Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Curve Tracking Control for Autonomous Vehicles with Rigidly Mounted Range Sensors

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

Abstract

In this paper, we present feedback control laws for an autonomous vehicle with rigidly mounted range sensors to track a desired curve. In particular, we consider a vehicle that has a group of rays around two center rays that are perpendicular to the velocity of the vehicle. Under such a sensor configuration, singularities are bound to occur in the curve tracking feedback control law when tracking concave curves. To overcome this singularity, we derive a hybrid strategy of switching between control laws when the vehicle gets close to singularities. Rigorous proof and extensive simulation results verify the validity of the proposed feedback control law.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Egerstedt, M., Hu, X., Stotsky, A.: Control of mobile platforms using a virtual vehicle approach. IEEE Trans. Automat. Contr. 46, 1777–1782 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Zhang, F., Justh, E., Krishnaprasad, P.S.: Boundary following using gyroscopic control. In: Proc. of 43rd IEEE Conf. on Decision and Control, pp. 5204–5209, Atlantis, 14–17 December 2004

  3. Zhang, F., O’Connor, A., Luebke, D., Krishnaprasad, P.S.: Experimental study of curvature-based control laws for obstacle avoidance. In: Proc. of IEEE International Conf. on Robotics and Automation, pp. 3849–3854, New Orleans, 24–27 April 2004

  4. Zhang, F., Leonard, N.E.: Coordinated patterns of unit speed particles on a closed curve. Syst. Control. Lett. 56, 397–407 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Zhang, F., Fiorelli, E., Leonard, N.E.: Exploring scalar fields using multiple sensor platforms: tracking level curves. In: Proc. of 46th IEEE Conf. on Decision and Control, pp. 3579–3584, New Orleans, 12–14 December 2007

  6. Zhang, F., Fratantoni, D.M., Paley, D., Lund, J., Leonard, N.E.: Control of coordinated patterns for ocean sampling. Int. J. Control 80, 1186–1199 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Reddy, P.V., Justh, E.W., Krishnaprasad, P.: Motion camouflage in three dimensions. In: Proc. of 45th IEEE Conf. on Decision and Control, pp. 3327–3332, San Diego, 13–15 December 2006

  8. Justh, E.W., Krishnaprasad, P.S.: Natural frames and interacting particles in three dimensions. In: Proc. of 44th IEEE Conf. on Decision and Control, pp. 2841–2846, Seville, 12–15 December 2005

  9. Samson, C.: Control of chained systems: application to path-following and time-varying point-stabilization of mobile robots. IEEE Trans. Automat. Contr. 40, 64–77 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Frezza, R., Picci, G.: On line path following by recursive spline updating. In: Proc. of 34th IEEE Conf. on Decision and Control, pp. 4047–4052, New Orleans, 13–15 December 1995

  11. Ma, Y., Koseck’a, J., Sastry, S.: Vision guided navigation for a nonholonomic mobile robot. In: Proc. of 36th IEEE Conference on Decision and Control, pp. 3069–3074, San Diego, 10–12 December 1997

  12. Justh, E.W., Krishnaprasad, P.S.: Steering laws for motion camouflage. R. Soc. Lond. Proc. Ser. A 462, 3629–3643 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, K., Baillieul, J.: Data-rate requirements for nonlinear feedback control. In: Proc. of 6th IFAC Symp. Nonlinear Contr. Sys., pp. 1277–1282, Stuttgart, 1–3 September 2004

  14. Micaelli, A., Samson, C.: Trajectory tracking for unicycle-type and two-steering-wheels mobile robots. INRIA, Tech. Rep. (1993)

  15. Andersson, S.B., Park, J.: Tip steering for fast imaging in AFM. In: Proc. of American Control Conference, pp. 2469–2474, Portland, 8–10 June 2005

  16. Clark, J., Fierro, R.: Cooperative hybrid control of robotic sensors for perimeter detection and tracking. In: Proc. of American Control Conference, pp. 3500–3505, Portland, 8–10 June 2005

  17. Corke, P., Detweiler, C., Dunbabin, M., Hamilton, M., Rus, D., Vasilescu, I.: Experiments with underwater robot localization and tracking. In: Proc. of IEEE International Conference on Robotics and Automation, pp. 4556–4561, Roma, 10–14 April 2007

  18. Carmo, M.D.: Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs (1976)

    MATH  Google Scholar 

  19. Dickmanns, E.D., Graefe, V.: Applications of dynamic monocular machine vision. Mach. Vis. Appl. 1, 241–261 (1988)

    Article  Google Scholar 

  20. Dickmanns, E.D. Mysliwetz, B.D.: Recursive 3-d road and relative ego-state estimation. IEEE Trans. Pattern Anal. Mach. Intell. 14, 199–213 (1992)

    Article  Google Scholar 

  21. Raviv, D., Herman, M.: A nonreconstruction approach for road following. Proc. SPIE Intell. Robots Comput. Vis. 1608, 2–12 (1992)

    Google Scholar 

  22. Sasiadek, J.Z., Dulba, I.: 3D local trajectory planner for UAV. J. Intell. Robot. Syst 29, 191–210 (2000)

    Article  MATH  Google Scholar 

  23. Sasiadek, J.Z., Dulba, I.: A heuristic approach to robot path planning based on task requirements using a genetic algorithm. J. Intell. Robot. Syst 16, 65–88 (1996)

    Article  Google Scholar 

  24. Cagigas, D., Abascal, J.: A hierarchical extension of the D* algorithm. J. Intell. Robot. Syst 42, 393–413 (2005)

    Article  Google Scholar 

  25. Wooden, D., Egerstedt, M.: On finding globally optimal paths through weighted colored graphs. In: Proc. of 45th IEEE Conf. on Decision and Control, pp. 3849–3854, San Diego, 13–15 December 2006

  26. Sun, J., Mehta, T., Wooden, D., Powers, M., Regh, J., Balch, T., Egerstedt, M.: Learning from examples in unstructured, outdoor environments. J. Field Robot. 23, 1019–1036 (2006)

    Article  Google Scholar 

  27. Wooden, D., Egerstedt, M.: Oriented visibility graphs: Low-complexity planning in real-time environments. In: Proc. of IEEE Conf. on Robotics and Automation, pp. 2354 – 2359, Orlando, May 2006

  28. Wooden, D.: A guide to vision-based map building. IEEE Robot. Autom. Mag 13, 94–98 (2006)

    Article  Google Scholar 

  29. Hespanha, J.P., Morse, A.S.: Stability of switched systems with average dwell-time. In: Proc. of 38th IEEE Conference on Decision and Control, pp. 2655–2660, Phoenix, 7–10 December 1999

  30. Liberzon, D., Morse, A.S.: Benchmark problems in stability and design of switched systems. IEEE Control Syst. Mag. 19, 59–70 (1999)

    Article  Google Scholar 

  31. Branicky, M.: Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr. 43(4), 475–482 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  32. DeCarlo, S.P.R., Branicky, M.S., Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE 88(2), 1069–1082 (2000)

    Article  Google Scholar 

  33. Tomlin, C., Sastry, S.: Switching through singularities. In: Proc. of 36th IEEE Conf. on Decision and Control, pp. 1–6, San Diego, 10–12 December 1997

  34. Khalil, H.K.: Nonlinear Systems, 3rd ed. Prentice Hall, Englewood Cliffs (2002)

    MATH  Google Scholar 

  35. Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., Haker, S.: Differential and numerically invariant signature curves applied to object recognition. Int. J. Comput. Vis. 26, 107–135 (1998)

    Article  Google Scholar 

  36. Zhang, F., Leonard, N.: Generating contour plots using multiple sensor platforms. In: Proc. of IEEE Symposium on Swarm Intelligence, pp. 309–314, Pasadena, 8–10 June 2005

  37. Duttagupta, S., Ramamritham, K., Ramanathan, P.: Distributed boundary estimation using sensor networks. In: Proc. of IEEE International Conference on Mobile Adhoc and Sensor Systems (MASS), pp. 316–325, Vancouver, 9–12 October 2006

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fumin Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, J., Zhang, F. & Egerstedt, M. Curve Tracking Control for Autonomous Vehicles with Rigidly Mounted Range Sensors. J Intell Robot Syst 56, 177–197 (2009). https://doi.org/10.1007/s10846-009-9308-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-009-9308-z

Keywords