Skip to main content
SpringerLink
Log in

A Smooth Time–Varying PID Controller for Nonholonomic Mobile Robots Subject to Matched Disturbances

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

Abstract

In this paper we present the design of a robust controller for nonholonomic differential wheeled mobile robot moving on the plane and subject to constant unknown disturbances. The proposed controller is smooth, time-variant and has a (simple) PID-like structure. Also, as analytically proved, it achieves global asymptotic convergence to zero of the position and orientation (regulation) errors despite the perturbations. Realistic simulations in the Gazebo-ROS environment validate the effectiveness of our approach.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lizarraga, D.: Obstructions to the existence of universal stabilizers for smooth control systems. Syst. Math. Control Signals Syst. 16(4), 255–277 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brockett, R.: Asymptotic stability and feedback stabilization. Diff. Geometric Control Theory, 181–191 (1983)

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

    Article  Google Scholar 

  4. Dixon, W., Jiang, Z., Dawson, D.: Global exponential setpoint control of wheeled mobile robots: A lyapunov approach. Automatica 36(11), 1741–1746 (2000)

    Article  MATH  Google Scholar 

  5. Kavraki, L.E., Svestka, P., Latombe, J.-C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces, Robotics and Automation. IEEE Trans. 12(4), 566–580 (1996)

    Google Scholar 

  6. Jiang, Z., Nijmeijer, H.: Tracking control of mobile robots: a case study in backstepping. Automatica 33, 1393–1399 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jiang, Z., Pomet, J.: Combining backstepping and time-varying techniques for a new set of adaptive controllers. In: Proceedings of the IEEE Conference on Decision and Control, pp 2207–2212 (1994)

  8. Song, B., Karl, H.: Dynamic Surface Control of Uncertain Nonlinear Systems. Springer, An LMI approach (2011)

    Book  MATH  Google Scholar 

  9. Dixon, W.E., Dawson, D.M., Zergeroglu, E.: Robust control of a mobile robot system with kinematic disturbances. In: Proceedings of the International Conference on Control Applications, pp 437–442 (2000)

  10. Yang, J.-M., Kim, J.-H.: Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots. IEEE Trans. Robot. Autom. 15(3), 578–587 (1999)

    Article  Google Scholar 

  11. Guldner, J., Utkin, V.: Stabilization of nonholonomic mobile robots using lyapunov functions for navigation and sliding mode control. In: Proceedings of the IEEE Conference on Decision and Control, pp 2967–2972 (1994)

  12. Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. CRC Press, New York (1998)

    Book  MATH  Google Scholar 

  13. Nuño, E., Loría, A., Hernández, T., Panteley, E.: Distributed consensus-formation of force-controlled nonholonomic robots with time-varying delays. In: Automatica, pp 1–7 (2020)

  14. Maghenem, M., Loría, A., Nuño, E., Panteley, E.: Distributed full-consensus control of nonholonomic vehicles under non-differentiable measurements delays. In: IEEE Control Systems Letters, pp 97–102 (2021)

  15. Romero, J.G., Nuño, E.: Global stabilization of nonholonomic mobile robots via a smooth output feedback time-varying controller. In: IEEE 15th International Conference on Control and Automation (ICCA), pp 393–398 (2019)

  16. Donaire, A., Romero, J.G., Perez, T., Ortega, R.: Smooth Stabilisation of Nonholonomic Robots Subject to Disturbances. In: IEEE International Conference on Robotics and Automation (ICRA), pp 4385–4390. Seattle, USA (2015)

  17. Ferguson, J., Donaire, A., Middleton, R.H.: Integral control of port-hamiltonian systems: nonpassive outputs without coordinate transformation. IEEE Transaction on Automatic Control 62(11), 5947–5953 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ferguson, J., Donaire, A., Ortega, R., Middleton, R.H.: Matched disturbance rejection for energy-shaping controlled underactuated mechanical systems. In: IEEE 56th Annual Conference on Decision and Control (CDC), pp 1484–1489 (2017)

  19. Tzafestas, S.G.: Introduction to Mobile Robot Control. Elsevier, New York (2013)

    Google Scholar 

  20. Khalil, H.: Nonlinear Systems. Prentice-Hall, New York (1996)

    Google Scholar 

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

  22. Shojaei, K., Shahri, A.M., Tarakameh, A., Tabibian, B.: Adaptive trajectory tracking control of a differential drive wheeled mobile robot. Robotica 29(3), 391–402 (2011)

    Article  Google Scholar 

Download references

Funding

Partial financial support was received from the following institutions.

Funder 1: Consejo Nacional de Ciencia y Tecnología. Country: Mexico. Award Number: CB-282807. Grant Recipient: E. Nuño.

Funder 2: Asociación Mexicana de Cultura, A.C. Country: Mexico. Award Number: Not applicable Grant Recipient: J.G. Romero and R. Cisneros.

Author information

Authors and Affiliations

  1. Departamento Académico de Sistemas Digitales, ITAM, Ciudad de México, 01080, Mexico

    Jose Guadalupe Romero & Rafael Cisneros

  2. Department of Computer Science, CUCEI, University of Guadalajara, Guadalajara, Mexico

    Emmanuel Nuño

  3. DTIS, ONERA and Université Paris-Saclay, F-91123, Palaiseau, France

    Esteban Restrepo

  4. Parasol Lab, Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL, 61820, USA

    Marco Morales

  5. Department of Computer Science, Instituto Tecnológico Autónomo de México (ITAM), Ciudad de México, 01080, Mexico

    Marco Morales

Authors
  1. Jose Guadalupe Romero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emmanuel Nuño
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Esteban Restrepo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rafael Cisneros
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Marco Morales
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

JGR: Conceptualization, Formal Analysis, Writing ∙ EN: Formal Analysis, Writing ∙ ER: Writing, Simulation ∙RC: Writing, Simulation ∙ MM: Writing, Simulation.

Corresponding author

Correspondence to Rafael Cisneros.

Ethics declarations

Conflict of Interests

The authors have no conflicts of interest to declare.

Additional information

Publisher’s Note

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

This article is supported by the Asociación Mexicana de Cultura A.C and by the Mexican CONACyT Basic Scientific Research grant CB-282807.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Romero, J.G., Nuño, E., Restrepo, E. et al. A Smooth Time–Varying PID Controller for Nonholonomic Mobile Robots Subject to Matched Disturbances. J Intell Robot Syst 105, 13 (2022). https://doi.org/10.1007/s10846-022-01622-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-022-01622-3

Keywords

Search

Navigation