Automatic Adaptive Control of the Vehicle Trailer when Reversing

Authors: Kruglov S.P., Kovyrshin S.V. Published: 26.12.2021
Published in issue: #4(137)/2021  
DOI: 10.18698/0236-3933-2021-4-75-92

Category: Informatics, Computer Engineering and Control | Chapter: System Analysis, Control, and Information Processing  
Keywords: driver assistance system for a vehicle with a trailer, adaptive control system, current identification algorithm, uncontrolled external distur-bances, reference model, trailer jackknifing angle

The paper considers the problem of constructing a driver assistance system for a car with a trailer when reversing, functioning under apriori uncertainty of parameters of the controlled object car-trailer and uncontrollable disturbances. The mathematical model of the controlled object car-trailer and the basic relations, necessary for the synthesis of the control law are substantiated. Stability conditions of motion taking into account the notions of short and long trailer and the influence of disturbances are evaluated. The relative angular speed of the trailer, i.e., the angular speed of the trailer divided by the speed of the vehicle, is used as the controlled variable. An adaptive control law on the deviation of the the vehicle steered wheels to achieve the value of the controlled variable set by the driver using an implicit reference model is formed. Apriori uncertainty is eliminated by approximate estimates of trailer length and current parametric identification of the control object mathematical model. The current estimates delivered by the identifier are immediately used to synthesize the control law. The rationale for the operation of the adaptive control system is based on simplified adaptability conditions. The synthesized control law is aimed at preventing from reaching the folding angle with a short trailer and limiting the coupling angle with a long trailer. Automatic formation of warning signals, in particular about trailer folding, is proposed, and model examples showing efficiency of the proposed control system are given


[1] Bin Y., Shim T., Feng N., et al. Path tracking control for backing-up tractor-trailer system via model predictive control. Proc. CCDC, 2012, pp. 198--203. DOI: https://doi.org/10.1109/CCDC.2012.6242930

[2] Werling M., Reinish P., Heidingsfeld M., et al. Reversing the general one-trailer system: asymptotic curvature stabilization and path tracking. IEEE Trans. Intell. Transp. Syst., 2014, vol. 15, no. 2, pp. 627--636. DOI: https://doi.org/10.1109/TITS.2013.2285602

[3] Lavoie E.M., Trombley R.A., Nave C., et al. Trailer backup assist system. Patent US 9248858. Appl. 22.10.2013, publ. 02.02.2016.

[4] Josef V. Trailer backing-up assistant using ultrasound sensors based control units to safely back-up the car with trailer. Proc. 17th Int. Conf. on Mechatronics --- Mechatronika (ME). Prague, 2016, pp. 1--6.

[5] Pilutti T.E., Trombley R.A., Hafner M., et al. Control for trailer backup assist system. Patent US 9493187. Appl. 15.11.2016, publ. 18.04.2018.

[6] Hafner M., Pilutti T. Control for automated trailer backup. SAE Tech. Paper, 2017, no. 2017-01-0040. DOI: https://doi.org/10.4271/2017-01-0040

[7] Lavoie E.M., Kyrtsos C. Trailer curvature control with adaptive trailer length estimation. Patent US 9623904. Appl. 12.01.2015, publ. 18.04.2017.

[8] Kruglov S.P., Kovyrshin S.V., Shornikov K.A. Adaptivnaya sistema pomoshchi pri dvizhenii zadnim khodom avtomobilya s pritsepom [Adaptive assistance system when reversing vehicle with trailer]. Patent RU 2702199. Appl. 12.03.2018, publ. 04.10.2019 (in Russ.).

[9] Kratkiy avtomobil’nyy spravochnik NIIAT. T. 2, 4 [NIIAT short car guide. Vol. 2, 4]. Moscow, Transport Publ., 2004.

[10] Litvinov A.S., Farobin Ya.E. Avtomobil’. Teoriya ekspluatatsionnykh svoystv [Automobile. Theory of operational properties]. Moscow, Mashinostroenie Publ., 1989.

[11] Bronshteyn I.N., Semendyaev K.A. Spravochnik po matematike dlya inzhenerov i uchashchikhsya vtuzov [Mathematics handbook for engineers and students of technical colleges]. Moscow, Nauka Publ., 1986.

[12] Ljung L. System identification. Theory for the user. ‎ New Jersey, Prentice Hall Englewood Cliffs, 1987.

[13] Kruglov S.P. Convergence of the residual identification error in the control system with parametrical adaptation. Informatsionnye tekhnologii i matematicheskoe modelirovanie v upravlenii slozhnymi sistemami [Information Technology and Mathematical Modeling in The Management of Complex Systems], 2019, no. 1 (in Russ.). Available at: https://ismm.irgups.ru/en/node/143

[14] Kruglov S.P. Usloviya adaptiruemosti sistem upravleniya s identifikatorom i etalonom. Saarbucken, LAMBERT Academic Publ., 2012.

[15] Денисенко В.В. Компьютерное управление технологическим процессом, экспериментом, оборудованием. М., Горячая линия--Телеком, 2009.