Journal of Optimization Theory and Applications

, Volume 138, Issue 2, pp 275–296 | Cite as

Minimum-Time Travel for a Vehicle with Acceleration Limits: Theoretical Analysis and Receding-Horizon Implementation

Article

Abstract

A methodology is proposed to generate minimum-time optimal velocity profiles for a vehicle with prescribed acceleration limits along a specified path. The necessary optimality conditions are explicitly derived, allowing the construction of the optimal solution semianalytically. A receding horizon implementation is also proposed for the on-line implementation of the velocity optimizer. Robustness of the receding horizon algorithm is guaranteed by the use of an adaptive scheme that determines the planning and execution horizons. Application to a real-life scenario with a comparison between the infinite and finite receding horizon schemes provides a validation of the proposed methodology.

Keywords

Minimum time velocity profile Acceleration limits Receding horizon 

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References

  1. 1.
    Hendrikx, J., Meijlink, T., Kriens, R.: Application of optimal control theory to inverse simulation of car handling. Veh. Syst. Dyn. 26, 449–461 (1996) CrossRefGoogle Scholar
  2. 2.
    Casanova, D., Sharp, R.S., Symonds, P.: Minimum time maneuvering: the significance of Yaw inertia. Veh. Syst. Dyn. 34, 77–115 (2000) CrossRefGoogle Scholar
  3. 3.
    Casanova, D., Sharp, R.S., Symonds, P.: On minimum time optimisation of formula one cars: the influence of vehicle mass. In: Proceedings of AVEC 2000. Ann-Arbor, MI, August 22–24, 2000 Google Scholar
  4. 4.
    Velenis, E., Tsiotras, P.: Minimum time vs. maximum exit velocity path optimization during cornering. In: 2005 IEEE International Symposium on Industrial Electronics, Dubrovnic, Croatia, pp. 355–360, June 2005 Google Scholar
  5. 5.
    Spenko, M.: Hazard avoidance for high-speed Rough-Terrain unmanned ground vehicles. Ph.D. Thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology (2005) Google Scholar
  6. 6.
    Metz, D., Williams, D.: Near time-optimal control of racing vehicles. Automatica 25(6), 841–857 (1989) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gadola, M., Vetturi, D., Cambiaghi, D., Manzo, L.: A tool for lap time simulation. In: Proceedings of SAE Motorsport Engineering Conference and Exposition, Dearborn, MI (1996) Google Scholar
  8. 8.
    Lepetic, M., Klancar, G., Skrjanc, I., Matko, D., Potocnic, B.: Time optimal path planning considering acceleration limits. Robot. Auton. Syst. 45, 199–210 (2003) CrossRefGoogle Scholar
  9. 9.
    Bobrow, J., Dubowsky, S., Gibson, J.: On the optimal control of robotic manipulators with actuator constraints. In: Proceedings of the American Control Conference, San Francisco, CA, pp. 782–787, June 1983 Google Scholar
  10. 10.
    Bobrow, J., Dubowsky, S., Gibson, J.: Time-optimal control of robotic manipulators along specified paths. Int. J. Robot. Res. 4(3), 3–17 (1985) CrossRefGoogle Scholar
  11. 11.
    Shin, K., McKay, N.: Minimum-time control of robotic manipulators with geometric path constraints. IEEE Trans. Automat. Contr. 30(6), 531–541 (1985) MATHCrossRefGoogle Scholar
  12. 12.
    Anonymous: Inertial and GPS measurement system. Report from Silverstone F1 Test, Technical Report, Oxford Technical Solutions, Oxfordshire, UK (2002) Google Scholar
  13. 13.
    Schouwenaars, T., De Moor, B., Feron, E., How, J.: Mixed integer programming for multi-vehicle path planning. In: Proceedings of the 2001 European Control Conference, Porto, Portugal, pp. 2603–2608, September 2001 Google Scholar
  14. 14.
    Bellingham, J., Richards, A., How, J.: Receding horizon control of autonomous aerial vehicles. In: Proceedings of the American Control Conference, Anchorage, AK, pp. 3741–3746, May 8–10, 2002 Google Scholar
  15. 15.
    Schouwenaars, T., Feron, E., How, J.: Safe receding horizon path planning for autonomous vehicles. In: Proceedings of the 40th Allerton Conference on Communication, Control and Computing, Monticello, IL, October 2002 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.School of Engineering and DesignBrunel UniversityUxbridgeUK
  2. 2.D. Guggenheim School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA

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