Longitudinal Modeling of a Road Vehicle: 4-Wheel Traction
(1) Calequela J. T. Manuel Mail (Federal University of Technology - Paraná, Brazil)
(2) Max M. D. Santos Mail (Federal University of Technology - Paraná, Brazil)
(3) Giane G. Lenzi Mail (Federal University of Technology - Paraná, Brazil)
(4) * Angelo M. Tusset Mail (Federal University of Technology-Paraná (UTFPR), Brazil)
*corresponding author

Abstract


This paper presents the longitudinal modeling of a 4-wheel traction vehicle represented in a block diagram using Matlab®/Simulink® software. The proposed modeling is suitable to be implemented in automatic parallel, oblique, or perpendicular parking systems considering speed cases between 5 km/h and 30 km/h. For the computational simulations, it was considered that the vehicle starts at rest and goes up a referenced or determined slope in degrees (°), with a sufficient rear reaction force to allow the vehicle to move until the engine produces sufficient torque. For the model of the tire variant, the magic formula (characterized by the sum of five vectors about an axis) was used. Three input signals were considered, slope, wind, and accelerator variation were considered in numerical simulations. The output signals are rear and normal front forces, vehicle speed, angular velocity, and engine acceleration. The longitudinal modeling proposed allows for easily reproducing the results and assigning new parameters to validate a Project, contributing positively both to the automotive industries and in innovation-based scientific research.

Keywords


Computational modeling; 4-Wheel traction; Longitudinal dynamics; Calibration parameters; Vehicular system; Engine performance

   

DOI

https://doi.org/10.31763/ijrcs.v2i2.698 		      

Article metrics

10.31763/ijrcs.v2i2.698 Abstract views : 1670 | PDF views : 493

   

Cite

How to cite item
   

Full Text

Download

References


[1] R. Anbazhagan, B. Satheesh, and K. Gopalakrishnan, “Mathematical modeling and simulation of modern cars in the role of stability analysis,” Indian Journal of Science and Technology, vol. 6, no. 5, pp. 4633-4641, 2013, http://dx.doi.org/10.17485/ijst/2013/v6isp5.9.

[2] H. P. Oliveira, A. J. Sousa, A. P. Moreira, P. J. Costa, and A. D. Rodi, “Modeling and assessing of omni-directional robots with three and four wheels,” Contemporary Robotics: Challenges and Solutions, pp. 109-138, 2009, http://dx.doi.org/10.5772/7796.

[3] Y. J. Chen, Q. S. Lei, X. Zhang, G. H. Zheng, and Y. F. Zhang, “Suspension System Dynamics Modeling and Simulation Analysis,” DEStech Transactions on Engineering and Technology Research (icamm), 2017, http://dx.doi.org/10.12783/dtetr/icamm2016/7397.

[4] J. Kong, M. Pfeiffer, G. Schildbach, and F. Borrelli, “Kinematic and dynamic vehicle models for autonomous driving control design,” IEEE Intelligent Vehicles Symposium (IV), pp. 1094-1099, 2015, https://doi.org/10.1109/IVS.2015.7225830.

[5] A. Elhefnawy, H. Ragheb, A. M. Sharaf, and S. Hegazy, “On the control strategies for vehicle stability enhancement,” International Journal of Heavy Vehicle Systems, vol. 27, no. 5, pp. 622-647, 2020, https://doi.org/10.1504/IJHVS.2020.111263.

[6] H. Haiyan, and H. Qiang, “Three-dimensional modeling and dynamic analysis of four-wheel-steering vehicles,” Acta Mechanica Sinica, vol. 19, no. 1, pp. 79-88, 2003, https://doi.org/10.1007/BF02487456.

[7] A. Chebly, R. Talj, and A. Charara, “Coupled longitudinal and lateral control for an autonomous vehicle dynamics modeled using a robotics formalism,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 12526-12532, 2017, https://doi.org/10.1016/j.ifacol.2017.08.2190.

[8] Z. Alqarni, “Improved Control Strategy for 4 WD Electric Vehicle Using Direct Torque Control Technique with Space Vector Modulation,” 2022 IEEE 12th Annual Computing and Communication Workshop and Conference (CCWC), pp. 0816-0822, 2022, https://doi.org/10.1109/CCWC54503.2022.9720858.

[9] P. Wrzecioniarz, W. Ambroszko, and A. Pindel, “Limitations of vehicle movement resistances: aerodynamic resistance,” AUTOBUSY–Technika, Eksploatacja, Systemy Transportowe, vol. 19, no. 12, pp. 252-255, 2018, https://doi.org/10.24136/atest.2018.393.

[10] T. H. Hsu, J. F. Liu, P. N. Yu, W. S. Lee, and J. S. Hsu, “Development of an automatic parking system for vehicle,” IEEE Vehicle Power and Propulsion Conference, pp. 1-6, 2008, https://doi.org/10.1109/VPPC.2008.4677655.

[11] A. Gupta, R. Divekar, and M. Agrawal, “Autonomous parallel parking system for Ackerman steering four wheelers,” IEEE International Conference on Computational Intelligence and Computing Research, pp. 1-6, 2010, https://doi.org/10.1109/ICCIC.2010.5705869.

[12] C. J. T. Manuel, “Design and development of algorithms and control strategies for automatic parking systems: advanced driver assistance system,” Master's thesis, Universidade Tecnológica Federal do Paraná, 2020, http://repositorio.utfpr.edu.br/jspui/handle/1/24096.

[13] J. Huang, Y. Chen, X. Peng, L. Hu, and D. Cao, “Study on the driving style adaptive vehicle longitudinal control strategy,” IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 4, pp. 1107-1115, 2020, https://doi.org/10.1109/JAS.2020.1003261.

[14] T. Chen, H. Huang, Q. Li, Z. Mo, Z. Feng, and J. Huang, “Drive Control Strategy Design for FSEC Racing Car,” Proceedings of China SAE Congress 2020: Selected Papers. Springer, Singapore, pp. 255-276, 2022, https://doi.org/10.1007/978-981-16-2090-4_15.

[15] J. Antunes, A. Antunes, P. Outeiro, C. Cardeira, and P. Oliveira, “Testing of a torque vectoring controller for a Formula Student prototype,” Robotics and Autonomous Systems, vol. 113, pp. 56-62, 2019, https://doi.org/10.1016/j.robot.2018.12.010.

[16] A. Buyval, A. Gabdullin, A. Klimchik, “Model Predictive Path Integral Control for Car Driving with Dynamic Cost Map,” Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics, vol. 1, pp. 248-254, 2018, https://doi.org/10.5220/0006901702480254.

[17] B. M. Notaroš, R. McCullough, S. B. Manić, and A. A. Maciejewski, “Computer‐assisted learning of electromagnetics through MATLAB programming of electromagnetic fields in the creativity thread of an integrated approach to electrical engineering education,” Computer Applications in Engineering Education, v. 27, n. 2, p. 271-287, 2019, https://doi.org/10.1002/cae.22073.

[18] R. Attia, R. Orjuela, and M. Basset, “Combined longitudinal and lateral control for automated vehicle guidance,” Vehicle System Dynamics, vol. 52, no. 2, pp. 261-279, 2014, https://doi.org/10.1080/00423114.2013.874563.

[19] Y. Chen, S. Chen, T. Zhang, S. Zhang, and N. Zheng, “Autonomous vehicle testing and validation platform: Integrated simulation system with hardware in the loop,” 2018 IEEE Intelligent Vehicles Symposium (IV), pp. 949-956, 2018, https://doi.org/10.1109/IVS.2018.8500461.

[20] B. M. Nguyen, H. V. Nguyen, M. Ta-Cao, and M. Kawanishi, “Longitudinal Modelling and Control of In-Wheel-Motor Electric Vehicles as Multi-Agent Systems,” Energies, vol. 13, no. 20, pp. 5437, 2020, https://doi.org/10.3390/en13205437.

[21] G. Rill and A. A. Castro, “Road Vehicle Dynamics: Fundamentals and Modeling with MATLAB® (2nd ed),” CRC Press, 2020, https://doi.org/10.1201/9780429244476.

[22] Mathworks, “Vehicle with four-wheel drive, 2020, https://www.mathworks.com/help/physmod/sdl/ug/vehicle-with-four-wheel-drive.html.

[23] A. Szántó, and G. A. Szíki, “Review of Modern Vehicle Powertrains and Their Modelling and Simulation in MATLAB/Simulink,” International Journal of Engineering and Management Sciences, vol. 5, no. 2, pp. 232-250, 2020, https://doi.org/10.21791/IJEMS.2020.2.29.

[24] J. Tarnawski, and T. Karla, “Real-time simulation in non real-time environment,” 21st International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 577-582, 2016, https://doi.org/10.1109/MMAR.2016.7575200.

[25] S. Lekshmi, and P. S. Lal Priya, “Mathematical modeling of Electric vehicles-A survey,” Control Engineering Practice, vol. 92, pp. 104138, 2019, https://doi.org/10.1016/j.conengprac.2019.104138.

[26] S. Sundar, T. Sudarsanan, and R. Krishnan, “Review of Design and Fabrication of four wheel Steering system,” International Journal of Recent Trends in Engineering and Research (IJRTER), vol. 4, no. 10, pp. 1034-1049, 2018, https://doi.org/10.23883/IJRTER.2018.4386.3THDB.

[27] C. Habermehl, G. Jacobs, and S. Neumann, “A modeling method for gear transmission efficiency in transient operating conditions,” Mechanism and Machine Theory, vol. 153, pp. 103996, 2020, https://doi.org/10.1016/j.mechmachtheory.2020.103996.

[28] H. Dugoff, P. S. Fancher, and L. Segel, “An analysis of tire traction properties and their influence on vehicle dynamic performance,” SAE transactions, vol. 79, pp. 1219-1243, 1970, https://doi.org/10.4271/700377.

[29] T. Chen, X. Xu, L. Chen, H. Jiang, Y. Cai, and Y. Li, “Estimation of longitudinal force, lateral vehicle speed and yaw rate for four-wheel independent driven electric vehicles,” Mechanical Systems and Signal Processing, vol. 101, pp. 377-388, 2018, https://doi.org/10.1016/j.ymssp.2017.08.041.

[30] S. Yang, Y. Lu, and S. Li, “An overview on vehicle dynamics,” International Journal of Dynamics and Control, vol. 1, no. 4, pp. 385-395, 2013, https://doi.org/10.1007/s40435-013-0032-y.

[31] M. Viehweger, C. Vaseur, S. van Aalst, M. Acosta, E. Regolin, A. Alatorre, W. Desmet, F. Naets, V. Ivanov, A. Ferrara, and A. Victorino, “Vehicle state and tyre force estimation: demonstrations and guidelines,” Vehicle system dynamics, vol. 59, no. 5, pp. 675-702, 2021, https://doi.org/10.1080/00423114.2020.1714672.

[32] J. Zhang, Y. Yang, M. Hu, Z. Yang, and C. Fu, “Longitudinal-Vertical Comprehensive Control for Four-Wheel Drive Pure Electric Vehicle Considering Energy Recovery and Ride Comfort,” Energy, vol. 236, pp. 121417, 2021, https://doi.org/10.1016/j.energy.2021.121417.

[33] J. Woo, J. Park, C. Yu, and N. Kim, “Dynamic model identification of unmanned surface vehicles using deep learning network,” Applied Ocean Research, vol. 78, pp. 123-133, 2018, https://doi.org/10.1016/j.apor.2018.06.011.

[34] A. O. Kiyakli, and H. Solmaz, “Modeling of an electric vehicle with MATLAB/Simulink,” International Journal of automotive science and technology, vol. 2, no. 4, pp. 9-15, 2018, https://doi.org/10.30939/ijastech..475477.

[35] D. W. Karmiadji, M. Gozali, M. Setiyo, T. Raja, and T. A. Purnomo, “Comprehensive Analysis of Minibuses Gravity Center: A Post-Production Review for Car Body Industry,” Mechanical Engineering for Society and Industry, vol. 1, no. 1, pp. 31-40, 2021, https://doi.org/10.31603/mesi.5250.

[36] G. Park, and S. B. Choi, “An Integrated Observer for Real-Time Estimation of Vehicle Center of Gravity Height,” IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 9, pp. 5660-5671, 2020, https://doi.org/10.1109/TITS.2020.2988508.

[37] J. R. Piechna, K. Kurec, J. Broniszewski, M. Remer, A. Piechna, K. Kamieniecki, K, and P. Bibik, “Influence of the Car Movable Aerodynamic Elements on Fast Road Car Cornering,” Energies, vol. 15, no. 3, pp. 689, 2022, https://doi.org/10.3390/en15030689.

[38] F. J. Morales, and F. G. Benitez, “Considerations on the operation of inertial continuous variable transmissions,” Mechanism and Machine Theory, vol. 144, pp. 103672, 2020, https://doi.org/10.1016/j.mechmachtheory.2019.103672.

[39] T. D. Gillespie, “Fundamentals of vehicle dynamics,” SAE Technical Paper, vol. 114, 1992, https://www.sae.org/publications/technical-papers/content/R-114/.

[40] Q. Wu, Y. Sun, M. Spiryagin, and C. Cole, “Railway track longitudinal force model,” Vehicle System Dynamics, vol. 59, no. 1, pp. 155-170, 2021, https://doi.org/10.1080/00423114.2019.1673445.

[41] İ. C. Güleryüz, and Ö. Başer, “Modelling the longitudinal braking dynamics for heavy-duty vehicles,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 235, no. (10-11), pp. 2802-2817, 2021, https://doi.org/10.1177/09544070211004508.

[42] P. Shakouri, A. Ordys, M. Askari, and D. S. Laila, “Longitudinal vehicle dynamics using Simulink/Matlab,” UKACC International Conference on Control, pp. 1-6, 2010, https://doi.org/10.1049/ic.2010.0410.

[43] M. P. Bauskar, D. Y. Dhande, S. Vadgeri, and S. R. Patil, “Study of aerodynamic drag of sports utility vehicle by experimental and numerical method,” Materials Today: Proceedings, vol. 16, pp. 750-757, 2019, https://doi.org/10.1016/j.matpr.2019.05.155.

[44] M. Amodeo, A. Ferrara, R. Terzaghi, and C. Vecchio, “Wheel slip control via second-order sliding-mode generation,” IEEE Transactions on Intelligent Transportation Systems, vol. 11, no. 1, pp. 122-131, 2009, https://doi.org/10.1109/TITS.2009.2035438.

[45] U. Kiencke, “Realtime estimation of adhesion characteristic between tyres and road,” IFAC Proceedings, vol. 26, no. 2, pp. 15-18, 1993, https://doi.org/10.1016/S1474-6670(17)48673-3.

[46] A. Genovese, and F. Timpone, “Tyre Mechanics and Thermal Effects on Tyre Behaviour,” B. Lenzo (eds) Vehicle Dynamics, CISM International Centre for Mechanical Sciences, Springer, Cham, vol. 603, pp. 139-192, 2022, https://doi.org/10.1007/978-3-030-75884-4_3.

[47] C. Liu, J. Zhou, A. Gerhard, J. Kubenz, and G. Prokop, “Characterization of the Vehicle Roll Movement with the Dynamic Chassis Simulator,” Vehicle and Automotive Engineering. Springer, Cham, pp. 129-141, 2018, https://doi.org/10.1007/978-3-319-75677-6_11.

[48] B. M. Nguyen, S. Hara, H. Fujimoto, and Y. Hori, “Slip control for IWM vehicles based on hierarchical LQR,” Control Engineering Practice, vol. 93, pp. 104179, 2019, https://doi.org/10.1016/j.conengprac.2019.104179.

[49] K. El Majdoub, F. Giri, H. Ouadi, L. Dugard, and F. Z. Chaoui, “Vehicle longitudinal motion modeling for nonlinear control,” Control Engineering Practice, vol. 20, no. 1, pp. 69-81, 2012, https://doi.org/10.1016/j.conengprac.2011.09.005.

[50] E. Esmailzadeh, G. R. Vossoughi, and A. Goodarzi, “Dynamic modeling and analysis of a four motorized wheels electric vehicle,” Vehicle System Dynamics, vol. 35, no. 3, pp. 163-194, 2001, https://doi.org/10.1076/vesd.35.3.163.2047.

[51] H. Zhou, F. Jia, H. Jing, Z. Liu, and L. Güvenç, “Coordinated longitudinal and lateral motion control for four wheel independent motor-drive electric vehicle,” IEEE transactions on Vehicular Technology, vol. 67, no. 5, pp. 3782-3790, 2018, https://doi.org/10.1109/TVT.2018.2816936.

[52] K. Miura, S. Tokunaga, N. Ota, Y. Tange, and T. Azumi, “Autoware toolbox: Matlab/simulink benchmark suite for ROS-based self-driving software platform,” Proceedings of the 30th International Workshop on Rapid System Prototyping (RSP'19), pp. 8-14, 2019, https://doi.org/10.1145/3339985.3358494.

[53] N. Deo, A. Rangesh and M. M. Trivedi, “How would surround vehicles move? a unified framework for maneuver classification and motion prediction,” IEEE Transactions on Intelligent Vehicles, vol. 3, no. 2, pp. 129-140, 2018, https://doi.org/10.1109/TIV.2018.2804159.

[54] Z. Zhang, C. Wang, W. Zhao, and J. Feng, “Longitudinal and lateral collision avoidance control strategy for intelligent vehicles,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 236, no. (2-3) pp. 268–286, 2022, https://doi.org/10.1177/09544070211024048.

[55] T. Yang, Z. Bai, Z. Li, N. Feng, and L. Chen, “Intelligent Vehicle Lateral Control Method Based on Feedforward + Predictive LQR Algorithm,” Actuators, vol. 10, no. 9, p. 228, Sep. 2021, http://dx.doi.org/10.3390/act10090228.

[56] D. Schramm, M. Hiller, and R. Bardini, “Vehicle Dynamics: Modeling and Simulation,” Springer, Berlin, Heidelberg, 2018, https://doi.org/10.1007/978-3-662-54483-9.

[57] M. Tomasikova, D. Sojcak, A. Nieoczym, and F. Brumercik, “Experimental data in vehicle modeling,” LOGI–Scientific Journal on Transport and Logistics, vol. 8, no. 1, pp. 82-87, 2017, https://doi.org/10.1515/logi-2017-0010.

[58] M. Yue, X. Wei, and Z. Li Z, “Adaptive sliding-mode control for two-wheeled inverted pendulum vehicle based on zero-dynamics theory,” Nonlinear Dynamics, vol. 76, no 1, pp. 459-471, 2014, https://doi.org/10.1007/s11071-013-1139-6.

[59] Renault Captur, “Manual of proprietary,” 2020, https://www.renault.com.br/manuais/captur.html.

[60] C. J. T. Manuel, M. M. D. Santos, A. M. Tusset, “Mathematical modeling attributed to kinematics and dynamics of a vehicle with 4-wheels,” The European Physical Journal Special Topics, vol. 230, no. 18, pp. 3663-3672, 2021, https://doi.org/10.1140/epjs/s11734-021-00238-2.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Calequela J. T. Manuel, Max M. D. Santos, Giane G. Lenzi, Angelo Marcelo Tusset

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 

About the JournalJournal PoliciesAuthor Information

International Journal of Robotics and Control Systems
e-ISSN: 2775-2658
Website: https://pubs2.ascee.org/index.php/IJRCS
Email: ijrcs@ascee.org
Organized by: Association for Scientific Computing Electronics and Engineering (ASCEE), Peneliti Teknologi Teknik Indonesia, Department of Electrical Engineering, Universitas Ahmad Dahlan and Kuliah Teknik Elektro
Published by: Association for Scientific Computing Electronics and Engineering (ASCEE)
Office: Jalan Janti, Karangjambe 130B, Banguntapan, Bantul, Daerah Istimewa Yogyakarta, Indonesia