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A Free-Trajectory Quasi-steady-state Optimal-Control Method for Minimum-Time Problems of Cars and Motorcycles

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Abstract

Minimum-lap-time problems are commonly solved employing quasi-steady-state models on a predetermined trajectory or dynamic models on a free (non-predetermined) trajectory. The current work deals with a third approach, that combines a free-trajectory minimum-lap-time method, together with a quasi-steady-state description of the vehicle. The method is based on the computation of the well known g-g diagrams, which summarise the quasi-steady-state performance of the vehicle. This information is employed for the solution of an optimal-control problem, that allows to determine the optimal trajectory. Numerical models of high complexity can be employed, since all their features (e.g. tyre limits, power limits, aerodynamic drag and downforce, suspensions, etc.) are included in the related g-g diagrams, and do not affect the complexity of the optimal control problem that need be solved. The method allows to employ even experimental g-g diagrams in place of numerical ones, and is suitable for application to both cars and motorcycles.

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References

  1. Metz, D., Williams, D.: Near time-optimal control of racing vehicles. Automatica 25(6), 841–857 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Gadola, M., Vetturi, D., Cambiaghi, D., Manzo, L.: A tool for lap time simulation. Technical report 1996-12-01, SAE Technical Paper (1996)

    Google Scholar 

  3. Siegler, B., Deakin, A., Crolla, D.: Lap time simulation: comparison of steady state, quasi-static and transient racing car cornering stategies. In: Society of Automobile Engineers (ed.) 2000 SAE Motorsports Engineering Conference and Exposition, No. paper 2000-01-3563, p. 9. SAE International (2000)

    Google Scholar 

  4. Brayshaw, D., Harrison, M.: A quasi steady state approach to race car lap simulation in order to understand the effects of racing line and centre of gravity location. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 219(6), 725–739 (2005)

    Article  Google Scholar 

  5. Brayshaw, D., Harrison, M.: Use of numerical optimization to determine the effect of the roll stiffness distribution on race car performance. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 219(10), 1141–1151 (2005)

    Article  Google Scholar 

  6. Savaresi, S.M., Spelta, C., Ciotti, D., Sofia, M., Rosignoli, E., Bina, E.: Virtual selection of the optimal gear-set in a race car. Int. J. Veh. Syst. Model. Test. 3(1–2), 47–67 (2008)

    Google Scholar 

  7. Kelly, D.P., Sharp, R.S.: Time-optimal control of the race car: influence of a thermodynamic tyre model. Veh. Syst. Dyn. 50(4), 641–662 (2012)

    Article  Google Scholar 

  8. Völkl, T., Muehlmeier, M., Winner, H.: Extended steady state lap time simulation for analyzing transient vehicle behavior. SAE Int. J. Passeng. Cars Mech. Syst. 6, 283–292 (2013)

    Article  Google Scholar 

  9. Tremlett, A., Assadian, F., Purdy, D., Vaughan, N., Moore, A., Halley, M.: Quasi-steady-state linearisation of the racing vehicle acceleration envelope: a limited slip differential example. Veh. Syst. Dyn. 52(11), 1416–1442 (2014)

    Article  Google Scholar 

  10. Hendrikx, J., Meijlink, T., Kriens, R.: Application of optimal control theory to inverse simulation of car handling. Veh. Syst. Dyn. 26(6), 449–461 (1996)

    Article  Google Scholar 

  11. Cossalter, V., Da Lio, M., Lot, R., Fabbri, L.: A general method for the evaluation of vehicle manoeuvrability with special emphasis on motorcycles. Veh. Syst. Dyn. 31(2), 113–135 (1999)

    Article  Google Scholar 

  12. Casanova, D., Sharp, R.S., Symonds, P.: Minimum time manoeuvring: the significance of yaw inertia. Veh. Syst. Dyn. 34(2), 77–115 (2000)

    Article  Google Scholar 

  13. Casanova, D.: On minimum time vehicle manoeuvring: the theoretical optimal lap. Ph.D. thesis, School of Engineering, Cranfield University (2000)

    Google Scholar 

  14. Bertolazzi, E., Biral, F., Da Lio, M.: Symbolic-numeric efficient solution of optimal control problems for multibody systems. J. Comput. Appl. Math. 185(2), 404–421 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kelly, D.P.: Lap time simulation with transient vehicle and tyre dynamics. Ph.D. thesis, Cranfield University (2008)

    Google Scholar 

  16. Bobbo, S., Cossalter, V., Massaro, M., Peretto, M.: Application of the optimal maneuver method for enhancing racing motorcycle performance. Int. J. Passeng. Cars Mech. Syst. 1(1), 1311–1318 (2009)

    Google Scholar 

  17. Tavernini, D., Massaro, M., Velenis, E., Katzourakis, D., Lot, R.: Minimum time cornering: the effect of road surface and car transmission layout. Veh. Syst. Dyn. 51(10), 1533–1547 (2013)

    Article  Google Scholar 

  18. Tavernini, D., Velenis, E., Lot, R., Massaro, M.: The optimality of the handbrake cornering technique. J. Dyn. Syst. Meas. Control 136(4), 041019 (2014)

    Article  Google Scholar 

  19. Perantoni, G., Limebeer, D.J.N.: Optimal control for a formula one car with variable parameters. Veh. Syst. Dyn. 52(5), 653–678 (2014)

    Article  Google Scholar 

  20. Limebeer, D.J.N., Perantoni, G., Rao, A.V.: Optimal control of formula one car energy recovery systems. Int. J. Control 87(10), 2065–2080 (2014)

    MathSciNet  MATH  Google Scholar 

  21. Masouleh, M.I., Limebeer, D.J.N.: Optimizing the aero-suspension interactions in a formula one car. IEEE Trans. Control Syst. Technol. 24(3), 912–927 (2016)

    Article  Google Scholar 

  22. Tremlett, A., Massaro, M., Purdy, D., Velenis, E., Assadian, F., Moore, A., Halley, M.: Optimal control of motorsport differentials. Veh. Syst. Dyn. 53(12), 1772–1794 (2015)

    Article  Google Scholar 

  23. Tremlett, A., Limebeer, D.J.N.: Optimal tyre usage for a formula one car. Veh. Syst. Dyn. 54(10), 1448–1473 (2016)

    Article  Google Scholar 

  24. Dal Bianco, N., Lot, R., Gadola, M.: Minimum time optimal control simulation of a GP2 race car. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 232(9), 1180–1195 (2017)

    Article  Google Scholar 

  25. Dal Bianco, N., Bertolazzi, E., Biral, F., Massaro, M.: Comparison of direct and indirect methods for minimum lap time optimal control problems. Veh. Syst. Dyn. 57(5), 1–32 (2019)

    Google Scholar 

  26. Limebeer, D.J.N., Massaro, M.: Dynamics and Optimal Control of Road Vehicles. Oxford University Press, Oxford (2018)

    Book  MATH  Google Scholar 

  27. Veneri, M., Massaro, M.: A free-trajectory quasi-steady-state optimal-control method for minimum lap-time of race vehicles. Veh. Syst. Dyn. 1–22 (2019)

    Google Scholar 

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Correspondence to Matteo Massaro .

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Veneri, M., Massaro, M. (2020). A Free-Trajectory Quasi-steady-state Optimal-Control Method for Minimum-Time Problems of Cars and Motorcycles. In: Klomp, M., Bruzelius, F., Nielsen, J., Hillemyr, A. (eds) Advances in Dynamics of Vehicles on Roads and Tracks. IAVSD 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-38077-9_146

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  • DOI: https://doi.org/10.1007/978-3-030-38077-9_146

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38076-2

  • Online ISBN: 978-3-030-38077-9

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