Skip to main content
SpringerLink
Log in

Control of a wheeled system taking into account its inertial properties

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

Mechanical wheeled systems (WS) such as a wheeled tractor, a motor car, a mobile robot, etc. are studied. The well-known trajectory problem, i.e., the problem of controlling the WS motion along a given trajectory, is considered. This problem was solved earlier in the framework of kinematic WS models. The present paper deals with general WS models that additionally take into account inertial properties such as the WS masses and/or moments of inertia. We establish that the WS are subjected to rather significant perturbing forces. A control law stabilizing the WS motion along a given trajectory is constructed.

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. I. Kolmanovsky and N. H. McClamroch, “Developments in Nonholonomic Control Problems,” IEEE Contr. Syst. Mag. 15(6), 20–36 (1995).

    Article  Google Scholar 

  2. A. Micaelli and C. Samson, “Trajectory Tracking for Two-Steering-Wheels Mobile Robots,” in Proc. Symp. Robot Control’94. Capri (1994), pp. 500–506.

    Google Scholar 

  3. P. Morin and C. Samson, “Motion Control of Wheeled Mobile Robots,” in Springer Handbook Robotics (Springer, New York, 2008), pp. 799–826.

    Chapter  Google Scholar 

  4. P. Morin and C. Samson, “Control of Nonholonomic Mobile Robots Based on the Transverse Function Approach,” IEEE Trans. Robotics 25(5), 1058–1073 (2009).

    Article  MathSciNet  Google Scholar 

  5. M. Werling, L. Groll, and G. Bretthauer, “Invariant Trajectory Tracking with a Full-Size Autonomous Road Vehicle,” IEEE Trans. Robotics 26(4), 758–765 (2010).

    Article  Google Scholar 

  6. J. Ackermann, J. Guldner, W. Sienel, et al., “Linear and Nonlinear Controller Design for Robust Automatic Steering,” IEEE Trans. Control Syst. Technol. 3(1), 132–143 (1995).

    Article  Google Scholar 

  7. Z. Li, Y. Yang, and J. Li, “Adaptive Motion/Free Control of Mobile Under-Actuated Manipulators with Dynamic Coupling and Output Feedback,” IEEE Trans. Control Syst. Technol. 18(5), 1068–1079 (2010).

    Article  Google Scholar 

  8. L. Cordesses, C. Cariou, and M. Berducat, “Combine Harvester Control Using Real Time Kinematic GPS,” Precision Agricult. 2(2), 147–161 (2000).

    Article  Google Scholar 

  9. R. L. Mailer, “Soil Cultivation Implement Control Apparatus and Method,” Invention No. US2004/0111202Al (June 10, 2004).

    Google Scholar 

  10. I. Barabanov, A. Khvalkov, and L. B. Rapoport, “Methods and Apparatuses for Estimating the Position of a Mobile User in a System of Satellite Differential Navigation,” US Patent No. US7102563 B2 (February 26, 2004; Published on September 5, 2009).

    Google Scholar 

  11. L. B. Rapoport, M. Ya. Tkachenko, V. G. Mogil’nitskii, et al., “Integrated System of Satellite and Inertial Navigation: Experimental Results and Application to Mobile Robot Control,” Giroskop. Navigats. 56(1), 16–28 (2007).

    Google Scholar 

  12. V. I. Matyukhin, “The Control of aWheeled Mechanical System,” Prikl. Mat. Mekh. 71(2), 237–249 (2007) [J.Appl. Math.Mech. (Engl. Transl.) 71 (2), 208–220 (2007)].

    MathSciNet  MATH  Google Scholar 

  13. V. I. Matyukhin, “A Control of a Wheeled System with Account of Side Slip,” Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 4, 166–176 (2007) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 46 (4), 663–673 (2007)].

    Google Scholar 

  14. V. I. Matyukhin, “Wheeled System Control under Nondeterminacy Conditions,” Avtomat. Telemekh., No. 5, 76–94 (2009) [Automat. Remote Control (Engl. Transl.)].

    Google Scholar 

  15. V. I. Matyukhin, “Stabilization of the Motions of Mechanical Systems with Non-Holonomic Constraints,” Prikl. Mat. Mekh. 63(5), 725–735 (1999) [J. Appl.Math. Mech. (Engl. Transl.) 63 (5), 685–694 (1999)].

    MathSciNet  MATH  Google Scholar 

  16. V. I. Matyukhin, “The Controllability of Non-Holonomic Mechanical Systems with Constrained Controls,” Prikl. Mat. Mekh. 68(5), 758–775 (2004) [J. Appl. Math. Mech. (Engl. Transl.) 68 (5), 675–690 (2004)].

    MathSciNet  MATH  Google Scholar 

  17. V. I. Matyukhin, Control of Mechanical Systems (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

  18. V. V. Dobronravov, Foundations of Mechanics of Nonholonomic Systems (Vysshaya Shkola, Moscow, 1970) [in Russian].

    Google Scholar 

  19. P. V. Lineikin, “On Rolling of a Motor Car,” in Proc. Saratov Road Institute (1949)

    Google Scholar 

  20. Yu. G. Martynenko, “The Theory of the Generalized Magnus Effect for Non-Holonomic Mechanical Systems,” Prikl. Mat. Mekh. 68(6), 948–957 (2004) [J. Appl. Math. Mech. (Engl. Transl.) 68 (6), 847–855 (2004)].

    MathSciNet  MATH  Google Scholar 

  21. Yu. G. Martynenko, “Motion Control of Mobile Wheeled Robots,” Fund. Prikl. Mat. 11(8), 29–80 (2005).

    Google Scholar 

  22. L. G. Lobos, Nonholonomic Models of Wheeled Vehicles (Naukova Dumka, Kiev, 1986) [in Russian].

    Google Scholar 

  23. I. V. Novozhilov, “On Skidding in Braking,” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 4, 45–50 (1973) [Mech. Solids (Engl. Transl.)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya 65, V-342, GSP-7, Moscow, 117997, Russia

    V. I. Matyukhin

Authors
  1. V. I. Matyukhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Matyukhin.

Additional information

Original Russian Text © V.I. Matyukhin, 2013, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2013, No. 3, pp. 10–21.

About this article

Cite this article

Matyukhin, V.I. Control of a wheeled system taking into account its inertial properties. Mech. Solids 48, 243–253 (2013). https://doi.org/10.3103/S0025654413030023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654413030023

Keywords

Search

Navigation