Abstract
In this paper, a new optimization method for the trajectory optimization problem is presented. This new method allows to predict racing lines described by cubic splines (problems solved in most cases by stochastic methods) in times like deterministic methods. The proposed Double Gradient Method (DGM) is not affected by the dimensionality of the problem. Comparison of the results with data collected from professional drivers has shown that the DGM is reliable for lap time simulations with race line optimization. It can help drivers find the fastest racing line, be used for embedded algorithm development or for autonomous vehicle competitions.
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References
Gadola, M., Cambiaghi, D., Manzo, L., Vetturi, D.: “A Tool for Lap Time Simulation,” SAE Technical Paper 962529, Dezembro 1996
Koutrik, S.V.: Optimal control for race car minimum time maneuvering. Maritime and Materials Engineering—Delft University of Technology, Delft, Faculty of Mechanical (2015)
Casanova, D.: On minimum time vehicle manoeuvring: the theoretical optimal lap. Cranfield University, School of Mechanical Engineering (2000)
Kelly, D.P.: Lap time simulation with transient vehicle and tyre dynamics. Cranfield University School of Engineering, Automotive Studies Group (2008)
Biral, F., Lot, R.: A Curvilinear Abscissa Approach for the Lap Time Optimization of Racing Vehicles, Cape Town (2014)
Bianco, N.D., Lot, R., Gadola, M.: Minimum time optimal control simulation of a GP2 Race Car. J. Automob. Eng. 232(9), 1180–1195 (2018)
Herrmann, T., Passigato, F., Betz, J., Lienkamp, M.: Minimum Race-Time Planning-Strategy for an Autonomous Electric Racecar (2020). arXiv:2005.07127
Lovato, S., Massaro, M.: A three-dimensional free-trajectory quasi-steady-state optimal-control method for minimum-lap-time of race vehicles. Veh. Syst. Dyn. (2021). https://doi.org/10.1080/00423114.2021.1878242
Bastos, E.A.: Otimização de Seções Retangulares de Concreto Armado Submetidas à Flexo-Compressão Oblíqua Utilizando Algoritmos Genéticos. Universidade Federal do Rio de Janeiro, Rio de Janeiro (2004)
Chaves, A.A.: Heurísticas Híbridas com Busca Através de Agrupamentos para o Problema do Caxeiro Viajante com Coleta de Prêmios. Instituto Nacional de Pesquisas Espaciais, São José dos Campos (2005)
Gross, J.C.: Derivative-Free Methods for High-Dimensional Optimization with Application to Centrifugal Pump Design. University of Cambridge, Cambridge (2021)
Lenzo, B., ROSSI, V.: A simple mono-dimensional approach for lap time optimisation. Appl. Sci. 1498(10) (2020)
Jain, A., Morari, M.: Computing the Racing Line Using Bayesian Optimization, 12 Feb. 2020
Srinivasan, S., Sa, I., Zyner, A., Reijgwart, V., Valls, M.I., Siegwart, R.: End-to-End velocity estimation for autonomous. IEEE Robot. Autom. Lett. 5(4), 6869–6875 (2020)
Kapania, N.R., Subosits, J., Gerdes, J.C.: A sequential two-step algorithm for fast generation of vehicle racing trajectories, ASME. J. Dyn. Sys. Meas. Control 138(9) (2016)
Garlick, S., Bradley, A.: Real-Time Optimal Trajectory Planning for Autonomous Vehicles and Lap Time Simulation Using Machine Learning, 18 Mar. 2021
Konar, A.: Artificial Intelligence and Soft Computing: Behavioral and Cognitive Modeling of the Human Brain. CRC Press, Boca Raton (1999)
Filho, J.L.R., Treleaven, P.C., Alippi, C.: Genetic algorithm programming environments. IEEE Computer Society Press, pp. 28–43 (1994)
Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)
Mór, F.N.: An evolutionary approach for the task mapping problem. Pontifícia Universidade Católica do Rio Grande do Sul, Porto Alegre (2016)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)
Spendley, W., Hext, G.R., Himsworth, F.R.: Sequential application of simplex designs in optimisation and evolutionary operation. Technometrics 4, 441 (1962)
Gao, F., Han, L.: Implementing the Nelder-Mead simplex algorithm with adaptive parameters. Comput. Optim. Appl. 51, 259–277 (2012)
Ravindran, A., Ragsdell, K.M., Reklaitis, G.V.: Engineering Optimization: Methods and Applications, 2ª Wiley, Hoboken, New Jersey (2006)
Giuliani, C.M.: Estratégias de Otimização não Diferenciável Aplicadas à Maximização da Produção de Campos de Petróleo. Universidade Federal de Santa Catarina, Florianópolis (2013)
Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. MPS/SIAM, Philadelphia (2000)
Yuan, Y.-X.: Recent advances in trust region algorithms. Math. Program. 151, 249–281 (2015)
Aflak, O.: Bézier Interpolation—Create smooth shapes using Bézier curves,” 9 Maio (2020)
Farin, G.E.: Curves and Surfaces for Computer-Aided Geometric Design—A Practical Guide, 3rd ed. Arizona: Academic Press Inc. (2014)
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The Authors would like to thank Bahia Research Foundation (FAPESB) for the financial support (grant 0342/2021).
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Macêdo, A.R., Youssef, E.S.E., da Costa, M.V.A. (2024). Double Gradient Method: A New Optimization Method for the Trajectory Optimization Problem. In: Youssef, E.S.E., Tokhi, M.O., Silva, M.F., Rincon, L.M. (eds) Synergetic Cooperation between Robots and Humans. CLAWAR 2023. Lecture Notes in Networks and Systems, vol 811. Springer, Cham. https://doi.org/10.1007/978-3-031-47272-5_14
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