiv: https://arxiv.org/abs/2501.12355
  3. D. Zelazo, S.-ichi Tanigawa, and B. Schulze, “Forced Symmetric Formation Control,” IEEE Transactions on Control of Network Systems, 1–12, 2025.
    zelazo2025TCNS.pdf DOI: 10.1109/TCNS.2025.3525814
  4. C. Xu, D. Zelazo, and B. Wu, “Distributed Prescribed-Time Coordinated Control of Spacecraft Formation Flying under Input Saturation,” Advances in Space Research, 74(5):2302–2315, 2024.
    Xu2023b_J.pdf DOI: https://doi.org/10.1016/j.asr.2024.05.077
  5. C. Xu, D. Zelazo, and B. Wu, “Bearing-based formation control of second-order multiagent systems with bounded disturbances,” International Journal on Robust and Nonlinear Control, 34(1):167–199, 2024.
    Xu2023a_J.pdf DOI: https://doi.org/10.1002/rnc.6966
  6. J. Shi and D. Zelazo, “Bearing-only Formation Control with Directed Sensing,” in 63rd Israel Annual Conference on Aerospace Sciences, Haifa, Israel, May 2024.
    Shi_IACAS2024.slides
  7. M. Sewlia and D. Zelazo, “Bearing-Based Formation Stabilization Using Event-Triggered Control,” International Journal on Robust and Nonlinear Control, 34(6):4375–4387, 2024.
    Sewlia2023a_J.pdf DOI: 10.1002/rnc.7185
  8. J. Shi, “Bearing-only Formation Control with Directed Sensing,” mastersthesis, Technion - Israel Institute of Technology, Autonomous Systems and Robotics, 2024.
    Shi2024.pdf
  9. Z. Sun, S. Zhao, and D. Zelazo, “Characterizing bearing persistence in directed graphs,” in IFAC World Congress, Yokohama, Japan, Jul. 2023.
    Sun2023a_C.pdf DOI: 10.1016/j.ifacol.2023.10.1307 Sun2023a_C.poster
  10. D. Zelazo, B. Shulze, and S.-I. Tanigawa, “Stabilization of Symmetric Formations,” in IFAC World Congress, Yokohama, Japan, Jul. 2023.
    Zelazo2023a_C.pdf Zelazo2023a_C.slides DOI: 10.1016/j.ifacol.2023.10.301
  11. M. Fabris and D. Zelazo, “Bearing-based Autonomous Communication Relay Positioning under Field-of-View Constraints,” Advanced Control for Applications, 4(2):e103, 2022.
    Fabris2021b_J.pdf DOI: 10.1002/adc2.103
  12. B. Pozzan, G. Michieletto, A. Cenedese, and D. Zelazo, “Heterogeneous Formation Control: a Bearing Rigidity Approach,” in IEEE Conference on Decision and Control, Austin, Texas, Dec. 2021.
    Pozzan2021a.pdf DOI: 10.1109/cdc45484.2021.9683374
  13. G. Michieletto, A. Cenedese, and D. Zelazo, “A Unified Dissertation on Bearing Rigidity Theory,” IEEE Transactions on Control of Network Systems, 8(4):1624–1636, 2021.
    Michieletto2021_J.pdf DOI: 10.1109/TCNS.2021.3077712
  14. M. Sewlia, “Distributed Event-Triggered Control for Multi-Agent Systems with Second-Order Dynamics,” mastersthesis, Technion - Israel Institute of Technology, Aerospace Engineering Department, 2020.
    Sewlia2020.pdf
  15. T. Ikeda, D. Zelazo, and K. Kashima, “Maximum Hands-Off Distributed Bearing-Based Formation Control,” in IEEE Conference on Decision and Control, Nice, France, Dec. 2019.
    Ikeda2019a.pdf DOI: 10.1109/cdc40024.2019.9029574
  16. D. Zelazo and S. Zhao, “Formation Control and Rigidity Theory,” Snapshots of Modern Mathematics from Oberwolfach, (12):1–16, 2019.
    Zelazo2019a_J.pdf DOI: 10.14760/SNAP-2019-017-EN
  17. A. Jain and D. Zelazo, “Temporal Circular Formation Control with Bounded Trajectories in a Uniform Flowfield,” in 27th Mediterranean Conference on Control and Automation, Akko, Israel, Jul. 2019.
    Jain2019a.pdf Jain2019a.slides DOI: 10.1109/med.2019.8798531
  18. Q. Van Tran, M. H. Trinh, D. Zelazo, D. Mukherjee, and H.-S. Ahn, “Finite-Time Bearing-Only Formation Control via Distributed Global Orientation Estimation,” IEEE Transactions on Control of Network Systems, 6(2):702–712, 2019.
    VanTran2019.pdf DOI: 10.1109/tcns.2018.2873155
  19. S. Zhao and D. Zelazo, “Bearing Rigidity Theory and its Applications for Control and Estimation of Network Systems: Life beyond distance rigidity,” IEEE Control Systems Magazine, 39(2):66–83, 2019.
    Zhao2017_J.pdf DOI: 10.1109/mcs.2018.2888681
  20. M. H. Trinh, S. Zhao, Z. Sun, D. Zelazo, B. D. O. Anderson, and H. Ahn, “Bearing-Based Formation Control of A Group of Agents with Leader-First Follower Structure,” IEEE Transactions on Automatic Control, 64(2):598–613, 2019.
    Hoang2016a_J.pdf DOI: 10.1109/tac.2018.2836022
  21. D. Goldenberg, “Cooperative Object Manipulation A Rigidity Approach,” mastersthesis, Technion - Israel Institute of Technology, Aerospace Engineering Department, 2019.
    Goldenberg2019.pdf
  22. D. Frank, D. Zelazo, and F. Allgöwer, “Bearing-Only Formation Control with Limited Visual Sensing: Two Agent Case,” in 7th IFAC Workshop on Distributed Estimation and Control in Networked System , Groningen, The Netherlands, Sep. 2018.
    Frank2018.pdf DOI: 10.1016/j.ifacol.2018.12.006
  23. M. H. Trinh, D. Muhkerjee, D. Zelazo, and H.-S. Ahn, “Formations on Directed Cycles with Bearing-Only Measurements,” International Journal of Robust and Nonlinear Control, 28(3):1074–1096, 2018.
    Hoang2016b_J.pdf DOI: 10.1002/rnc.3921
  24. Y. Liu, J. M. Montenbruck, D. Zelazo, M. Odelga, S. Rajappa, H. H. Bülthoff, F. Allgöwer, and A. Zell, “A Distributed Control Approach to Formation Balancing and Maneuvering of Multiple Multirotor UAVs,” IEEE Transactions on Robotics, 34(4):870–882, 2018.
    Liu_IEEETRo2019.pdf DOI: 10.1109/TRO.2018.2853606 Liu_IEEETRo2019.video
  25. D. Frank, “Bearing-only Formation Control with Limited View Constraints,” mastersthesis, University of Stuttgart, 2018.
    Frank2019.pdf
  26. M. H. Trinh, D. Mukherjee, D. Zelazo, and H.-S. Ahn, “Finite-time bearing-only formation control,” in IEEE Conference on Decision and Control, Melbourne, Australia, Dec. 2017.
    Trinh2017c.pdf DOI: 10.1109/cdc.2017.8263876
  27. S. Zhao, Z. Sun, D. Zelazo, M. H. Trinh, and H.-S. Ahn, “Laman Graphs are Generically Bearing Rigid in Arbitrary Dimensions,” in IEEE Conference on Decision and Control, Melbourne, Australia, Dec. 2017.
    Zhao2017a.pdf DOI: 10.1109/cdc.2017.8264151
  28. J. M. Montenbruck, D. Zelazo, and F. Allgöwer, “Fekete Points, Formation Control, and the Balancing Problem,” IEEE Transactions on Automatic Control, 62(10):5069–5081, 2017.
    Montenbruck2016a_J.pdf DOI: 10.1109/tac.2017.2679073
  29. S. Zhao and D. Zelazo, “Translational and Scaling Formation Maneuver Control via a Bearing-Based Approach,” IEEE Transactions on Control of Network Systems, 4(3):429–438, 2017.
    Zhao2015b_J.pdf DOI: 10.1109/tcns.2015.2507547 Zhao2015b_J.video
  30. M. H. Trinh, D. Mukherjee, D. Zelazo, and H.-S. Ahn, “Planar Bearing-only Cyclic Pursuit for Target Capture,” in IFAC World Congress, Toulouse, France, Jul. 2017.
    Trinh2017b.pdf DOI: 10.1016/j.ifacol.2017.08.1759
  31. D. Mukherjee, M. H. Trinh, D. Zelazo, and H.-S. Ahn, “Bearing-only Cyclic Pursuit in 2-D for Capture of Moving Target,” in 57th Israel Annual Conference on Aerospace Sciences , Tel-Aviv, Israel, Feb. 2017.
  32. F. Schiano, A. Franchi, D. Zelazo, and P. R. Giordano, “A Rigidity-Based Decentralized Bearing Formation Controller for Groups of Quadrotor UAVs,” in IEEE/RSJ International Conference on Intelligent Robots and Systems, Daejeon, Korea, Sep. 2016.
    Schiano2016a.pdf DOI: 10.1109/iros.2016.7759748 Schiano2016a.video
  33. S. Zhao and D. Zelazo, “Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization,” IEEE Transactions on Automatic Control, 61(6):1255–1268, 2016.
    Zhao2014a_J.pdf DOI: 10.1109/tac.2015.2459191 Zhao2014a_J.video
  34. S. Zhao and D. Zelazo, “Localizability and distributed protocols for bearing-based network localization in arbitrary dimensions,” Automatica, 69:334–341, 2016.
    Zhao2015a_J.pdf DOI: 10.1016/j.automatica.2016.03.010
  35. O. Rozenheck, “Distance-Constrained Formation Tracking Control,” mastersthesis, Technion - Israel Institute of Technology, Aerospace Engineering Department, 2016.
    Rozenheck2016.pdf
  36. M. M. Montenbruck, D. Zelazo, and F. Allgöwer, “Retraction Balancing and Formation Control,” in 54th IEEE Conference on Decision and Control, Osaka, Japan, Dec. 2015.
    Montenbruck2015.pdf DOI: 10.1109/cdc.2015.7402784
  37. D. Zelazo, P. R. Giordano, and A. Franchi, “Bearing-Only Formation Control Using an SE(2) Rigidity Theory,” in 54th IEEE Conference on Decision and Control, Osaka, Japan, Dec. 2015.
    Zelaxo2015c1.pdf DOI: 10.1109/cdc.2015.7403182
  38. S. Zhao and D. Zelazo, “Bearing-Based Formation Stabilization with Directed Interaction Topologies,” in 54th IEEE Conference on Decision and Control, Osaka, Japan, Dec. 2015.
    Zhao2015c1.pdf DOI: 10.1109/cdc.2015.7403181
  39. S. Zhao and D. Zelazo, “Bearing-Based Formation Maneuvering,” in IEEE International Symposium on Intelligent Control, Sydney, Australia, Sep. 2015.
    Zhao2015c2.pdf DOI: 10.1109/isic.2015.7307285 Zhao2015c2.video
  40. O. Rozenheck, S. Zhao, and D. Zelazo, “A Proportional-Integral Controller for Distance-Based Formation Tracking,” in European Control Conference, Linz, Austria, Jul. 2015.
    Rozenheck2014b.pdf Rozenheck2014b.slides DOI: 10.1109/ecc.2015.7330781
  41. S. Zhao and D. Zelazo, “Bearing-Based Distributed Control and Estimation of Multi-Agent Systems,” in European Control Conference, Linz, Austria, Jul. 2015.
    Zhao2014a.pdf DOI: 10.1109/ecc.2015.7330866
  42. O. Rozenheck, S. Zhao, and D. Zelazo, “Formation Velocity Tracking with Proportional Control,” in 55th Israel Annual Conference on Aerospace Sciences , Haifa, Israel, Feb. 2015.
    Rozenheck2014a.pdf
  43. S. Zhao and D. Zelazo, “Bearing-Constrained Formation Control Using Bearing Measurements,” in 55th Israel Annual Conference on Aerospace Sciences, Haifa, Israel, Feb. 2015.
  44. D. Zelazo, A. Franchi, H. H. Bülthoff, and P. Robuffo Giordano, “Decentralized Rigidity Maintenance Control with Range-only Measurements for Multi-Robot Systems,” International Journal of Robotics Research, 34(1):105–128, 2015.
    Zelazo2013a_J.pdf DOI: 10.1177/0278364914546173 Zelazo2013a_J.video
  45. D. Zelazo, A. Franchi, and P. R. Giordano, “Rigidity Theory in SE(2) for Unscaled Relative Position Estimation Using Only Bearing Measurements,” in European Control Conference, Strasbourg, France, Jun. 2014.
    Zelazo2014.pdf Zelazo2014.slides DOI: 10.1109/ECC.2014.6862558
  46. D. Zelazo, A. Franchi, F. Allgöwer, H. H. Bülthoff, and P. Robuffo Giordano, “Rigidity Maintenance Control for Multi-Robot Systems,” in Proceedings of Robotics: Science and Systems, Sydney, Australia, Jul. 2012.
    Zelazo2012c.pdf DOI: 10.15607/rss.2012.viii.060
  47. D. Zelazo and F. Allgöwer, “Growing Optimally Rigid Formations,” in American Control Conference, Montreal, Canada, 2012.
    Zelazo2012.pdf DOI: 10.1109/acc.2012.6315460
  48. D. Zelazo, A. Rahmani, J. Sandhu, and M. Mesbahi, “Decentralized Formation Control via the Edge Laplacian,” in American Control Conference, Seattle, WA, Jun. 2008.
    Zelazo2008a.pdf DOI: 10.1109/ACC.2008.4586588