Skip to main content
SpringerLink
Log in
Book cover

Robot Motion Planning and Control pp 171–253Cite as

Feedback control of a nonholonomic car-like robot

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 229))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Aicardi, G. Casalino, A. Bicchi, and A. Balestrino, “Closed loop steering of unicycle-like vehicles via Lyapunov techniques,” IEEE Robotics & Automation Mag., vol. 2, no. 1, pp. 27–35, 1995.

    Google Scholar 

  2. J. C. Alexander and J. H. Maddocks, “On the kinematics of wheeled mobile robots,” Int. J. of Robotics Research, vol. 8, no. 5, pp. 15–27, 1989.

    Google Scholar 

  3. A. Astolfi, “Exponential stabilization of a mobile robot,” 3rd European Control Conf., Roma, I, pp. 3092–3097, 1995.

    Google Scholar 

  4. M. K. Bennani and P. Rouchon, “Robust stabilization of flat and chained systems,” 3rd European Control Conf., Roma, I, pp. 2642–2646, 1995.

    Google Scholar 

  5. A. M. Bloch, M. Reyhanoglu, and N. H. McClamroch, “Control and stabilization of nonholonomic dynamic systems,” IEEE Trans. on Automatic Control, vol. 37, no. 11, pp. 1746–1757, 1992.

    Google Scholar 

  6. R. W. Brockett, “Asymptotic stability and feedback stabilization,” in Differential Geometric Control Theory, R. W. Brockett, R. S. Millman, H. J. Sussmann (Eds.), Birkhäuser, Boston, MA, pp. 181–191, 1983.

    Google Scholar 

  7. G. Campion, B. d'Andrea-Novel, and G. Bastin, “Modeling and state feedback control of nonholonomic mechanical systems,” 30th IEEE Conf. on Decision and Control, Brighton, UK, pp. 1184–1189, 1991.

    Google Scholar 

  8. C. Canudas de Wit and O. J. Sørdalen, “Exponential stabilization of mobile robots with nonholonomic constraints,” IEEE Trans. on Automatic Control, vol. 37, no. 11, pp. 1791–1797, 1992.

    Google Scholar 

  9. C. Canudas de Wit, H. Khennouf, C. Samson, and O. J. Sørdalen, “Nonlinear control design for mobile robots,” in Recent Trends in Mobile Robots, Y. F. Zheng (Ed.), World Scientific Publisher, 1993.

    Google Scholar 

  10. C. Canudas de Wit and H. Khennouf, “Quasi-continuous stabilizing controllers for nonholonomic systems: Design and robustness considerations,” 3rd European Control Conf., Roma, I, pp. 2630–2635, 1995.

    Google Scholar 

  11. J.-M. Coron, “Global asymptotic stabilization for controllable systems without drift,” Mathematics of Control, Signals, and Systems, vol. 5, pp. 295–312, 1992.

    Google Scholar 

  12. J.-M. Coron, “Links between local controllability and local continuous stabilization,” 2nd IFAC Symp. on Nonlinear Control System Design, Bordeaux, F, pp. 477–482, 1992.

    Google Scholar 

  13. B. d'Andrea-Novel, G. Bastin, and G. Campion, “Dynamic feedback linearization of nonholonomic wheeled mobile robots,” 1992 IEEE Int. Conf. on Robotics and Automation, Nice, F, pp. 2527–2532, 1992.

    Google Scholar 

  14. A. De Luca and M. D. Di Benedetto, “Control of nonholonomic systems via dynamic compensation,” Kybernetica, vol. 29, no. 6, pp. 593–608, 1993.

    Google Scholar 

  15. E. D. Dickmanns and A. Zapp, “Autonomous high speed road vehicle guidance by computer vision,” 10th IFAC World Congr., München, D, pp. 221–226, 1987.

    Google Scholar 

  16. M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Design of trajectory stabilizing feedback for driftless flat systems,” 3rd European Control Conf., Roma, I, pp. 1882–1887, 1995.

    Google Scholar 

  17. L. Gurvits and Z. Li, “Smooth time-periodic feedback solutions for nonholonomic motion planning,” in Nonholonomic Motion Planning, Z. Li, J. Canny (Eds.), Kluwer Academic Publishers, Norwell, MA, pp. 53–108, 1992.

    Google Scholar 

  18. A. Isidori, Nonlinear Control Systems, 3rd Edition, Springer-Verlag, London, UK, 1995.

    Google Scholar 

  19. T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.

    Google Scholar 

  20. H. K. Khalil, Nonlinear Systems, Macmillan, New York, NY, 1992.

    Google Scholar 

  21. I. V. Kolmanovsky, M. Reyhanoglu, and N. H. McClamroch, “Discontinuous feedback stabilization of nonholonomic systems in extended power form,” 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, pp. 3469–3474, 1994.

    Google Scholar 

  22. M. Krstić, I. Kanellakopoulos, and P. Kokotović, Nonlinear and Adaptive Control Design, John Wiley & Sons, New York, NY, 1995.

    Google Scholar 

  23. G. Lafferriere and H. J. Sussmann, “Motion planning for controllable systems without drift,” 1991 IEEE Int. Conf. on Robotics and Automation, Sacramento, CA, pp. 1148–1153, 1991.

    Google Scholar 

  24. J.-P. Laumond, “Controllability of a multibody mobile robot,” IEEE Trans. on Robotics and Automation, vol. 9, no. 6, pp. 755–763, 1993.

    Google Scholar 

  25. P. Lucibello and G. Oriolo, “Stabilization via iterative state steering with application to chained-form systems,” 35th IEEE Conf. on Decision and Control, Kobe, J, pp. 2614–2619, 1996.

    Google Scholar 

  26. S. Monaco and D. Normand-Cyrot, “An introduction to motion planning under multirate digital control,” 31st IEEE Conf. on Decision and Control, Tucson, AZ, pp. 1780–1785, 1992.

    Google Scholar 

  27. P. Morin and C. Samson, “Time-varying exponential stabilization of chained systems based on a backstepping technique,” 35th IEEE Conf. on Decision and Control, Kobe, J, pp. 1449–1454, 1996.

    Google Scholar 

  28. R. M. Murray and S. S. Sastry, “Nonholonomic motion planning: Steering using sinusoids,” IEEE Trans. on Automatic Control, vol. 38, no. 5, pp. 700–716, 1993.

    Google Scholar 

  29. R. M. Murray, “Control of nonholonomic systems using chained forms,” Fields Institute Communications, vol. 1, pp. 219–245, 1993.

    Google Scholar 

  30. R. M. Murray and R. T. M'Closkey, “Converting smooth, time-varying, asymptotic stabilizers for driftless systems to homogeneous, exponential stabilizers,” 3rd European Control Conf., Roma, I, pp. 2620–2625, 1995.

    Google Scholar 

  31. J. I. Neimark and F. A. Fufaev, Dynamics of Nonholonomic Systems, American Mathematical Society, Providence, RI, 1972.

    Google Scholar 

  32. G. Oriolo, S. Panzieri, and G. Ulivi, “An iterative learning controller for nonholonomic robots,” 1996 IEEE Int. Conf. on Robotics and Automation, Minneapolis, MN, pp. 2676–2681, 1996.

    Google Scholar 

  33. J.-B. Pomet, “Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift,” Systems & Control Lett., vol. 18, pp. 147–158, 1992.

    Google Scholar 

  34. J.-B. Pomet, B. Thuilot, G. Bastin, and G. Campion, “A hybrid strategy for the feedback stabilization of nonholonomic mobile robots,” 1992 IEEE Int. Conf. on Robotics and Automation, Nice, F, pp. 129–134, 1992.

    Google Scholar 

  35. J.-B. Pomet and C. Samson, “Time-varying exponential stabilization of nonholonomic systems in power form,” INRIA Rep. 2126, Dec. 1993.

    Google Scholar 

  36. P. Rouchon, M. Fliess, J. Lévine, and P. Martin, “Flatness and motion planning: The car with n trailers,” 2nd European Control Conf., Gröningen, NL, pp. 1518–1522, 1993.

    Google Scholar 

  37. M. Sampei, T. Tamura, T. Itoh, and M. Nakamichi, “Path tracking control of trailer-like mobile robot,” 1991 IEEE/RSJ Int. Work. on Intelligent Robots and Systems, Osaka, J, pp. 193–198, 1991.

    Google Scholar 

  38. C. Samson, “Velocity and torque feedback control of a nonholonomic cart,” in Advanced Robot Control, C. Canudas de Wit (Ed.), Birkhäuser, Boston, MA, pp. 125–151, 1991.

    Google Scholar 

  39. C. Samson and K. Ait-Abderrahim, “Feedback control of a nonholonomic wheeled cart in cartesian space,” 1991 IEEE Int. Conf. on Robotics and Automation, Sacramento, CA, pp. 1136–1141, 1991.

    Google Scholar 

  40. C. Samson, M. Le Borgne, B. Espiau, Robot Control: The Task Function Approach,” Oxford Science Publications, Oxford, UK, 1991.

    Google Scholar 

  41. C. Samson and K. Ait-Abderrahim, “Feedback stabilization of a nonholonomic wheeled mobile robot, 1991 IEEE/RSJ Int. Work. on Intelligent Robots and Systems,” Osaka, J, pp. 1242–1247, 1991.

    Google Scholar 

  42. C. Samson, “Path following and time-varying feedback stabilization of a wheeled mobile robot,” 2nd Int. Conf. on Automation, Robotics and Computer Vision, Singapore, 1992.

    Google Scholar 

  43. C. Samson, “Time-varying feedback stabilization of car-like wheeled mobile robots,” Int. J. of Robotics Research, vol. 12, no. 1, pp. 55–64, 1993.

    Google Scholar 

  44. C. Samson, “Control of chained systems. Application to path following and time-varying point-stabilization of mobile robots,” IEEE Trans. on Automatic Control, vol. 40, no. 1, pp. 64–77, 1995.

    Google Scholar 

  45. E. D. Sontag, “Feedback stabilization of nonlinear systems,” in Robust Control of Linear Systems and Nonlinear Control, M. A. Kaashoek, J. H. van Schuppen, A. C. M. Ran (Eds.), Birkhäuser, Cambridge, MA, pp. 61–81, 1990.

    Google Scholar 

  46. O. J. Sørdalen, “Conversion of the kinematics of a car with n trailers into a chained form,” 1993 IEEE Int. Conf. on Robotics and Automation, Atlanta, GA, vol. 1, pp. 382–387, 1993.

    Google Scholar 

  47. O. J. Sørdalen and C. Canudas de Wit, “Exponential control law for a mobile robot: Extension to path following,” IEEE Trans. on Robotics and Automation, vol. 9, no. 6, pp. 837–842, 1993.

    Google Scholar 

  48. O. J. Sørdalen, “Feedback control of nonholonomic mobile robots,” Ph. D. Thesis, The Norwegian Institute of Technology, Trondheim, NO, Mar. 1993.

    Google Scholar 

  49. O. J. Sørdalen and O. Egeland, “Exponential stabilization of nonholonomic chained systems,” IEEE Trans. on Automatic Control, vol. 40, no. 1, pp. 35–49, 1995.

    Google Scholar 

  50. H. J. Sussmann and W. Liu, “Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories,” Tech. Rep. SYCON-91-02, Rutgers University, Feb. 1991.

    Google Scholar 

  51. A. R. Teel, R. M. Murray, and G. Walsh, “Nonholonomic control systems: From steering to stabilization with sinusoids,” 31st IEEE Conf. on Decision and Control, Tucson, AZ, pp. 1603–1609, 1992.

    Google Scholar 

  52. D. Tsakiris, C. Samson, and P. Rives, “Vision-based time-varying stabilization of a mobile manipulator,” 6th Int. Conf. on Control, Automation, Robotics and Vision, Singapore, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Università di Roma “La Sapienza”, Italy

    A. De Luca & G. Oriolo

  2. INRIA, Sophia-Antipolis, France

    C. Samson

Authors
  1. A. De Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Oriolo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Samson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. -P. Laumond

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag London Limited

About this chapter

Cite this chapter

De Luca, A., Oriolo, G., Samson, C. (1998). Feedback control of a nonholonomic car-like robot. In: Laumond, J.P. (eds) Robot Motion Planning and Control. Lecture Notes in Control and Information Sciences, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036073

Download citation

  • DOI: https://doi.org/10.1007/BFb0036073

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76219-5

  • Online ISBN: 978-3-540-40917-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation