Skip to main content
SpringerLink
Log in

Infimum of Path Length of Nonholonomic Vehicle with Finitely Bounded Curvature Radius

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

Abstract

In this paper, we address the shortest path problem of point-to-point maneuver for a new nonholonomic wheeled vehicle. The vehicle performs forward-only motion which is adopted by Dubins car, while the curvature radius of its path is restricted to a finitely bounded interval which is different from that of Dubins car with a lower-bounded curvature radius. We first provide the infimum of the path length of the vehicle of point-to-point maneuver without a start or final orientation constraint. Then we study the infimum of the path length of the vehicle for point-to-point maneuver with a start and final orientation constraints. Next, we derive the explicit expressions for the candidate infimums. The infimum of the length path is the minimum of the candidates. Moreover, several examples are provided to verify the main results. The results in this paper extend the results on the existence of the shortest path of Dubins car to the new type of nonholonomic vehicles.

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. Dubins, L.E.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79, 497–516 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chitsaz, H., LaValle, S.M., Balkcom, D.J., et al.: Minimum wheel-rotation paths for differential-drive mobile robots. Int. J. Robot. Res. 28, 66–80 (2009)

    Article  Google Scholar 

  3. Agarwal, P.K., Biedl, T., Lazard, S., et al.: Curvature-constrained shortest paths in a convex polygon. SIAM J. Comput. 31, 1814–1851 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Esquivel, W.D., Chiang, L.E.: Nonholonomic path planning among obstacles subject to curvature restrictions. Robotica 20, 49–58 (2002)

    Article  Google Scholar 

  5. Lee, J., Cheong, O., Kwon, W., et al.: Approximation of curvature-constrained shortest paths through a sequence of points. In: Lecture Notes in Computer Science vol. 1879. Springer, Berlin/Heidelberg (2000)

    Book  Google Scholar 

  6. Janiak, M., Tchon, K.: Constrained motion planning of nonholonomic systems. Syst. Control Lett. 60, 625–631 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ding, X.C., Rahmani, A., Egerstedt, M.: Multi-uav convoy protection: an optimal approach to path planning and coordination. IEEE Trans. Robot. 26, 256–268 (2010)

    Article  Google Scholar 

  8. Ny, J.L., Frazzoli, E., Feron, E.: The curvature-constrained traveling salesman problem for high point densities. In: Proceedings of IEEE International Conference Decision and Control, pp 5985–5990. New Orleans (2007)

  9. Chang, A., Brazil, M., Rubinstein, J., et al.: Curvature-constrained directional-cost paths in the plane. J. Global. Optim. 53, 663–681 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. Chang, A., Brazil, M., Thomas, D., et al.: Optimal curvature-constrained paths with anisotropic costs in the plane. In: Proceedings of the Australian Control Conference, pp 112–117. Melbourne (2011)

  11. Savla, K., Frazzoli, E., Bullo, F.: On the point-to-point and traveling salesperson problems for dubins vehicle. In: Proceedings of the IEEE American Control Conference, pp 786–791. Portland (2005)

  12. Backer, J., Kirkpatrick, D.: Finding curvature-constrained paths that avoid polygonal obstacles. In: Proceedings of the Symposium on the Computational Geometry, pp 66–73. New York (2007)

  13. Wang, H., Chen, Y., Soueres, P.: A geometric algorithm to compute time-optimal trajectories for a bidirectional steered robot. IEEE Trans. Robot. 25, 399–413 (2009)

    Article  Google Scholar 

  14. Lamiraux, F., Lammond, J.P.: Smooth motion planning for car-like vehicles. IEEE Trans. Robot. Autom. 17, 498–501 (2001)

    Article  Google Scholar 

  15. Wolek, A., Woolsey, C.: Disturbance rejection in dubins path planning. In: Proceedings of the IEEE American Control Conference, pp 4873–4878. Montreal (2012)

  16. Hota, S., Ghose, D.: A modified dubins method for optimal path planning of a miniature air vehicle converging to a straight line path. In: Proceedings of the IEEE American Control Conference, pp 2397–2402. Missouri (2009)

  17. Choi, H., Atkins, E.: Smooth transitions for a turning dubins vehicle. In: Proceedings of the AIAA Guidance, Navigation, and Control Conference. Toronto (2010)

  18. Filippis, L., Guglieri, G., Quagliotti, F.: Path planning strategies for uavs in 3d environments. J. Intell. Robot. Syst. 65, 247–264 (2012)

    Article  Google Scholar 

  19. Hwangbo, M., Kuffner, J., Kanade, T.: Efficient two-phase 3d motion planning for small fixed-wing uavs. In: Proceedings of the IEEE International Conference Robotics and Automation, pp 1035–1041. Roma (2007)

  20. Mahmoudian, N.: Efficient Motion Planning and Control for Underwater Gliders. PhD. Thesis. Virginia Polytechnic Institute and State University, Virginia (2009)

    Google Scholar 

  21. Mahmoudian, N., Woolsey, C.: Underwater glider motion control. In: Proceedings of the IEEE International Conference Decision and Control, pp 552–557. Cancun (2008)

  22. Mahmoudian, N., Geisbert, J., Woolsey, C.: Approximate analytical turning conditions for underwater gliders: implications for motion control and path planning. IEEE J. Ocean. Eng. 35, 131–143 (2010)

    Article  Google Scholar 

  23. Ito, S., Takeuchi, S., Sasaki, M.: Motion measurement of a two-wheeled skateboard and its dynamical simulation. Appl. Math. Model. 36, 2178–2191 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  24. Shammas, E.A., Choset, H., Rizzi, A.A.: Towards a unified approach to motion planning for dynamic underactuated mechanical systems with nonholonomic constraints. Int. J. Robot. Res. 26, 1075–1124 (2007)

    Article  Google Scholar 

  25. Agarwal, P., Wang, H.: Approximation algorithms for curvature-constrained shortest paths. SIAM J. Sci. Comput. 30, 1739–1772 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  26. Wang, H., Chen, Y., Soueres, P.: A geometric algorithm to compute time-optimal trajectories for a bidirectional steered robot. IEEE Trans. Robot. 25, 399–413 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Medicine, Tsinghua University, Beijing, 100084, China

    Baiquan Su

  2. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China

    Tianmiao Wang

  3. School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China

    Rui Wu

  4. School of Engineering, University of Tokyo, Tokyo, 113-8656, Japan

    Junchen Wang

Authors
  1. Baiquan Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tianmiao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Junchen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baiquan Su.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, B., Wang, T., Wu, R. et al. Infimum of Path Length of Nonholonomic Vehicle with Finitely Bounded Curvature Radius. J Intell Robot Syst 79, 197–210 (2015). https://doi.org/10.1007/s10846-014-0053-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-014-0053-6

Keywords

Search

Navigation