Minimum-time optimal control for vehicles with active rear-axle steering, transfer case and variable parameters

References

• Harrer M, Pfeffer P. Steering handbook. Berlin: Springer; 2017.
   Google Scholar
• Breuer B, Bill KH. Brake technology handbook. Warrendale (PA): SAE International; 2008.
   Google Scholar
• de Castro R, Tanelli M, Araujo RE, et al. Minimum-time manoeuvring in electric vehicles with four wheel-individual-motors. Veh Syst Dyn. 2014;52:824–846. doi: 10.1080/00423114.2014.902973
   Web of Science ®Google Scholar
• Gudmundsson S. General aviation aircraft design. Oxford, Waltham (MA): Butterworth-Heinemann; 2014.
   Google Scholar
• Brayshaw DL, Harrison MF. 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. 2005;219:725–739. doi: 10.1243/095440705X11211
   Web of Science ®Google Scholar
• Candelpergher A, Gadola M, Vetturi D. Developments of a method for lap time simulation. In: SAE Conference Proceedings. 2000. p. 241–246.
   Google Scholar
• Patton C. Development of vehicle dynamics tools for motorsports [PhD dissertation]. Oregon State University; 2013.
   Google Scholar
• Siegler B, Deakin A, Crolla D. Lap time simulation: comparison of steady state, quasi-static and transient racing car cornering strategies. Proceedings of the 2000 SAE Motorsports Engineering Conference and Exposition. 2000.
   Google Scholar
• Waldmann P. Entwicklung eines Fahrzeugführungssystems zum Erlernen der Ideallinie auf Rennstrecken [PhD dissertation]. Shaker; 2009.
   Google Scholar
• Dal Bianco N, Bertolazzi E, Biral F, et al. Comparison of direct and indirect methods for minimum lap time optimal control problems. Veh Syst Dyn. 2018;57:665–696. doi: 10.1080/00423114.2018.1480048
   Web of Science ®Google Scholar
• Kelly M. An introduction to trajectory optimization: how to do your own direct collocation. SIAM Rev. 2017;59:849–904. doi: 10.1137/16M1062569
   Web of Science ®Google Scholar
• Betts J. Practical methods for optimal control and estimation using nonlinear programming. 2nd ed. Philadelphia (PA): SIAM; 2010.
   Google Scholar
• Casanova D, Sharp RS, Symonds P. Minimum time manoeuvring: the significance of yaw inertia. Veh Syst Dyn. 2000;34:77–115. doi: 10.1076/0042-3114(200008)34:2;1-G;FT077
   Web of Science ®Google Scholar
• Rao AV. A survey of numerical methods for optimal control. Adv Astronaut Sci. 2010;135:497–528.
   Google Scholar
• Wächter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program. 2005;1:25–57.
   Google Scholar
• Limebeer DJN, Perantoni G, Rao AV. Optimal control of formula one car energy recovery systems. Int J Control. 2014;87:2065–2080.
   Web of Science ®Google Scholar
• Bertolazzi E, Biral F, Da Lio M. Symbolic numeric indirect method for solving optimal control problems for large multibody systems. Multibody Syst Dyn. 2005;13:233–252. doi: 10.1007/s11044-005-3987-4
   Web of Science ®Google Scholar
• Hendrikx JPM, Imeljlink TJJ, Kriens RFC. Application of optimal control theory to inverse simulation of car handling. Veh Syst Dyn. 1996;26:449–461. doi: 10.1080/00423119608969319
   Web of Science ®Google Scholar
• Cossalter V, Da Lio M, Lot R, et al. A general method for the evaluation of vehicle manoeuvrability with special emphasis on motorcycles. Veh Syst Dyn. 1999;31:113–135. doi: 10.1076/vesd.31.2.113.2094
   Web of Science ®Google Scholar
• Casanova PT. On minimum time vehicle manoeuvring: the theoretical optimal lap [PhD dissertation]. Cranfield University; 2000.
   Google Scholar
• Kelly DP. Lap time simulation with transient vehicle and tyre dynamics [PhD dissertation]. Cranfield University; 2008.
   Google Scholar
• Bertolazzi E, Biral F, Da Lio M. Real-Time motion planning for multibody systems real life application examples. Multibody Syst Dyn. 2007;17:119–139. doi: 10.1007/s11044-007-9037-7
   Web of Science ®Google Scholar
• Lot R, Dal Bianco N. The significance of high-order dynamics in lap time simulations. 24th Int. Symposium on Dyn. of Veh. on Roads and Tracks (IAVSD). 2015.
   Google Scholar
• Dal Bianco N, Lot R, Gadola M. Minimum time optimal control simulation of a GP2 race car. Proc Inst Mech Eng, Part D. 2018;232:1180–1195. doi: 10.1177/0954407017728158
   Web of Science ®Google Scholar
• Tavernini D, Massaro M, Velenis E, et al. Minimum time cornering: the effect of road surface and car transmission layout. Veh Syst Dyn. 2013;51:1533–1547. doi: 10.1080/00423114.2013.813557
   Web of Science ®Google Scholar
• Perantoni G, Limebeer DJN. Optimal control for a Formula One car with variable parameters. Veh Syst Dyn. 2014;52:653–678. doi: 10.1080/00423114.2014.889315
   Web of Science ®Google Scholar
• Masouleh MI, Limebeer DJN. Optimizing the aero-suspension interactions in a Formula One car. IEEE Trans Control Syst Technol. 2016;24:912–927. doi: 10.1109/TCST.2015.2475396
   Web of Science ®Google Scholar
• Tremlett AJ, Limebeer DJN. Optimal tyre usage for a formula one car. Veh Syst Dyn. 2016;54:1448–1473. doi: 10.1080/00423114.2016.1213861
   Web of Science ®Google Scholar
• Falugi P, Kerrigan E, Van Wyk E. Imperial College London optimal control software user guide (ICLOCS). Available from: http://www.ee.ic.ac.uk/ICLOCS.
   Google Scholar
• Patterson MA, Rao AV. GPOPS-II: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans Math Softw. 2014;41:1:1–1:37. doi: 10.1145/2558904
   Web of Science ®Google Scholar
• de Castro R, Tanelli M, Araujo RE, et al. Torque allocation in electric vehicles with in-wheel motors: a performance-oriented approach. 52nd IEEE Conference on Decision and Control. 2013. p. 1538–1543.
   Google Scholar
• de Castro R, Tanelli M, Araujo RE, et al. Design of safety-oriented control allocation strategies for overactuated electric vehicles. Veh Syst Dyn. 2014;52:1017–1046. doi: 10.1080/00423114.2014.916811
   Web of Science ®Google Scholar
• de Castro R, Tanelli M, Araujo RE, et al. Minimum-time path-Following for highly redundant electric vehicles. IEEE Trans Control Syst Technol. 2016;24:487–501. doi: 10.1109/TCST.2015.2458773
   Web of Science ®Google Scholar
• Dunning I, Huchette J, Lubin M. JuMP: a modeling language for mathematical optimization. SIAM Rev. 2017;59:295–320. doi: 10.1137/15M1020575
   Web of Science ®Google Scholar
• Morin P, Samson C. Motion control of wheeled mobile robots. Springer; 2008. p. 799–826. (Springer Handbook of Robotics).
   Google Scholar
• Sharp RS, Casanova D, Symonds P. A mathematical model for driver steering control, with design, tuning and performance results. Veh Syst Dyn. 2000;33:289–326. doi: 10.1076/0042-3114(200005)33:5;1-Q;FT289
   Web of Science ®Google Scholar
• de Boor C. A practical guide to splines. Revised ed. New York (NY): Springer; 2001.
   Google Scholar
• Brandt C, Seidel HP, Hildebrandt K. Optimal spline approximation via L0-Minimization. In: Comput graph forum. 2015. p. 617–626.
   Google Scholar
• Goldenthal R, Bercovier M. Spline curve approximation and design by optimal control over the knots. Computing. 2004;72:53–64. doi: 10.1007/s00607-003-0046-y
   Web of Science ®Google Scholar
• Kang H, Chen F, Li Y, et al. Knot calculation for spline fitting via sparse optimization. Computer-Aided Design. 2015;58:179–188. doi: 10.1016/j.cad.2014.08.022
   Web of Science ®Google Scholar
• Van Loock W, Pipeleers G, De Schutter J, et al. A convex optimization approach to curve fitting with B-splines. IFAC Proc. 2011. Vol. 44, p. 2290–2295.
   Google Scholar
• Suchomski P. Method of optimal variable-knot spline interpolation in the L2 discrete norm. Int J Syst Sci. 1991;22:2263–2274. doi: 10.1080/00207729108910788
   Web of Science ®Google Scholar
• Perantoni G, Limebeer DJN. Optimal control of a formula one car on a three-Dimensional track– part 1: track modeling and identification. J Dyn Syst Meas Control. 2015;137:051019. doi: 10.1115/1.4028253
   Web of Science ®Google Scholar
• Bezanson J, Edelman A, Karpinski S, et al. Julia: a fresh approach to numerical computing. SIAM Rev. 2017;59:65–98. doi: 10.1137/141000671
   Web of Science ®Google Scholar
• MATLAB Mathematics documentation. [cited 2019 Nov 29]. Available from: https://de.mathworks.com/help/pdf_doc/matlab/math.pdf
   Google Scholar
• Reichensdoerfer E, Odenthal D, Wollherr D. On the stability of nonlinear wheel- slip zero dynamics in traction control systems. IEEE Trans Control Syst Technol. 2018;28:489–504. doi: 10.1109/TCST.2018.2880932
   Web of Science ®Google Scholar
• Pacejka HB. Tyre and vehicle dynamics. Oxford: Butterworth-Heinemann; 2006.
   Google Scholar
• Schramm D, Hiller M, Bardini R. Vehicle dynamics - modeling and simulation. Berlin, Heidelberg: Springer; 2014.
   Google Scholar
• Smakman HT. Functional integration of slip control with active suspension for improved lateral vehicle dynamics [PhD dissertation]. Herbert Utz Verlag; 2000.
   Google Scholar
• Revels J, Lubin M, Papamarkou T. Forward-mode automatic differentiation in Julia. arXiv:1607.07892 [cs.MS]. 2016.
   Google Scholar
• Nocedal J, Wright SJ. Numerical optimization. New York (NY): Springer; 2006.
   Google Scholar
• Do M, do Rosario de Pinho M, Domini IL, et al. On free time optimal control problems. Proc. of the 9th Brazilian Conf. on Dyn. Control and their Applic. 2019. p. 41–50.
   Google Scholar
• Grote K-H, Antonsson EK. Springer handbook of mechanical engineering. New York (NY): Springer; 2009.
   Google Scholar
• Gillespie TD. Fundamentals of vehicle dynamics. Warrendale (PA): SAE International; 1992.
   Google Scholar
• Piyabongkarn D, Grogg J, Yuan Q, et al. Dynamic modeling of torque-biasing devices for vehicle yaw control. SAE Automotive Dynamics; 2006.
   Google Scholar
• Rucco A, Notarstefano G, Hauser J. An efficient minimum-time trajectory generation strategy for two-track car vehicles. IEEE Trans Control Syst Technol. 2015;23:1505–1519. doi: 10.1109/TCST.2014.2377777
   Web of Science ®Google Scholar
• Limebeer DJN, Perantoni G. Optimal control of a formula one car on a three-dimensional track- part 2: optimal control. J Dyn Syst Meas Control. 2015;137. doi: 10.1115/1.4029466
   PubMed Web of Science ®Google Scholar