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Recent Advances in Formations of Multiple Robots

  • Group Robotics (M Gini and F Amigoni, Section Editors)
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Abstract

Purpose of Review

Formation control is a canonical problem in multi-robot systems, which focuses on the ability of a group of robots to travel in coordination through an area, while maintaining a certain shape or a particular behavior. The robot groups vary in their communication, computation, and sensing capabilities. Moreover, the formation control task itself may have various objectives. These divergences force the use of different models for controlling the formation and for analyzing the task performance. In this paper, we describe the formation control problem and survey recent advances focusing on aspects of maintaining a formation by a group of robots distinguished by the means of analysis.

Recent Findings

Various approaches may be applied for the sake of formation maintenance, whereas each approach possesses a different perspective in regard with formation control. Recent research focuses on combining those approaches, due to their applicability regarding certain scenarios. For instance, consensus-based control and collision avoidance are usually intertwined together for the sake of reaching a consensus in a manner which is collision-free. Furthermore, machine learning (ML)–based methods for navigating a robot team through unknown complex environments can be incorporated, where the robot team aims to reach a goal position while avoiding collisions and maintaining connectivity. Moreover, recent approaches focus on developing new mechanisms or adapt existing ones for formation control for tolerating limitations in sensing, communication, and coordination, preferably distributively while providing performance guarantees.

Conclusion

Such combined approaches yield that the means of analysis, which can be applied to each one separately, can also be utilized in an intertwined manner, and thus provide us with novel methods for preserving formation. Whereas some approaches were vastly investigated (e.g., consensus-based formation control) and need to be adapted to distributed imperfect settings, others still require further insight for unveiling brand new architectures and tools (e.g., ML-based formation control).

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References

  1. Amigoni F, Banfi J, Basilico N. Multirobot exploration of communication-restricted environments: a survey. IEEE Intell Syste 2017;32(6):48–57.

    Article  Google Scholar 

  2. Tuci E, Alkilabi MHM, Akanyeti O. Cooperative object transport in multi-robot systems: a review of the state-of-the-art. Front Robot AI 2018;5:59.

    Article  Google Scholar 

  3. Dong X, Li Q, Ren Z, Zhong Y. Formation-containment control for high-order linear time-invariant multi-agent systems with time delays. J Franklin Inst 2015;352(9):3564–3584.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ramachandran RK, Preiss JA, Sukhatme GS. 2019. Resilience by reconfiguration: exploiting heterogeneity in robot teams. arXiv:1903.04856.

  5. Shapira Y, Agmon N. Path planning for optimizing survivability of multi-robot formation in adversarial environments. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS); 2015. p. 4544–4549.

  6. Mosteo AR, Montijano E, Tardioli D. Optimal role and position assignment in multi-robot freely reachable formations. Automatica 2017;81:305–313.

    Article  MathSciNet  MATH  Google Scholar 

  7. MacAlpine P, Price E, Stone P. Scram: scalable collision-avoiding role assignment with minimal-makespan for formational positioning. In: AAAI; 2015. p. 2096–2102.

  8. Bose K, Adhikary R, Kundu MK, Sau B. Arbitrary pattern formation on infinite grid by asynchronous oblivious robots. Theor Comput Sci 2020;815:213–227.

    Article  MathSciNet  MATH  Google Scholar 

  9. Flocchini P, Prencipe G, Santoro N, Viglietta G. Distributed computing by mobile robots: uniform circle formation. Distrib Comput 2017;30(6):413–457.

    Article  MathSciNet  MATH  Google Scholar 

  10. Hyondong O, Shirazi AR, Sun C, Jin Y. Bio-inspired self-organising multi-robot pattern formation: a review. Robot Auton Syst 2017;91:83–100.

    Article  Google Scholar 

  11. Wang Y, Cheng L, Hou Z-G, Yu J, Tan M. Optimal formation of multirobot systems based on a recurrent neural network. IEEE Trans Neural Netw Learn Syst 2015;27(2):322–333.

    Article  MathSciNet  Google Scholar 

  12. Wan S, Lu J, Fan P. Semi-centralized control for multi robot formation. In: 2017 2nd International Conference on Robotics and Automation Engineering (ICRAE). IEEE; 2017. p. 31–36.

  13. Dutta A, Dasgupta P, Nelson C. Distributed configuration formation with modular robots using (sub) graph isomorphism-based approach. Auton Robot 2019;43(4):837–857.

    Article  Google Scholar 

  14. Dutta A, Dasgupta P. 2016. formation and Information collection by modular robotic systems. In: Simultaneous configuration IEEE international conference on robotics and automation (ICRA). IEEE; 2016, p. 5216–5221.

  15. Beard RW, Lawton J, Hadaegh FY. A coordination architecture for spacecraft formation control. IEEE Trans Control Syst Technol 2001;9(6):777–790.

    Article  Google Scholar 

  16. Oh K-K, Park M-C, Ahn H-S. A survey of multi-agent formation control. Automatica 2015; 53:424–440.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ren W. Consensus strategies for cooperative control of vehicle formations. IET Control Theory Appl 2007;1(2):505–512.

    Article  Google Scholar 

  18. Peng Z, Yang S, Wen G, Rahmani A. 2014. Distributed consensus-based robust adaptive formation control for nonholonomic mobile robots with partial known dynamics. Math Probl Eng. 2014:

  19. Wei H, Lv Q, Duo N, Wang G, Liang B. Consensus algorithms based multi-robot formation control under noise and time delay conditions. Appl Sci 2019;9(5):1004.

    Article  Google Scholar 

  20. Wang C, He P, Li H, Tian J, Wang K, Li Y. Noise-tolerance consensus formation control for multi-robotic networks. Trans Inst Meas Control. 2020;42(8):1569–1581.

    Article  Google Scholar 

  21. Aditya P, Apriliani E, Zhai G, Arif DK. 2019. Formation control of multi-robot motion systems and state estimation using extended kalman filter. In: International Conference on Electrical Engineering and Informatics (ICEEI). IEEE; 2019, p. 99–104.

  22. Listmann KD, Masalawala MV, Adamy J. 2009. Consensus for formation control of nonholonomic mobile robots. In: IEEE international conference on robotics and automation. IEEE; 2009, p. 3886–3891.

  23. Briñón-Arranz L, Renzaglia A, Schenato L. Multirobot symmetric formations for gradient and hessian estimation with application to source seeking. IEEE Trans Robot 2019;35(3):782–789.

    Article  Google Scholar 

  24. Zhu S, Wang D, Low CB. Cooperative control of multiple uavs for source seeking. J Intell Robot Syst 2013;70(1-4):293–301.

    Article  Google Scholar 

  25. Antonelli G, Arrichiello F, Caccavale F, Marino A. Decentralized time-varying formation control for multi-robot systems. Int Jo Robot Res 2014;33(7):1029–1043.

    Article  Google Scholar 

  26. Goodwine B. Modeling a multi-robot system with fractional-order differential equations. In: 2014 IEEE International Conference On Robotics and Automation (ICRA). IEEE; 2014, p.1763–1768.

  27. Heymans N, Bauwens J-C. Fractal rheological models and fractional differential equations for viscoelastic behavior. Rheol Acta 1994;33(3):210–219.

    Article  Google Scholar 

  28. Mayes J. 2012. Reduction and approximation in large and infinite potential-driven flow networks. Citeseer.

  29. Habibi G, Kingston Z, Xie W, Jellins M, McLurkin J. 2015. estimation and Motion controllers for collective transport by multi-robot systems. In: Distributed centroid IEEE International Conference on Robotics and Automation (ICRA). IEEE; 2015, p. 1282–1288.

  30. Bo G, Dai L, Cimini LJ. Routing strategies in multihop cooperative networks. IEEE Trans Wirel Commun 2009;8(2):843–855.

    Article  Google Scholar 

  31. McLurkin J, Yamins D. Dynamic task assignment in robot swarms. In Robotics: Science and Systems, vol. 8. Citeseer; 2005.

  32. Montijano E, Cristofalo E, Zhou D, Schwager M, Saguees C. Vision-based distributed formation control without an external positioning system. IEEE Trans Robot 2016;32(2):339–351.

    Article  Google Scholar 

  33. Aranda M, López-Nicolás G, Sagüés C, Mezouar Y. Formation control of mobile robots using multiple aerial cameras. IEEE Trans Robot 2015;31(4):1064–1071.

    Article  Google Scholar 

  34. Kuriki Y, Namerikawa T. Formation control with collision avoidance for a multi-uav system using decentralized mpc and consensus-based control. SICE J Control Measur Syst Integr 2015;8(4):285–294.

    Article  Google Scholar 

  35. Alonso-Mora J, Montijano E, Nägeli T, Hilliges O, Schwager M, Rus D. Distributed multi-robot formation control in dynamic environments. Auton Robot 2019;43(5):1079–1100.

    Article  Google Scholar 

  36. Alonso-Mora J, Baker S, Rus D. Multi-robot formation control and object transport in dynamic environments via constrained optimization. Int J Robot Res 2017;36(9):1000–1021.

    Article  Google Scholar 

  37. Deng G, Zhang H, Zhong H, Miao Z, Li L, Yu M, Jonathan Wu QM. 2019. Distributed Multi-robot formation control based on two-layer nearest neighbor information (tnni) consensus. In: IEEE International Conference on Systems, Man and Cybernetics (SMC). IEEE; 2019, p. 1091–1097.

  38. Rahimi R, Abdollahi F, Naqshi K. Time-varying formation control of a collaborative heterogeneous multi agent system. Robot Auton Syst 2014;62(12):1799–1805.

    Article  Google Scholar 

  39. Kokotovic PV. The joy of feedback: nonlinear and adaptive. IEEE Control Syst Mag 1992;12(3): 7–17.

    Article  Google Scholar 

  40. Burns A, Schulze B, John A St. Persistent multi-robot formations with redundancy. In: Distributed Autonomous Robotic Systems. Springer; 2018. p. 133–146.

  41. Chen Z, Jiang C, Guo Y. 2019. Distance-based formation control of a three-robot system. In: Chinese Control And Decision Conference (CCDC). IEEE; 2019, p. 5501–5507.

  42. Abichandani P, Levin K, Bucci D. 2019. Decentralized formation coordination of multiple quadcopters under communication constraints. In: International Conference on Robotics and Automation (ICRA). IEEE; 2019. p. 3326–3332.

  43. Otte M, Correll N. Any-com multi-robot path-planning with dynamic teams: multi-robot coordination under communication constraints. In: Experimental Robotics. Springer; 2014, p. 743–757.

  44. Otte M, Correll N. Any-com multi-robot path-planning: Maximizing collaboration for variable bandwidth. In: Distributed autonomous robotic systems. Springer; 2013, p. 161–173.

  45. Pan Z, Wang D, Deng H, Li K. A virtual spring method for the multi-robot path planning and formation control. Int J Control Autom Syst 2019;17(5):1272–1282.

    Article  Google Scholar 

  46. Zhang F, Chen W. 2007. Self-healing for mobile robot networks with motion synchronization. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE: 2007. p. 3107–3112.

  47. Cao K, Qiu Z, Xie L. Relative docking and formation control via range and odometry measurements. IEEE Trans Control Netw Syst 2019;7(2):912–922.

    Article  MathSciNet  MATH  Google Scholar 

  48. Mei W, Bullo F. 2017. Lasalle invariance principle for discrete-time dynamical systems: a concise and self-contained tutorial. arXiv:1710.03710.

  49. Fidan B, Dasgupta S, Anderson BDO. Adaptive range-measurement-based target pursuit. Int J Adapt Control Signal Process 2013;27(1-2):66–81.

    Article  MathSciNet  MATH  Google Scholar 

  50. Güler S, Fidan B, Dasgupta S, Anderson BDO, Shames I. Adaptive source localization based station keeping of autonomous vehicles. IEEE Trans Autom Control 2016;62(7):3122–3135.

    Article  MathSciNet  MATH  Google Scholar 

  51. Nguyen T. M., Qiu Z, Cao M, Nguyen T. H. , Xie L. Single landmark distance-based navigation. IEEE Trans Control Syst Technol 2020;28(5):2021–2028.

    Article  Google Scholar 

  52. Jiang B, Deghat M, Anderson BDO. Simultaneous velocity and position estimation via distance-only measurements with application to multi-agent system control. IEEE Trans Autom Control 2016;62(2): 869–875.

    Article  MathSciNet  MATH  Google Scholar 

  53. He Y, Zhu L, Sun G, Dong M. Study on formation control system for underwater spherical multi-robot. Microsyst Technol 2019;25(4):1455–1466.

    Article  Google Scholar 

  54. Hauri S, Alonso-Mora J, Breitenmoser A, Siegwart R, Beardsley P. Multi-robot formation control via a real-time drawing interface. In: Field and service robotics. Springer; 2014. p. 175–189.

  55. Reynolds CW. Flocks, herds and schools: A distributed behavioral model. In: Proceedings of the 14th annual conference on Computer graphics and interactive techniques; 1987. p. 25–34.

  56. Olfati-Saber R. Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Trans Autom Control 2006;51(3):401–420.

    Article  MathSciNet  MATH  Google Scholar 

  57. Alonso-Mora J, Breitenmoser A, Rufli M, Beardsley P, Siegwart R. Optimal reciprocal collision avoidance for multiple non-holonomic robots. In: Distributed autonomous robotic systems. Springer; 2013. p. 203–216.

  58. Jia Y, Wang L. Leader–follower flocking of multiple robotic fish. IEEE/ASME Trans Mechatron 2014;20(3):1372–1383.

    Article  Google Scholar 

  59. Gunn T, Anderson J. Dynamic heterogeneous team formation for robotic urban search and rescue. J Comput Syst Sci 2015;81(3):553–567.

    Article  Google Scholar 

  60. Cai X, De Queiroz M. Adaptive rigidity-based formation control for multirobotic vehicles with dynamics. IEEE Trans Control Syst Technol 2014;23(1):389–396.

    Article  Google Scholar 

  61. Derhami V, Momeni Y. Applying reinforcement learning in formation control of agents. In: Intelligent Distributed Computing IX. Springer; 2016. p. 297–307.

  62. Khan A, Tolstaya E, Ribeiro A, Kumar V. Graph policy gradients for large scale robot control. In: Conference on Robot Learning; 2020. p. 823–834.

  63. Jiang C, Chen Z, Guo Y. Learning decentralized control policies for multi-robot formation. In: 2019 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM). IEEE; 2019p. 758–765. This study uses deep-learning for learning control policies to achieve multi-robot formation from the robot’s local observation without inter-robot communication.

  64. Lin J, Yang X, Zheng P, Cheng H. 2019. End-to-end decentralized multi-robot navigation in unknown complex environments via deep reinforcement learning. In: IEEE International Conference on Mechatronics and Automation (ICMA). IEEE; 2019, p. 2493–2500.

  65. Schulman J, Wolski F, Dhariwal P, Radford A, Klimov O. 2017. Proximal policy optimization algorithms. arXiv:1707.06347.

  66. Xiao H, Philip Chen C L. Leader-follower consensus multi-robot formation control using neurodynamic-optimization-based nonlinear model predictive control. IEEE Access 2019;7:43581–43590.

    Article  Google Scholar 

  67. Desai JP. Modeling multiple teams of mobile robots: a graph theoretic approach. In: Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No. 01CH37180), vol. 1. IEEE; 2001. p. 381–386.

  68. Kaminka GA, Lupu I, Agmon N. Construction of optimal control graphs in multi-robot systems. In: Distributed Autonomous Robotic Systems. Springer; 2018, p. 163–175.

  69. Yoo SJ, Park BS. Connectivity-preserving approach for distributed adaptive synchronized tracking of networked uncertain nonholonomic mobile robots. IEEE Trans Cybern 2017;48(9):2598–2608.

    Article  Google Scholar 

  70. Yoo SJ, Park BS. Connectivity preservation and collision avoidance in networked nonholonomic multi-robot formation systems: Unified error transformation strategy. Automatica 2019;103:274–281.

    Article  MathSciNet  MATH  Google Scholar 

  71. Dai Y, Kim Y, Wee S, Lee D, Lee S. A switching formation strategy for obstacle avoidance of a multi-robot system based on robot priority model. ISA Trans 2015;56:123–134.

    Article  Google Scholar 

  72. Lee S-M, Kim H, Myung H, Yao X. Cooperative coevolutionary algorithm-based model predictive control guaranteeing stability of multirobot formation. IEEE Trans Control Syst Technol 2014;23(1): 37–51.

    Google Scholar 

  73. Benzerrouk A, Adouane L, Martinet P. Stable navigation in formation for a multi-robot system based on a constrained virtual structure. Robot Auton Syst 2014;62(12):1806–1815.

    Article  Google Scholar 

  74. Adouane L. 2009. Orbital obstacle avoidance algorithm for reliable and on-line mobile robot navigation. Portuguese Journal Robotica N79, automacao controlo and instrumentacao.

  75. Kim D-H, Kim J-H. A real-time limit-cycle navigation method for fast mobile robots and its application to robot soccer. Robot Auton Syst 2003;42(1):17–30.

    Article  MATH  Google Scholar 

  76. Jie MS, Baek JH, Hong YS, Lee KW. Real time obstacle avoidance for mobile robot using limit-cycle and vector field method. In: International Conference on Knowledge-Based and Intelligent Information and Engineering Systems. Springer; 2006, p. 866–873.

  77. Choi S, Kim J. 2019. Three dimensional formation control to pursue an underwater evader utilizing underwater robots measuring the sound generated from the evader. IEEE Access 7:150720–150728.

  78. Reddy P V, Justh E W, Krishnaprasad PS. Motion Camouflage in three dimensions. In: proceedings of the 45th IEEE Conference on Decision and Control. . IEEE; 2006. p. 3327–3332.

  79. Liu C, He J, Zhu S, Chen C. Dynamic topology inference via external observation for multi-robot formation control. In: 2019 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM). IEEE; 2019. pages p. 6 This research presents the topology inference problem of multi-robot formation control systems via external observation, which is first to require no prior knowledge of system dynamics.

  80. Nascimento TP, Conceiċao AGS, Moreira AP. Multi-robot nonlinear model predictive formation control: the obstacle avoidance problem. Robotica 2016;34(3):549.

    Article  Google Scholar 

  81. Peng L, Guan F, Perneel L, Fayyad-Kazan H, Timmerman M. Decentralized multi-robot formation control with communication delay and asynchronous clock. J Intell Robot Syst 2018;89(3-4): 465–484.

    Article  Google Scholar 

  82. Houska B, Ferreau HJ, Diehl M. An auto-generated real-time iteration algorithm for nonlinear mpc in the microsecond range. Automatica 2011;47(10):2279–2285.

    Article  MathSciNet  MATH  Google Scholar 

  83. Xu D, Zhang X, Zhu Z, Chen C, Yang P. Behavior-based formation control of swarm robots. mathematical Problems in Engineering; 2014.

  84. Vásárhelyi G, Cs V, Somorjai G, Tarcai N, Szörényi T, Nepusz T, Vicsek T. 2014. Outdoor flocking and Formation flight with autonomous aerial robots. In: IEEE/RSJ International Conference on Intelligent Robots and SystemsIEEE; 2014. p. 3866–3873.

  85. Dang AD, La HM, Horn J. Distributed formation control for autonomous robots following desired shapes in noisy environment. In: IEEE international conference on multisensor fusion and integration for intelligent systems (MFI). IEEE; 2016. p. 285–290.

  86. Huang J, Wu W, Ning Y, Zhou N, Xu Z. 2019. A behavior control scheme for multi-robot systems under human intervention. In: Chinese Control Conference (CCC)IEEE; 2019. p. 6189–6193.

  87. Shen D, Sun W, Sun Z. Adaptive pid formation control of nonholonomic robots without leader’s velocity information. ISA Trans 2014;53(2):474–480.

    Article  Google Scholar 

  88. Gallardo N, Pai K, Erol BA, Benavidez P, Mo J. 2016. Parrot bebop drone. In: Formation control implementation using kobuki turtlebots World Automation Congress (WAC)IEEE; 2016. p. 1–6.

  89. Li G, St-Onge D, Pinciroli C, Gasparri A, Garone E, Beltrame G. This work suggests distributed behaviors for progressively deployed swarm robots, and shows how a formation can gradually grow in time, with guaranteed convergence for the joining process. Auton Robot 2019;43(6):1505–1521.

    Article  Google Scholar 

  90. Dutta A, Ufimtsev V, Asaithambi A. Correlation clustering based coalition formation for multi-robot task allocation. In: Proceedings of the 34th ACM/SIGAPP Symposium on Applied Computing. 2019. p. 906–913.

  91. Bansal N, Blum A, Chawla S. Correlation clustering. Mach Learn 2004;56(1-3):89–113.

    Article  MathSciNet  MATH  Google Scholar 

  92. Demaine ED, Immorlica N. Correlation clustering with partial information. In: Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques. Springer; 2003. p. 1–13.

  93. Ge X, Han Q-L, Zhang X-M. Achieving cluster formation of multi-agent systems under aperiodic sampling and communication delays. IEEE Trans Ind Electron 2017;65(4):3417– 3426.

    Article  Google Scholar 

  94. Khalil HK. Universal integral controllers for minimum-phase nonlinear systems. IEEE Trans Autom Control 2000;45(3):490–494.

    Article  MathSciNet  MATH  Google Scholar 

  95. Sutton RS, Barto AG. 2018. Reinforcement an introduction learning. MIT press.

  96. Liu Y, Bucknall R. A survey of formation control and motion planning of multiple unmanned vehicles. Robotica 2018;36(7):1019–1047.

    Article  Google Scholar 

  97. Abichandani P, Benson HY, Kam M. Decentralized multi-vehicle path coordination under communication constraints. In: 2011 IEEE/RSJ International Conference On Intelligent Robots and Systems. IEEE; 2011. p. 2306–2313.

  98. Abichandani P, Mallory K, Hsieh M-yA. Experimental multi-vehicle path coordination under communication connectivity constraints. In: Experimental Robotics. Springer; 2013. p. 183–197.

  99. Abichandani P, Torabi S, Basu S, Benson H. Mixed integer nonlinear programming framework for fixed path coordination of multiple underwater vehicles under acoustic communication constraints. IEEE J Ocean Eng 2015;40(4):864–873.

    Article  Google Scholar 

  100. Kanayama Y, Kimura Y, Miyazaki F, Noguchi T. A stable tracking control method for an autonomous mobile robot. In: Proceedings IEEE International Conference on Robotics and Automation. IEEE; 1990. p. 384–389.

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  1. Department of Computer Science, Bar Ilan University, Ramat Gan, Israel

    Saar Cohen & Noa Agmon

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  1. Saar Cohen
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Cohen, S., Agmon, N. Recent Advances in Formations of Multiple Robots. Curr Robot Rep 2, 159–175 (2021). https://doi.org/10.1007/s43154-021-00049-2

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