Formation control with obstacle avoidance of second-order multi-agent systems under directed communication topology


This paper addresses the obstacle avoidance problem of formation control for the multi-agent systems modeled by double integrator dynamics under a directed interconnection topology. The control task is finished by a leader-follower formation scheme combined with an artificial potential field (APF) method. The leader-follower scheme is carried out by taking the desired trajectory with the desired velocity as virtual leader, while the APF method is carried out by dealing with the obstacles as the high potential points. When the obstacle avoidance tasks are finished, the artificial potential forces degrade the formation performance, so their undesired effects are treated as disturbances, which is analyzed by the robust H performance. Based on Lyapunov stability theory, it is proved that the proposed formation approach can realize the control objective. The result is also extended to the switching multi-agent formation. The effectiveness of the proposed formation scheme is further confirmed by simulation studies.

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  1. 1

    Yu W W, Chen G R, Wang Z D, et al. Distributed consensus filtering in sensor networks. IEEE Trans Syst Man Cybern B, 2009, 39: 1568–1577

    Article  Google Scholar 

  2. 2

    Abdessameud A, Tayebi A. Attitude synchronization of a group of spacecraft without velocity measurements. IEEE Trans Autom Control, 2009, 54: 2642–2648

    MathSciNet  Article  MATH  Google Scholar 

  3. 3

    Hoffmann G M, Tomlin C J. Decentralized cooperative collision avoidance for acceleration constrained vehicles. In: Proceedings of Conference on Decision and Control, 2008. 4357-4363

  4. 4

    Fua C H, Ge S S. COBOS: cooperative backoff adaptive scheme for multirobot task allocation. IEEE Trans Robot, 2005, 21: 1168–1178

    Article  Google Scholar 

  5. 5

    Cui R, Ge S S, Ren B. Synchronized altitude tracking control of multiple unmanned helicopters. In: Proceedings of American Control Conference, 2010. 4433-4438

  6. 6

    Abdessameud A, Tayebi A. Formation control of VTOL unmanned aerial vehicles with communication delays. Automatica, 2011, 47: 2383–2394

    MathSciNet  Article  MATH  Google Scholar 

  7. 7

    Ge S S, Fua C H, Lim K W. Multi-robot formations: queues and artificial potential trenches. In: Proceedings of IEEE International Conference on Robotics and Automation, 2004. 3345-3350

  8. 8

    Cui R, Ge S S, How B V E, et al. Leader-follower formation control of underactuated autonomous underwater vehicles. Ocean Eng, 2010, 37: 1491–1502

    Article  Google Scholar 

  9. 9

    Consolini L, Morbidi F, Prattichizzo D, et al. Leader-follower formation control of nonholonomic mobile robots with input constraints. Automatica, 2008, 44: 1343–1349

    MathSciNet  Article  MATH  Google Scholar 

  10. 10

    Lewis M A, Tan K H. High precision formation control of mobile robots using virtual structures. Auton Robot, 1997, 4: 387–403

    Article  Google Scholar 

  11. 11

    Balch T, Arkin R C. Behavior-based formation control for multirobot teams. IEEE Trans Robot Autom, 1998, 14: 926–939

    Article  Google Scholar 

  12. 12

    Wen G, Chen C L P, Liu Y J, et al. Neural network-based adaptive leader-following consensus control for a class of nonlinear multiagent state-delay systems. IEEE Trans Cybern, 2017, 47: 2151–2160

    Article  Google Scholar 

  13. 13

    Ma C, Li T, Zhang J. Consensus control for leader-following multi-agent systems with measurement noises. J Syst Sci Complex, 2010, 23: 35–49

    MathSciNet  Article  MATH  Google Scholar 

  14. 14

    Liu J W, Huang J. Leader-following consensus of linear discrete-time multi-agent systems subject to jointly connected switching networks. Sci China Inf Sci, 2018, 61: 112208

    MathSciNet  Article  Google Scholar 

  15. 15

    Wang Z X, Fan J B, Jiang G P, et al. Consensus in nonlinear multi-agent systems with nonidentical nodes and sampled-data control. Sci China Inf Sci, 2018, 61: 122203

    MathSciNet  Article  Google Scholar 

  16. 16

    Ren W, Sorensen N. Distributed coordination architecture for multi-robot formation control. Robot Auton Syst, 2008, 56: 324–333

    Article  MATH  Google Scholar 

  17. 17

    Xiao F, Wang L, Chen J, et al. Finite-time formation control for multi-agent systems. Automatica, 2009, 45: 2605–2611

    MathSciNet  Article  MATH  Google Scholar 

  18. 18

    Wen G, Chen C L P, Feng J, et al. Optimized multi-agent formation control based on an identifier-actor-critic reinforcement learning algorithm. IEEE Trans Fuzzy Syst, 2018, 26: 2719–2731

    Article  Google Scholar 

  19. 19

    Wang C Y, Zuo Z Y, Gong Q H, et al. Formation control with disturbance rejection for a class of Lipschitz nonlinear systems. Sci China Inf Sci, 2017, 60: 070202

    MathSciNet  Article  Google Scholar 

  20. 20

    Liu C L, Tian Y P. Formation control of multi-agent systems with heterogeneous communication delays. Int J Syst Sci, 2009, 40: 627–636

    MathSciNet  Article  MATH  Google Scholar 

  21. 21

    Xie G, Wang L. Moving formation convergence of a group of mobile robots via decentralised information feedback. Int J Syst Sci, 2009, 40: 1019–1027

    MathSciNet  Article  MATH  Google Scholar 

  22. 22

    Khatib O. Real-time obstacle avoidance for manipulators and mobile robots. Int J Robot Res, 1986, 5: 90–98

    Article  Google Scholar 

  23. 23

    Wen G, Ge S S, Tu F, et al. Artificial potential-based adaptive H synchronized tracking control for accommodation vessel. IEEE Trans Ind Electron, 2017, 64: 5640–5647

    Article  Google Scholar 

  24. 24

    Yan J, Guan X P, Tan F X. Target tracking and obstacle avoidance for multi-agent systems. Int J Autom Comput, 2010, 7: 550–556

    Article  Google Scholar 

  25. 25

    Zavlanos M M, Pappas G J. Potential fields for maintaining connectivity of mobile networks. IEEE Trans Robot, 2007, 23: 812–816

    Article  Google Scholar 

  26. 26

    Chen B S, Lee C H, Chang Y C. H tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach. IEEE Trans Fuzzy Syst, 1996, 4: 32–43

    Article  Google Scholar 

  27. 27

    Yang Y S, Zhou C J. Adaptive fuzzy H stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach. IEEE Trans Fuzzy Syst, 2005, 13: 104–114

    Article  Google Scholar 

  28. 28

    Lin P, Jia Y, Li L. Distributed robust consensus control in directed networks of agents with time-delay. Syst Control Lett, 2008, 57: 643–653

    MathSciNet  Article  MATH  Google Scholar 

  29. 29

    Lin P, Jia Y. Robust H consensus analysis of a class of second-order multi-agent systems with uncertainty. IET Control Theory Appl, 2010, 4: 487–498

    MathSciNet  Article  Google Scholar 

  30. 30

    Xue D, Yao J, Wang J. H formation control and obstacle avoidance for hybrid multi-agent systems. J Appl Math, 2013, 2013: 1–11

    MathSciNet  Article  Google Scholar 

  31. 31

    Wen G, Chen C L P, Liu Y J. Formation control with obstacle avoidance for a class of stochastic multiagent systems. IEEE Trans Ind Electron, 2018, 65: 5847–5855

    Article  Google Scholar 

  32. 32

    Wang J L, Wu H N. Leader-following formation control of multi-agent systems under fixed and switching topologies. Int J Control, 2012, 85: 695–705

    MathSciNet  Article  MATH  Google Scholar 

  33. 33

    Tanner H G, Jadbabaie A, Pappas G J. Stable flocking of mobile agents part I: dynamic topology. In: Proceedings of Conference on Decision and Control, 2003. 2016-2021

  34. 34

    Chai W W. Synchronization in Complex Networks of Nonlinear Dynamical Systems. Singapore: World Scientific, 2007

    Google Scholar 

  35. 35

    Lu W, Chen T. New approach to synchronization analysis of linearly coupled ordinary differential systems. Phys D-Nonlinear Phenom, 2006, 213: 214–230

    MathSciNet  Article  MATH  Google Scholar 

  36. 36

    Liu Y J, Wen G X, Chen C L P, et al. Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems. IET Control Theory Appl, 2015, 9: 1927–1934

    MathSciNet  Article  Google Scholar 

  37. 37

    Liberzon D. Switching in Systems and Control. Boston: Birkhäuser, 2003

    Google Scholar 

  38. 38

    Liu L, Liu Y J, Tong S C. Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems. IEEE Trans Cybern, 2019, 49: 2536–2545

    Article  Google Scholar 

  39. 39

    Liu L, Liu Y J, Tong S C. Fuzzy based multi-error constraint control for switched nonlinear systems and its applications. IEEE Trans Fuzzy Syst, 2018. doi:

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This work was supported in part by Shandong Provincial Natural Science Foundation (Grant Nos. ZR2018MF015, ZR2018MF023), in part by National Natural Science Foundation of China (Grant Nos. 61751202, 61572540), in part by Doctoral Scientific Research Staring Fund of Binzhou University (Grant No. 2016Y14). We would like to thank the mobility program of Shandong University of Science and Technology for the support in the work.

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Correspondence to Guoxing Wen.

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Wen, G., Chen, C.L.P., Dou, H. et al. Formation control with obstacle avoidance of second-order multi-agent systems under directed communication topology. Sci. China Inf. Sci. 62, 192205 (2019).

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  • formation control
  • obstacle avoidance
  • artificial potential field method
  • H performance
  • second-order multi-agent system
  • directed topology