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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Metz, D., Williams, D.: Near time-optimal control of racing vehicles. Automatica 25(6), 841–857 (1989)
Gadola, M., Vetturi, D., Cambiaghi, D., Manzo, L.: A tool for lap time simulation. Technical report 1996-12-01, SAE Technical Paper (1996)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Casanova, D., Sharp, R.S., Symonds, P.: Minimum time manoeuvring: the significance of yaw inertia. Veh. Syst. Dyn. 34(2), 77–115 (2000)
Casanova, D.: On minimum time vehicle manoeuvring: the theoretical optimal lap. Ph.D. thesis, School of Engineering, Cranfield University (2000)
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)
Kelly, D.P.: Lap time simulation with transient vehicle and tyre dynamics. Ph.D. thesis, Cranfield University (2008)
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)
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)
Tavernini, D., Velenis, E., Lot, R., Massaro, M.: The optimality of the handbrake cornering technique. J. Dyn. Syst. Meas. Control 136(4), 041019 (2014)
Perantoni, G., Limebeer, D.J.N.: Optimal control for a formula one car with variable parameters. Veh. Syst. Dyn. 52(5), 653–678 (2014)
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)
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)
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)
Tremlett, A., Limebeer, D.J.N.: Optimal tyre usage for a formula one car. Veh. Syst. Dyn. 54(10), 1448–1473 (2016)
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)
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)
Limebeer, D.J.N., Massaro, M.: Dynamics and Optimal Control of Road Vehicles. Oxford University Press, Oxford (2018)
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)
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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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