Skip to main content
Log in

Fully distributed event-triggered control for multi-robot systems based on modal space framework

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In tasks that require improved mechanical strength and load-bearing capacity, such as the handling of heavy or large-volume objects, multi-robot collaborative control is of utmost importance. In this paper, a novel control framework is introduced for multi-robot cooperation, aiming to address the challenges presented by dynamic coupling, anisotropy, the lack of velocity information, and the significant network transmission load within large-scale robot cooperation systems. This framework draws upon insights from both vibration theory and control theory. Firstly, a novel decoupling modal space is presented for multi-robots to complete a collaborative task, which means each control channel is not affected by the coupling of other control channels. Then, a distributed filter is designed for systems to avoid the use of velocity measurement information, which ensures that the output feedback control of multiple robots is realized and makes the estimation error converge to zero uniformly, exponentially and globally. Moreover, distributed adaptive event-triggered protocols are developed that are independent of network scale and do not rely on global information. In this study, the controller and communication do not need to be continuously updated. Finally, experimental demonstrations are provided to show the effectiveness of the proposed control algorithms.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

Similar content being viewed by others

Data availability statement

All data included in this study are available upon request from the corresponding author.

References

  1. Zhao, Y.M., Lin, Y., Xi, F., Guo, S.: Calibration-based iterative learning control for path tracking of industrial robots. IEEE Trans. Ind. Electron. 62(5), 2921–2929 (2014)

    ADS  Google Scholar 

  2. Kawasaki, H., Ueki, S., Ito, S.: Decentralized adaptive coordinated control of multiple robot arms without using a force sensor. Automatica 42(3), 481–488 (2006)

    MathSciNet  Google Scholar 

  3. Chung, S.J., Slotine, J.J.E.: Cooperative robot control and concurrent synchronization of lagrangian systems. IEEE Trans. Robot. 25(3), 686–700 (2009)

    Google Scholar 

  4. Kamel, M.A., Yu, X., Zhang, Y.: Fault-tolerant cooperative control design of multiple wheeled mobile robots. IEEE Trans. Control Syst. Technol. 26(2), 756–764 (2018)

    Google Scholar 

  5. Wang, Y., Wang, D., Yang, S., Shan, M.: A practical leader-follower tracking control scheme for multiple nonholonomic mobile robots in unknown obstacle environments. IEEE Trans. Control Syst. Technol. 27(4), 1685–1693 (2019)

    Google Scholar 

  6. Ding, S., Zhao, T., Gao, F., Tang, Z., Jin, B.: Research on a motion-inhibition fuzzy control method for moored ship with multi-robot system. Ocean Eng. 248, 110795 (2022)

    Google Scholar 

  7. Li, L., Zhang, H., Xing, Z., Ma, Z.: Theoretical analysis and verification of particles moving along the arc-shaped surface in vibration machinery. Nonlinear Dyn. 109(3), 1341–1378 (2022)

    Google Scholar 

  8. Li, C., Li, P., Miao, X.: Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer. Nonlinear Dyn. 104(4), 3247–3267 (2021)

    MathSciNet  Google Scholar 

  9. Xu, C., Liu, G., Li, C., Zhu, Y., Zhao, J.: Dynamic modeling and identification of low impact docking mechanism based on symmetric excitation trajectory. Nonlinear Dyn. 111(11), 9919–9937 (2023)

    Google Scholar 

  10. Luo, S., Sun, Q., Sun, M., Tan, P., Wu, W., Sun, H., Chen, Z.: On decoupling trajectory tracking control of unmanned powered parafoil using ADRC-based coupling analysis and dynamic feedforward compensation. Nonlinear Dyn. 92, 1619–1635 (2018)

    Google Scholar 

  11. Lin, X., Yu, Y., Sun, C.: A decoupling control for quadrotor UAV using dynamic surface control and sliding mode disturbance observer. Nonlinear Dyn. 97(1), 781–795 (2019)

    Google Scholar 

  12. Bhagat, U., Shirinzadeh, B., Clark, L., Chea, P., Qin, Y., Tian, Y., Zhang, D.: Design and analysis of a novel flexure-based 3-DOF mechanism. Mech. Mach. Theory 74, 173–187 (2014)

    Google Scholar 

  13. Qin, Y., Shirinzadeh, B., Tian, Y., Zhang, D., Bhagat, U.: Design and computational optimization of a decoupled 2-DOF monolithic mechanism. IEEE/ASME Trans. Mechatron. 19(3), 872–881 (2013)

    Google Scholar 

  14. Wang, F., Huo, Z., Liang, C., Shi, B., Tian, Y., Zhao, X., Zhang, D.: A novel actuator-internal micro/nano positioning stage with an arch-shape bridge-type amplifier. IEEE Trans. Ind. Electron. 66(12), 9161–9172 (2018)

    Google Scholar 

  15. Chang, Q., Chen, W., Liu, J., Yu, H., Deng, J., Liu, Y.: Development of a novel two-DOF piezo-driven fast steering mirror with high stiffness and good decoupling characteristic. Mech. Syst. Signal Process. 159, 107851 (2021)

    Google Scholar 

  16. Liu, P., Zheng, M., Ning, D., Zhang, N., Du, H.: Decoupling vibration control of a semi-active electrically interconnected suspension based on mechanical hardware-in-the-loop. Mech. Syst. Signal Process. 166, 108455 (2022)

    Google Scholar 

  17. Guo, Z., Tian, Y., Liu, C., Wang, F., Liu, X., Shirinzadeh, B., Zhang, D.: Design and control methodology of a 3-DOF flexure-based mechanism for micro/nano-positioning. Robot. Comput. Integr. Manuf. 32, 93–105 (2015)

    Google Scholar 

  18. Li, Y., Xu, Q.: Design and analysis of a totally decoupled flexure-based XY parallel micromanipulator. IEEE Trans. Robot. 25(3), 645–657 (2009)

    ADS  CAS  Google Scholar 

  19. Roy, N.K., Cullinan, M.A.: Design and characterization of a two-axis, flexure-based nanopositioning stage with 50 mm travel and reduced higher order modes. Precis. Eng. 53, 236–247 (2018)

    Google Scholar 

  20. Wang, F., Zhao, X., Huo, Z., Shi, B., Liang, C., Tian, Y., Zhang, D.: A 2-DOF nano-positioning scanner with novel compound decoupling-guiding mechanism. Mech. Mach. Theory 155, 104066 (2021)

    Google Scholar 

  21. Hou, R., Cui, L., Bu, X., Yang, J.: Distributed formation control for multiple non-holonomic wheeled mobile robots with velocity constraint by using improved data-driven iterative learning. Appl. Math. Comput. 395, 125829 (2021)

    MathSciNet  Google Scholar 

  22. Kou, L., Chen, Z., Xiang, J.: Cooperative fencing control of multiple vehicles for a moving target with an unknown velocity. IEEE Trans. Autom. Control 67(2), 1008–1015 (2022)

    MathSciNet  Google Scholar 

  23. Yu, X., Ding, N., Zhang, A., Qian, H.: Cooperative moving-target enclosing of networked vehicles with constant linear velocities. IEEE Trans. Cybern. 50(2), 798–809 (2018)

    PubMed  Google Scholar 

  24. Farhadi, F., Golestani, S.J., Teneketzis, D.: A surrogate optimization-based mechanism for resource allocation and routing in networks with strategic agents. IEEE Trans. Autom. Control 64(2), 464–479 (2018)

    MathSciNet  Google Scholar 

  25. Brown, P.N., Marden, J.R.: Optimal mechanisms for robust coordination in congestion games. IEEE Trans. Autom. Control 63(8), 2437–2448 (2017)

    MathSciNet  Google Scholar 

  26. Liu, H., Niu, B., Qin, J.: Reachability analysis for linear discrete-time systems under stealthy cyber attacks. IEEE Trans. Autom. Control 66(9), 4444–4451 (2021)

    MathSciNet  Google Scholar 

  27. Ren, W.: Distributed leaderless consensus algorithms for networked Euler–Lagrange systems. Int. J. Control 82(11), 2137–2149 (2009)

    MathSciNet  Google Scholar 

  28. Zhang, Y., Liu, Y.: Nonlinear second-order multi-agent systems subject to antagonistic interactions without velocity constraints. Appl. Math. Comput. 364, 124667 (2020)

    MathSciNet  Google Scholar 

  29. Zhao, Y., Duan, Z., Wen, G.: Distributed finite-time tracking of multiple Euler–Lagrange systems without velocity measurements. Int. J. Robust Nonlinear Control 25(11), 1688–1703 (2015)

    MathSciNet  Google Scholar 

  30. Hong, Y., Chen, G., Bushnell, L.: Distributed observers design for leader-following control of multi-agent networks. Automatica 44(3), 846–850 (2008)

    MathSciNet  Google Scholar 

  31. Mabrouk, M.: Triangular form for Euler–Lagrange systems with application to the global output tracking control. Nonlinear Dyn. 60(1), 87–98 (2010)

    MathSciNet  Google Scholar 

  32. Panteley, E., Lefeber, E., Loria, A., Nijmeijer, H.: Exponential tracking control of a mobile car using a cascaded approach. IFAC Proc. 31(27), 201–206 (1998)

    Google Scholar 

  33. Li, J., Zhang, G., Shan, Q., Zhang, W.: A novel cooperative design for USV-UAV systems: 3D mapping guidance and adaptive fuzzy control. IEEE Trans. Control Netw. Syst. 10(2), 564–574 (2022). https://doi.org/10.1109/TCNS.2022.3220705

    Article  Google Scholar 

  34. Zhang, G., Li, J., Jin, X., Liu, C.: Robust adaptive neural control for wing-sail-assisted vehicle via the multiport event-triggered approach. IEEE Trans. Cybern. 52(12), 12916–12928 (2021)

    Google Scholar 

  35. Yao, D., Li, H., Shi, Y.: Adaptive event-triggered sliding mode control for consensus tracking of nonlinear multi-agent systems with unknown perturbations. IEEE Trans. Cybern. 53(4), 2672–2684 (2023)

    PubMed  Google Scholar 

  36. Yao, D., Li, H., Shi, Y.: Event-based average consensus of disturbed mass via fully distributed sliding mode control. IEEE Trans. Autom. Control (2023). https://doi.org/10.1109/TAC.2023.3317505

    Article  Google Scholar 

  37. Ngo, V.T., Liu, Y.C.: Event-based communication and control for task-space consensus of networked Euler–Lagrange systems. IEEE Trans. Control Netw. Syst. 8(2), 555–565 (2021)

    MathSciNet  Google Scholar 

  38. Pepe, P.: Discrete-time systems with constrained time delays and delay-dependent Lyapunov functions. IEEE Trans. Autom. Control 65(4), 1724–1730 (2019)

    MathSciNet  Google Scholar 

  39. Maass, A.I., Vargas, F.J., Silva, E.I.: Optimal control over multiple erasure channels using a data dropout compensation scheme. Automatica 68, 155–161 (2016)

    MathSciNet  Google Scholar 

  40. Roset, B., Heemels, W., Lazar, M., Nijmeijer, H.: On robustness of constrained discrete-time systems to state measurement errors. Automatica 44(4), 1161–1165 (2008)

    MathSciNet  Google Scholar 

  41. Dimarogonas, D.V., Frazzoli, E., Johansson, K.H.: Distributed event-triggered control for multi-agent systems. IEEE Trans. Autom. Control 57(5), 1291–1297 (2011)

    MathSciNet  Google Scholar 

  42. Ding, L., Han, Q.L., Ge, X., Zhang, X.M.: An overview of recent advances in event-triggered consensus of multiagent systems. IEEE Trans. Cybern. 48(4), 1110–1123 (2017)

    Google Scholar 

  43. Guo, G., Ding, L., Han, Q.L.: A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems. Automatica 50(5), 1489–1496 (2014)

    MathSciNet  Google Scholar 

  44. Zhong, M., Ding, S.X., Han, Q.L., He, X., Zhou, D.: A Krein space-based approach to event-triggered h filtering for linear discrete time-varying systems. Automatica 135, 110001 (2022)

    MathSciNet  Google Scholar 

  45. Yu, H., Chen, T.: A new zeno-free event-triggered scheme for robust distributed optimal coordination. Automatica 129, 109639 (2021)

    MathSciNet  Google Scholar 

  46. Jiao, J., Trentelman, H.L., Camlibel, M.K.: A suboptimality approach to distributed \({H}_2\) control by dynamic output feedback. Automatica 121, 109164 (2020)

    MathSciNet  Google Scholar 

  47. Li, X., Tang, Y., Karimi, H.R.: Consensus of multi-agent systems via fully distributed event-triggered control. Automatica 116, 108898 (2020)

    MathSciNet  Google Scholar 

  48. Liu, W., Huang, J.: Cooperative global robust output regulation for a class of nonlinear multi-agent systems by distributed event-triggered control. Automatica 93, 138–148 (2018)

    MathSciNet  Google Scholar 

  49. Yang, D., Ren, W., Liu, X., Chen, W.: Decentralized event-triggered consensus for linear multi-agent systems under general directed graphs. Automatica 69, 242–249 (2016)

    MathSciNet  Google Scholar 

  50. Wan, S., Xu, Q.: Design and analysis of a new compliant XY micropositioning stage based on roberts mechanism. Mech. Mach. Theory 95, 125–139 (2016)

    ADS  Google Scholar 

  51. Bao, J., Wang, H., Liu, P.X.: Finite-time synchronization control for bilateral teleoperation systems with asymmetric time-varying delay and input dead zone. IEEE/ASME Trans. Mechatron. 26(3), 1570–1580 (2020)

    Google Scholar 

  52. Li, Y., Yang, C., Yan, W., Cui, R., Annamalai, A.: Admittance-based adaptive cooperative control for multiple manipulators with output constraints. IEEE Trans. Neural Netw. Learn. Syst. 30(12), 3621–3632 (2019)

    MathSciNet  PubMed  Google Scholar 

  53. Zhang, H., Song, A., Li, H., Chen, D., Fan, L.: Adaptive finite-time control scheme for teleoperation with time-varying delay and uncertainties. IEEE Trans. Syst. Man Cybern. Syst. 52(3), 1552–1566 (2022)

    Google Scholar 

  54. Zhang, B., Jia, Y., Du, J., Zhang, J.: Finite-time synchronous control for multiple manipulators with sensor saturations and a constant reference. IEEE Trans. Control Syst. Technol. 22(3), 1159–1165 (2014)

    Google Scholar 

  55. Zhao, D., Ni, W., Zhu, Q.: A framework of neural networks based consensus control for multiple robotic manipulators. Neurocomputing 140, 8–18 (2014)

    Google Scholar 

  56. Kang, Y., Yao, L., Wu, W.: Sensor fault diagnosis and fault tolerant control for the multiple manipulator synchronized control system. ISA Trans. 106, 243–252 (2020)

    PubMed  Google Scholar 

  57. Huntsberger, T.L., Trebi-Ollennu, A., Aghazarian, H., Schenker, P.S., Pirjanian, P., Nayar, H.D.: Distributed control of multi-robot systems engaged in tightly coupled tasks. Auton. Robots 17(1), 79–92 (2004)

    Google Scholar 

  58. Murakami, T., Oda, N., Miyasaka, Y., Ohnishi, K.: A motion control strategy based on equivalent mass matrix in multidegree-of-freedom manipulator. IEEE Trans. Ind. Electron. 42(2), 123–130 (1995)

    Google Scholar 

  59. De Schutter, J., Torfs, D., Bruyninckx, H., Dutré, S.: Invariant hybrid force/position control of a velocity controlled robot with compliant end effector using modal decoupling. Int. J. Robot. Res. 16(3), 340–356 (1997)

    Google Scholar 

  60. Yang, C., Zhao, J., Li, L., Agrawal, S.K.: Design and implementation of a novel modal space active force control concept for spatial multi-DOF parallel robotic manipulators actuated by electrical actuators. ISA Trans. 72, 273–286 (2018)

    PubMed  Google Scholar 

  61. Zhao, J., Yang, T., Ma, Z., Yang, C., Wang, Z., Xu, J.: Design of mg modal space sliding mode control for lower limb exoskeleton robot driven by electrical actuators. Mechatronics 78, 102610 (2021)

    Google Scholar 

  62. Weaver, W., Jr., Timoshenko, S.P., Young, D.H.: Vibration Problems in Engineering. Wiley, New York (1991)

    Google Scholar 

  63. Feng, Y., Yu, X., Man, Z.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38(12), 2159–2167 (2002)

    MathSciNet  Google Scholar 

  64. Liu, J., Wang, Q., Yu, Y.: Fixed-time consensus algorithm for second-order multi-agent systems with bounded disturbances. In: 2016 31st Youth Academic Annual Conference of Chinese Association of Automation (YAC), pp. 165–170. IEEE (2016)

Download references

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62373319, 61933009, 62073276; and in part by the Natural Science Foundation of Hebei Province under Grant F2022203036, F2021203109, F2022203025; in part by the Provincial Key Laboratory Performance Subsidy Project 22567612H.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by XZ, YY, JZ and JL. The first draft of the manuscript was written by XZ, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yana Yang.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zeng, X., Yang, Y., Zhao, J. et al. Fully distributed event-triggered control for multi-robot systems based on modal space framework. Nonlinear Dyn 112, 3605–3618 (2024). https://doi.org/10.1007/s11071-023-09199-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-09199-8

Keywords

Navigation