Skip to main content
Log in

Tracking Error Learning Control for Precise Mobile Robot Path Tracking in Outdoor Environment

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript


This paper presents a Tracking-Error Learning Control (TELC) algorithm for precise mobile robot path tracking in off-road terrain. In traditional tracking error-based control approaches, feedback and feedforward controllers are designed based on the nominal model which cannot capture the uncertainties, disturbances and changing working conditions so that they cannot ensure precise path tracking performance in the outdoor environment. In TELC algorithm, the feedforward control actions are updated by using the tracking error dynamics and the plant-model mismatch problem is thus discarded. Therefore, the feedforward controller gradually eliminates the feedback controller from the control of the system once the mobile robot has been on-track. In addition to the proof of the stability, it is proven that the cost functions do not have local minima so that the coefficients in TELC algorithm guarantee that the global minimum is reached. The experimental results show that the TELC algorithm results in better path tracking performance than the traditional tracking error-based control method. The mobile robot controlled by TELC algorithm can track a target path precisely with less than 10 cm error in off-road terrain.

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.

Similar content being viewed by others


  1. Amer, N.H., Zamzuri, H., Hudha, K., Kadir, Z.A.: Modelling and control strategies in path tracking control for autonomous ground vehicles: a review of state of the art and challenges. J. Intell. Robot. Syst. 86(2), 225–254 (2017).

    Article  Google Scholar 

  2. Blazic, S.: A novel trajectory-tracking control law for wheeled mobile robots. Robot. Auton. Syst. 59(11), 1001–1007 (2011)

    Article  Google Scholar 

  3. Cui, M., Liu, H., Liu, W., Qin, Y.: An adaptive unscented kalman filter-based controller for simultaneous obstacle avoidance and tracking of wheeled mobile robots with unknown slipping parameters. Journal of Intelligent & Robotic Systems. (2017)

  4. Goodarzi, F.A., Lee, T.: Global formulation of an extended kalman filter on se(3) for geometric control of a quadrotor uav. J. Intell. Robot. Syst. 88(2), 395–413 (2017).

    Article  Google Scholar 

  5. Huynh, H.N., Verlinden, O., Vande Wouwer, A.: Comparative application of model predictive control strategies to a wheeled mobile robot. J. Intell. Robot. Syst. 87(1), 81–95 (2017)

    Article  Google Scholar 

  6. Kanjanawanishkul, K., Zell, A.: Path following for an omnidirectional mobile robot based on model predictive control. In: 2009 IEEE International Conference on Robotics and Automation, pp 3341–3346 (2009)

  7. Kayacan, E., Kayacan, E., Chen, I.M., Ramon, H., Saeys, W.: On the comparison of model-based and model-free controllers in guidance, navigation and control of agricultural vehicles, pp 49–73. Springer International Publishing, Cham (2018)

    Google Scholar 

  8. Kayacan, E., Kayacan, E., Ramon, H., Saeys, W.: Modeling and identification of the yaw dynamics of an autonomous tractor. In: 2013 9Th Asian Control Conference (ASCC), pp 1–6 (2013).

  9. Kayacan, E., Kayacan, E., Ramon, H., Saeys, W.: Distributed nonlinear model predictive control of an autonomous tractor–trailer system. Mechatronics 24(8), 926–933 (2014)

    Article  Google Scholar 

  10. Kayacan, E., Kayacan, E., Ramon, H., Saeys, W.: Nonlinear modeling and identification of an autonomous tractor–trailer system. Comput. Electron. Agric. 106, 1–10 (2014)

    Article  Google Scholar 

  11. Kayacan, E., Kayacan, E., Ramon, H., Saeys, W.: Learning in centralized nonlinear model predictive control: application to an autonomous tractor-trailer system. IEEE Trans. Control Syst. Technol. 23(1), 197–205 (2015)

    Article  Google Scholar 

  12. Kayacan, E., Kayacan, E., Ramon, H., Saeys, W.: Robust tube-based decentralized nonlinear model predictive control of an autonomous tractor-trailer system. IIEEE/ASME Trans. Mechatron. 20(1), 447–456 (2015)

    Article  Google Scholar 

  13. Kayacan, E., Kayacan, E., Ramon, H., Saeys, W.: Towards agrobots: identification of the yaw dynamics and trajectory tracking of an autonomous tractor. Comput. Electron. Agric. 115, 78–87 (2015)

    Article  Google Scholar 

  14. Kayacan, E., Ramon, H., Saeys, W.: Robust trajectory tracking error model-based predictive control for unmanned ground vehicles. IEEE/ASME Trans. Mechatron. 21(2), 806–814 (2016)

    Article  Google Scholar 

  15. Kayacan, E., Zhang, Z., Chowdhary, G.: Embedded high precision control and corn stand counting algorithms for an ultra-compact 3d printed field robot. In: Proceedings of Robotics: Science and Systems. Pittsburgh, Pennsylvania. (2018)

  16. Klancar, G., Skrjanc, I.: Tracking-error model-based predictive control for mobile robots in real time. Robot. Auton. Syst. 55(6), 460–469 (2007)

    Article  Google Scholar 

  17. Li, M., Imou, K., Wakabayashi, K., Yokoyama, S.: Review of research on agricultural vehiclev autonomous guidance. International Journal of Agricultural & Biological Engineering 2(3), 1–16 (2009)

    Article  Google Scholar 

  18. Liao, Y., Ou, Y., Meng, S.: Wheeled mobile robot based on adaptive linear quadratic gaussian control. In: 2017 29Th Chinese Control and Decision Conference (CCDC), pp 5768–5775 (2017).

  19. Lins Barreto, J.C., Scolari Conceicao, A.G., Dorea, C.E.T., Martinez, L., De Pieri, E.R.: Design and implementation of model-predictive control with friction compensation on an omnidirectional mobile robot. IEEE/ASME Trans. Mechatron. 19(2), 467– 476 (2014)

    Article  Google Scholar 

  20. Martins, F.N., Celeste, W.C., Carelli, R., Sarcinelli-Filho, M., Bastos-Filho, T.F.: An adaptive dynamic controller for autonomous mobile robot trajectory tracking. Control. Eng. Pract. 16(11), 1354–1363 (2008)

    Article  Google Scholar 

  21. Normey-Rico, J.E., Alcal, I., Gmez-Ortega, J., Camacho, E.F.: Mobile robot path tracking using a robust pid controller. Control. Eng. Pract. 9(11), 1209–1214 (2001)

    Article  Google Scholar 

  22. Pan, Y., Cheng, C.A., Saigol, K., Lee, K., Yan, X., Theodorou, E., Boots, B.: Agile autonomous driving using end-to-end deep imitation learning. In: Proceedings of Robotics: Science and Systems. Pittsburgh, Pennsylvania. (2018)

  23. Seder, M., Baotić, M., Petrović, I.: Receding horizon control for convergent navigation of a differential drive mobile robot. IEEE Trans. Control Syst. Technol. 25(2), 653–660 (2017).

    Article  Google Scholar 

  24. Skrjanc, I., Klancar, G.: A comparison of continuous and discrete tracking-error model-based predictive control for mobile robots. Robot. Auton. Syst. 87, 177–187 (2017)

    Article  Google Scholar 

  25. Sun, N., Fang, Y., Chen, H., Lu, B.: Amplitude-saturated nonlinear output feedback antiswing control for underactuated cranes with double-pendulum cargo dynamics. IEEE Trans. Ind. Electron. 64(3), 2135–2146 (2017)

    Article  Google Scholar 

  26. Xiao, H., Li, Z., Yang, C., Zhang, L., Yuan, P., Ding, L., Wang, T.: Robust stabilization of a wheeled mobile robot using model predictive control based on neurodynamics optimization. IEEE Trans. Ind. Electron. 64(1), 505–516 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Erkan Kayacan.

Additional information

Publisher’s Note

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

The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000598.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kayacan, E., Chowdhary, G. Tracking Error Learning Control for Precise Mobile Robot Path Tracking in Outdoor Environment. J Intell Robot Syst 95, 975–986 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: