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Physics-Based Output-Feedback Consensus-Formation Control of Networked Autonomous Vehicles

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Hybrid and Networked Dynamical Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 493))

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Abstract

We describe a control method for multi-agent vehicles, to make them adopt a formation around a non-pre-specified point on the plane, and with common but non-pre-imposed orientation. The problem may be considered as part of a more complex maneuver in which the robots are summoned to a rendezvous to advance in formation. The novelty and most appealing feature of our control method is that it is physics-based; it relies on the design of distributed dynamic controllers that may be assimilated to second-order mechanical systems. The consensus task is achieved by making the controllers, not the vehicles themselves directly, achieve consensus. Then, the vehicles are steered into a formation by virtue of fictitious mechanical couplings with their respective controllers. We cover different settings of increasing technical difficulty, from consensus formation control of second-order integrators to second-order nonholonomic vehicles and in scenarii including both state- and output-feedback control. In addition, we address the realistic case in which the vehicles communicate over a common WiFi network that introduces time-varying delays. Remarkably, the same physics-based method applies to all the scenarii.

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Notes

  1. 1.

    To prove further see [23, p. 657] and [30].

References

  1. Abdessameud, A., Polushin, I.G., Tayebi, A.: Synchronization of Lagrangian systems with irregular communication delays. IEEE Trans. Autom. Control 59(1), 187–193 (2014)

    Article  MathSciNet  Google Scholar 

  2. Abdessameud, A., Tayebi, A.: On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints. Syst. Control Lett. 59(12), 812–821 (2010)

    Article  MathSciNet  Google Scholar 

  3. Abdessameud, A., Tayebi, A., Polushin, I.G.: Leader-follower synchronization of Euler–Lagrange systems with time-varying leader trajectory and constrained discrete-time communication. IEEE Trans. Autom. Control 62(5), 2539–2545 (May2017)

    Google Scholar 

  4. Barbashin, E.A., Krasovskiĭ, N.N.: Об устоЙчивости движеняи в целом. Dokl. Akad. Nauk. USSR 86(3), 453–456 (1952). Commonly (and wrongly) cited in English under: “On the stability of motion in the large”; Correct translation: “On the stability of motion in the whole

    Google Scholar 

  5. Bautista-Castillo, A., Lopez-Franco, C., Nuño, E.: Consensus-based formation control for multiple nonholonomic robots. In: 2016 IEEE International Autumn Meeting on Power Electronics and Computing (ROPEC). IEEE (2016)

    Google Scholar 

  6. Brockett, R.W.: Asymptotic stability and feedback stabilization. Differ. Geom. Control Theory 27(1), 181–191 (1983)

    MathSciNet  Google Scholar 

  7. Burkov, I.V., Zaremba, A.T.: Dynamics of elastic manipulators with electric drives. Izv. Akad. Nauk SSSR Mekh. Tverd. Tela 22(1), 57–64 (1987). Engl. transl. in Mechanics of Solids, Allerton Press

    Google Scholar 

  8. Cao, Y., Ren, W.: Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues. Springer (2011)

    Google Scholar 

  9. Cheng, Y., Jia, R., Du, H., Wen, G., Zhu, W.: Robust finite-time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback. Int. J. Robust Nonlinear Control 28(6), 2082–2096 (2018)

    Article  MathSciNet  Google Scholar 

  10. Consolini, L., Morbidi, F., Prattichizzo, D., Tosques, M.: On a class of hierarchical formations of unicycles and their internal dynamics. IEEE Trans. Autom. Control 57(4), 845–859 (2012)

    Article  MathSciNet  Google Scholar 

  11. Dimarogonas, D.V., Kyriakopoulos, K.J.: On the rendezvous problem for multiple nonholonomic agents. IEEE Trans. Autom. Control 52(5), 916–922 (2007)

    Google Scholar 

  12. Dixon, W.E., Dawson, D.M., Zhang, F., Zergeroglu, E.: Global exponential tracking control of a mobile robot system via a PE condition. IEEE Trans. Syst. Man. Cybernet. B 30(1), 129–142 (2000)

    Article  Google Scholar 

  13. Do, K.D., Jiang, Z.-P., Pan, J.: A global output-feedback controller for simultaneous tracking and stabilization of unicycle-type mobile robots. IEEE Trans. Robot. Autom. 20(3), 589–594 (2004)

    Article  Google Scholar 

  14. Dong, W.: Distributed observer-based cooperative control of multiple nonholonomic mobile agents. Int. J. Syst. Sc. 43(5), 797–808 (2012)

    Article  MathSciNet  Google Scholar 

  15. El-Hawwary, M.I., Maggiore, M.: Distributed circular formation stabilization for dynamic unicycles. IEEE Trans. Autom. Control 58(1), 149–162 (2013)

    Article  MathSciNet  Google Scholar 

  16. Génération Robots. Pioneer P3-DX mobile robot. Accessed May 06, 2021. [Online]. https://www.generationrobots.com/en/402395-robot-mobile-pioneer-3-dx.html

  17. González, A., Aragüés, R., López-Nicolás, G., Sagüés, C.: Stability analysis of nonholonomic multiagent coordinate-free formation control subject to communication delays. Int. J. Robust Nonlinear Control 28(14), 4121–4138 (2018)

    Article  MathSciNet  Google Scholar 

  18. Hernández, A.T., Loría, A., Nuño, E., Panteley, E.: Consensus-formation control of nonholonomic robots without velocity measurements. In: Proceedings of European Control Conference, pp. 674–679, St. Petersburg, Russia (2020)

    Google Scholar 

  19. Huang, J., Wen, C., Wang, W., Jiang, Z.-P.: Adaptive output feedback tracking control of a nonholonomic mobile robot. Automatica 50, 821–831 (2014)

    Article  MathSciNet  Google Scholar 

  20. Hui, Q.: Finite-time rendezvous algorithms for mobile autonomous agents. IEEE Trans. Autom. Control 56(1), 207–211 (2011)

    Article  MathSciNet  Google Scholar 

  21. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

  22. Jin, J., Gans, N.: Collision-free formation and heading consensus of nonholonomic robots as a pose regulation problem. Robot. Auton. Syst. 95(9), 25–36 (2017)

    Article  Google Scholar 

  23. Khalil, H.: Nonlinear Systems. Macmillan Publishing Co., 2nd ed., New York (1996)

    Google Scholar 

  24. Lee, D.: Passive decomposition and control of nonholonomic mechanical systems. IEEE Trans. Robot. 26(6), 978–992 (2010)

    Article  Google Scholar 

  25. Lee, T.C., Song, K.T., Lee, C.H., Teng, C.C.: Tracking control of unicycle-modeled mobile robots using a saturation feedback controller. IEEE Trans. Control Syst. Technol. 9(2), 305–318 (2001)

    Google Scholar 

  26. Li, Z., Ren, W., Liu, X., Fu, M.: Consensus of multi-agent systems with general linear and lipschitz nonlinear dynamics using distributed adaptive protocols. IEEE Trans. Autom. Control 58(7), 1786–1791 (2013)

    Article  MathSciNet  Google Scholar 

  27. Liang, X., Wang, H., Liu, Y., Chen, W., Liu, T.: Formation control of nonholonomic mobile robots without position and velocity measurements. IEEE Trans. Robot. 34(2), 434–446 (2018)

    Article  Google Scholar 

  28. Lin, Z., Francis, B., Maggiore, M.: Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans. Autom. Control 50(1), 121–127 (2005)

    Article  MathSciNet  Google Scholar 

  29. Lizárraga, D.A.: Obstructions to the existence of universal stabilizers for smooth control systems. Math. Control, Sign. Syst. 16, 255–277 (2004)

    Google Scholar 

  30. Loría, A.: From feedback to cascade-interconnected systems: breaking the loop. In: Proceedings of 47th IEEE Conference Decision Control, pp. 4109–4114, Cancun, Mex (2008)

    Google Scholar 

  31. Loría, A., Panteley, E., Teel, A.: A new persistency-of-excitation condition for UGAS of NLTV systems: Application to stabilization of nonholonomic systems. In: Proceedings of 5th European Control Conference, pp. 1363–1368, Karlsrühe, Germany (1999)

    Google Scholar 

  32. Maghenem, M.: Stability and stabilization of networked time-varying systems. Ph.D. thesis, Univ Paris Saclay, Gif sur Yvette (2017). https://tel.archives-ouvertes.fr/tel-01596158

  33. Maghenem, M., Loría, A., Nuño, E., Panteley, E.: Distributed full-consensus control of nonholonomic vehicles under non-differentiable measurement delays. IEEE Control Syst. Lett. 5(1), 97–102 (2021)

    Article  MathSciNet  Google Scholar 

  34. Mao, W., Wang, C., Chen, W., Li, X.: Observer-based consensus design for multi-agent systems with unavailable velocities of leader and followers. In: Proceedings of 32nd Chinese Control Conference, pp. 7030–7033 (2013)

    Google Scholar 

  35. Marshall, J.A., Broucke, M.E., Francis, B.A.: Formations of vehicles in cyclic pursuit. IEEE Trans. Autom. Control 49(11), 1963–1974 (2004)

    Article  MathSciNet  Google Scholar 

  36. Montijano, E., Thunberg, J., Hu, X., Sagüés, C.: Epipolar visual servoing for multirobot distributed consensus. IEEE Trans. Robot. 29(5), 1212–1225 (2013)

    Article  Google Scholar 

  37. Moshtagh, N., Jadbabaie, A.: Distributed geodesic control laws for flocking of nonholonomic agents. IEEE Trans. Autom. Control 52(4), 681–686 (2007)

    Article  MathSciNet  Google Scholar 

  38. Narendra, K.S., Annaswamy, A.M.: Stable Adaptive Systems. Prentice-Hall Inc, New Jersey (1989)

    Google Scholar 

  39. Neimark, J.I., Fufaev, F.A.: Dynamics of Nonholonomic Systems, vol. 33. A.M.S. Translations of Mathematical Monographs, Providence, RI (1972)

    Google Scholar 

  40. Ning, B., Han, Q.: Prescribed finite-time consensus tracking for multiagent systems with nonholonomic chained-form dynamics. IEEE Trans. Autom. Control 64(4), 1686–1693 (2019)

    Article  MathSciNet  Google Scholar 

  41. Nuño, E.: Consensus of Euler–Lagrange systems using only position measurements. IEEE Trans. Control Netw. Syst. 5(1), 489–498 (2018)

    Article  MathSciNet  Google Scholar 

  42. Nuño, E., Ortega, R.: Achieving consensus of Euler–Lagrange agents with interconnecting delays and without velocity measurements via passivity-based control. IEEE Trans. Control Syst. Technol. 26(1), 222–232 (2018)

    Article  Google Scholar 

  43. Nuño, E., Loría, A., Hernández, A.T., Maghenem, M., Panteley, E.: Distributed consensus-formation of force-controlled nonholonomic robots with time-varying delays. Automatica 120, 109114 (2020)

    Article  MathSciNet  Google Scholar 

  44. Nuño, E., Loría, A., Panteley, E.: Leaderless consensus formation control of cooperative multi-agent vehicles without velocity measurements. IEEE Control Syst. Lett. 6, 902–907 (2022)

    Article  MathSciNet  Google Scholar 

  45. Nuño, E., Loría, A., Panteley, E., Restrepo-Ochoa, E.: Rendezvous of nonholonomic robots via output-feedback control under time-varying delays. IEEE Trans. Control Syst. Technol. 30(6), 2707–2716 (2022)

    Article  Google Scholar 

  46. Nuño, E., Sarras, I., Loría, A., Maghenem, M., Cruz-Zavala, E., Panteley, E.: Strict Lyapunov-Krasovskii functionals for undirected networks of Euler–Lagrange systems with time-varying delays. Syst. Contr. Lett. 135, 104579 (2020)

    Google Scholar 

  47. Panteley, E., Lefeber, E., Loría, A., Nijmeijer, H.: Exponential tracking of a mobile car using a cascaded approach. In: IFAC Workshop on Motion Control, pp. 221–226, Grenoble, France (1998)

    Google Scholar 

  48. Panteley, E., Loría, A.: Synchronization and dynamic consensus of heterogeneous networked systems. IEEE Trans. Autom. Control 62(8), 3758–3773 (2017)

    Article  MathSciNet  Google Scholar 

  49. Panteley, H., Loría, A., Sukumar, S.: Strict lyapunov functions for consensus under directed connected graphs. In: Proceedings of European Control Conference (ECC), pp. 935–940, St. Petersburg, Russia (2020)

    Google Scholar 

  50. Poonawala, H.A., Satici, A.C., Spong, M.W.: Leader-follower formation control of nonholonomic wheeled mobile robots using only position measurements. In: Proceedings of 9th Asian Control Conference, pp. 1–6 (2013)

    Google Scholar 

  51. Poonawala, H.A., Spong, M.W.: Preserving strong connectivity in directed proximity graphs. IEEE Trans. Autom. Control 62(9), 4392–4404 (2017)

    Article  MathSciNet  Google Scholar 

  52. Ren, W., Beard, R.W.: Distributed Consensus in Multivehicle Cooperative Control. Springer (2005)

    Google Scholar 

  53. Restrepo, E., Loría, A., Sarras, I., Marzat, J.: Stability and robustness of edge-agreement-based consensus protocols for undirected proximity graphs. Int. J. Control (2020)

    Google Scholar 

  54. Restrepo-Ochoa, E., Loría, A., Sarras, I., Marzat, J.: Robust consensus of high-order systems under output constraints: application to rendezvous of underactuated UAVs. IEEE Trans. Autom. Control 68(1), 329–342 (2023)

    Article  MathSciNet  Google Scholar 

  55. Roza, A., Maggiore, M., Scardovi, L.: A Smooth Distributed Feedback for Global Rendezvous of Unicycles. IEEE Trans. Control Netw. Syst.5(1), 640–652 (2018)

    Google Scholar 

  56. Samson, C.: Time-varying stabilization of a car-like mobile robot. Technical report, INRIA Sophia-Antipolis, 1990. In: Proceedings in Advanced Robot Control, vol. 162. Springer, Berlin (1991)

    Google Scholar 

  57. Samson, C.: Control of chained system: application to path following and time-varying point stabilization of mobile robots. IEEE Trans. Autom. Control 40(1), 64–77 (1995)

    Article  MathSciNet  Google Scholar 

  58. Spong, M.: Modeling and control of elastic joint robots. ASME J. Dyn. Syst. Meas. Contr. 109, 310–319 (1987)

    Article  Google Scholar 

  59. Tzafestas, S.G.: Introduction to Mobile Robot Control. Elsevier Inc, First ed. (2013)

    Google Scholar 

  60. Wang, P., Ding, B.: Distributed RHC for tracking and formation of nonholonomic multi-vehicle systems. IEEE Trans. Autom. Control 59(6), 1439–1453 (2014)

    Article  MathSciNet  Google Scholar 

  61. Wang, X., Hong, Y.: Distributed observers for tracking a moving target by cooperative multiple agents with time delays. In: 2009 ICCAS-SICE, pp. 982–987 (2009)

    Google Scholar 

  62. Yang, C., Xie, W., Lei, C.,  Ma, B.: Smooth time-varying formation control of multiple nonholonomic agents. In: Proceedings of Chinese Intelligent of System Conference, pp. 283–291. Springer (2016)

    Google Scholar 

  63. Zhao, S.: Affine formation maneuver control of multiagent systems. IEEE Trans. Autom. Control 63(12), 4140–4155 (2018)

    Article  MathSciNet  Google Scholar 

  64. Zhao, X., Zheng, X., Ma, C., Li, R.: Distributed consensus of multiple Euler–Lagrange systems networked by sampled-data information with transmission delays and data packet dropouts. IEEE Trans. Autom. Sci. Eng. 14(3), 1440–1450 (2017)

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the “Agence Nationale de la Recherche” (ANR) under Grant HANDY ANR-18-CE40-0010.

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Correspondence to Emmanuel Nuño .

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Loría, A., Nuño, E., Panteley, E., Restrepo, E. (2024). Physics-Based Output-Feedback Consensus-Formation Control of Networked Autonomous Vehicles. In: Postoyan, R., Frasca, P., Panteley, E., Zaccarian, L. (eds) Hybrid and Networked Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 493. Springer, Cham. https://doi.org/10.1007/978-3-031-49555-7_3

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