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A novel parameter-dependent polynomial approach for robust automated lane keeping

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Abstract

This paper is concerned with a novel control technique for automated lane keeping of a vehicle, which takes advantage of an exact fuzzy modelling of bounded parametric uncertainties—both constant and varying—for a convex treatment of local characteristic polynomials, put together via parameter-dependent Lyapunov analysis. It is shown that the specificity of the proposed technique enlarges the feasibility chances of synthesizing a robust steering control law in contrast with only-Lyapunov-based designs. The proposal is put at test in simulation for the perturbed bicycle model.

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References

  1. Lima, P.F., Nilsson, M., Trincavelli, M., Mårtensson, J., Wahlberg, B.: Spatial model predictive control for smooth and accurate steering of an autonomous truck. IEEE Trans. Intell. Veh. 2(4), 238–250 (2017)

    Article  Google Scholar 

  2. Jiang, J., Astolfi, A.: Lateral control of an autonomous vehicle. IEEE Trans. Intell. Veh. 3(2), 228–237 (2018)

    Article  Google Scholar 

  3. Taniguchi, T., Tanaka, K., Wang, H.: Model construction, rule reduction and robust compensation for generalized form of Takagi–Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 9(2), 525–537 (2001)

    Article  Google Scholar 

  4. Du, H., Zhang, N., Naghdy, F.: Velocity-dependent robust control for improving vehicle lateral dynamics. Transp. Res. Part C 19(3), 454–468 (2011)

    Article  Google Scholar 

  5. Hu, C., Jing, H., Wang, R., Yan, F., Chadli, M.: Robust \({{H}_{\infty }}\) output-feedback control for path following of autonomous ground vehicles. Mech. Syst. Signal Process. 70, 414–427 (2016)

    Article  Google Scholar 

  6. Boyd, S., Ghaoui, L.E., Feron, E., Belakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. Studies In Applied Mathematics, vol. 15. SIAM, Philadelphia (1994)

    Book  Google Scholar 

  7. Tanaka, K., Wang, H.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2001)

    Book  Google Scholar 

  8. Wang, H., Tanaka, K., Griffin, M.: An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans. Fuzzy Syst. 4(1), 14–23 (1996)

    Article  Google Scholar 

  9. Du, H., Zhang, N., Dong, G.: Stabilizing vehicle lateral dynamics with considerations of parameter uncertainties and control saturation through robust yaw control. IEEE Trans. Veh. Technol. 59(5), 2593–2597 (2010)

    Article  Google Scholar 

  10. Jing, H., Wang, R., Chadli, M., Hu, C., Yan, F., Li, C.: Fault-tolerant control of four-wheel independently actuated electric vehicles with active steering systems. IFAC-PapersOnLine 48(21), 1165–1172 (2015)

    Article  Google Scholar 

  11. Son, Y., Kim, W., Lee, S., Chung, C.: Robust multirate control scheme with predictive virtual lanes for lane-keeping system of autonomous highway driving. In: IEEE Transactions on Vehicular Technology 64(8), (2015)

  12. Cerone, V., Regruto, D.: Robust performance controller design for vehicle lane keeping. In: 2003 European Control Conference (ECC), pp. 348–353. IEEE (2003)

  13. Marino, R., Scalzi, S., Netto, M.: Nested pid steering control for lane keeping in autonomous vehicles. Control Eng. Pract. 19(12), 1459–1467 (2011)

    Article  Google Scholar 

  14. Zhang, B., Du, H., Lam, J., Zhang, N., Li, W.: A novel observer design for simultaneous estimation of vehicle steering angle and sideslip angle. IEEE Trans. Indust. Electron. 63(7), 4357–4366 (2016)

    Article  Google Scholar 

  15. Du, H., Li, W.: Kinematics-based parameter-varying observer design for sideslip angle estimation. In: 2014 International Conference on Mechatronics and Control (ICMC), pp. 2042–2047. IEEE (2014)

  16. Frendi, S., Mellah, R., Seddiki, L., Akdag, H.: Tracking controller design of a sideslip angle and yaw rate for electrical vehicle bicycle model. IFAC-PapersOnLine 49(5), 169–174 (2016)

    Article  Google Scholar 

  17. Jing, H., Wang, R., Wang, J., Chen, N.: Robust \({{H}_{\infty }}\) dynamic output-feedback control for four-wheel independently actuated electric ground vehicles through integrated afs/dyc. J. Frankl. Inst. 355(18), 9321–9350 (2018)

    Article  MathSciNet  Google Scholar 

  18. Du, H., Zhang, N., Smith, W.: Robust yaw moment control for vehicle handling and stability. In: 2012 24th Chinese Control and Decision Conference (CCDC), pp. 4221–4226. IEEE (2012)

  19. Hatipoglu, C., Ozguner, U., Redmill, K.A.: Automated lane change controller design. IEEE Trans. Intell. Trans. Syst. 4(1), 13–22 (2003)

    Article  Google Scholar 

  20. Pohl, J., Birk, W., Westervall, L.: A driver-distraction-based lane-keeping assistance system. Proc. Inst. Mech. Eng. Part I 221(4), 541–552 (2007)

    Google Scholar 

  21. Sánchez, M., Bernal, M.: LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials. Int. J. Appl. Math. Comput. Sci. 29(2), 275–283 (2019)

    Article  MathSciNet  Google Scholar 

  22. Rajamani, R.: Vehicle Dynamics and Control. Springer Science & Business Media, New York (2011)

    MATH  Google Scholar 

  23. Wang, R., Hu, C., Yan, F., Chadli, M.: Composite nonlinear feedback control for path following of four-wheel independently actuated autonomous ground vehicles. IEEE Trans. Intell. Transp. Syst. 17(7), 2063–2074 (2016)

    Article  Google Scholar 

  24. Henrion, D., Sebek, M., Kucera, V.: Positive polynomials and robust stabilization with fixed-order controllers. IEEE Trans. Autom. Control 48(7), 1178–1186 (2003)

    Article  MathSciNet  Google Scholar 

  25. Henrion, D.: Course on LMI optimization with applications in control. Notes of the course (2003)

  26. Lofberg, J.: YALMIP: A toolbox for modeling and optimization in matlab. In: 2004 IEEE International Symposium on Computer Aided Control Systems Design, pp. 284–289 (2004)

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Acknowledgements

This work has been supported by the ECOS Nord - SEP CONACYT ANUIES Project (Mexico 291309 / France M17M08), the Mexican CONACYT scholarship 731421, the Regional Delegation for Research and Technology, the French Ministry of Higher Education and Research, the National Center for Scientific Research, and the ELSAT2020 project, co-funded by the European Regional Development Fund, the French state and the Hauts de France Region Council.

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Authors and Affiliations

  1. Department of Electrical Engineering, Sonora Institute of Technology, Ciudad Obregón, Mexico

    Jorge Álvarez & Miguel Bernal

  2. LAMIH, Université Polytecnique Hauts de France, Valenciennes, France

    Marcelino Sánchez & Sébastien Delprat

Authors
  1. Marcelino Sánchez
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  2. Jorge Álvarez
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  3. Sébastien Delprat
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  4. Miguel Bernal
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Correspondence to Miguel Bernal.

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Sánchez, M., Álvarez, J., Delprat, S. et al. A novel parameter-dependent polynomial approach for robust automated lane keeping. Int. J. Fuzzy Syst. 23, 1370–1378 (2021). https://doi.org/10.1007/s40815-020-01042-1

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  • DOI: https://doi.org/10.1007/s40815-020-01042-1

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