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Constraint optimization and key factor analysis based vehicle emergency braking strategy generator
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  • Published: 27 February 2026

Constraint optimization and key factor analysis based vehicle emergency braking strategy generator

  • Rui Xu1,
  • Shijie Xu1,
  • Peng Jiang1,
  • Xiangfen Zhang1,
  • Feiniu Yuan1,
  • Xiqiang Guan1,
  • Ziyou Chen2,
  • Ruifeng Zhai1,
  • Yixuan Wang1,
  • Tianyi Lu1 &
  • …
  • Wenhao Lu3 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Energy science and technology
  • Engineering
  • Mathematics and computing

Abstract

Enhancing vehicle emergency braking performance is crucial for vehicular safety and reliability. We have observed that the traditional vehicle dynamics based model predictive control (MPC) algorithm which is used to produce emergency braking strategy fails to achieve the minimization of emergency braking distance. To address this issue, this article employed a simulation based approach to improve emergency braking performance via machine learning based algorithms. We design a data optimization model which optimizes the longitudinal forces and slip ratios of the four wheels based on back-propagation neural network (BPNN) and constraint optimization algorithm to reduce emergency braking distance. In addition, a Balltree nearest neighbor search based generator is proposed to produce superior emergency braking strategies for real-time purpose. The experimental results demonstrate that the emergency braking strategy which we optimized achieves an average enhancement of 13% in emergency braking performance compared to the traditional MPC algorithm. Unlike other machine learning based algorithms that have a delay of over 0.01 s, the proposed generator has an execution time of 0.0008 s, meeting the delay requirements under emergency braking conditions.

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Data availability

The data that support the findings of this study are available from the corresponding author Zhang upon reasonable request.

References

  1. Lutanto, A., Fajri, A., Nugroho, K. C. & Falah, F. Advancements in automotive braking technology for enhanced safety: A review. MIRAE 1, 6–21. https://doi.org/10.70935/6n21wx31 (2025).

    Google Scholar 

  2. Sokolovskij, E. & Žuraulis, V. Advances in vehicle dynamics and road safety: Technologies, simulations, and applications. Appl. Sci. 14, 3735. https://doi.org/10.3390/app14093735 (2024).

    Google Scholar 

  3. Furlan, A. D. et al. Advanced vehicle technologies and road safety: a scoping review of the evidence. Accid. Anal. Prev. 147, 105741. https://doi.org/10.1016/j.aap.2020.105741 (2020).

    Google Scholar 

  4. Zhao, J., Yan, X., Zhou, Z. & Zhang, Z. Rule-adaptive lane-changing trajectory planning method for autonomous vehicles driven by dynamic risk information. Sci. Rep. 15, 31514. https://doi.org/10.1038/s41598-025-15382-1 (2025).

    Google Scholar 

  5. Meléndez-Useros, M., Jiménez-Salas, M. & Viadero-Monasterio, F. López Boada, B. L. Tire slip H∞ control for optimal braking depending on road condition. Sensors 23, 1417. https://doi.org/10.3390/s23031417 (2023).

    Google Scholar 

  6. Ricciardi, V. et al. A novel semi-empirical dynamic brake model for automotive applications. Tribol Int. 146, 106223. https://doi.org/10.1016/j.triboint.2020.106223 (2020).

    Google Scholar 

  7. El-Gindy, M. & El-Sayegh, Z. Road Vehicle Braking Performance. In: Road and Off-Road Vehicle Dynamics. Springer Cham https://doi.org/10.1007/978-3-031-36216-3_7 (2023).

    Google Scholar 

  8. Qiu, C. et al. Machine vision-based autonomous road hazard avoidance system for self-driving vehicles. Sci. Rep. 14, 12178. https://doi.org/10.1038/s41598-024-62629-4 (2024).

    Google Scholar 

  9. Henning-Günther, T. et al. Verifying safety of safety-critical systems with rare events via optimistic optimization. IEEE Open. J. Intell. Transp. Syst. 6, 1569–1579. https://doi.org/10.1109/OJITS.2025.3638166 (2025).

    Google Scholar 

  10. Chae, H. et al. Autonomous braking system via deep reinforcement learning. Proc. IEEE Intell. Transp. Syst. Conf. 1–6 (2017).

  11. Hashemi, A., Orzechowski, G., Mikkola, A. & McPhee, J. Multibody dynamics and control using machine learning. Multibody Syst. Dyn. 58, 397–431. https://doi.org/10.1007/s11044-023-09884-x (2023).

    Google Scholar 

  12. Sun, Y., Shi, W., Huang, X., Zhou, S. & Niu, Z. Edge learning with timeliness constraints: Challenges and solutions. IEEE Commun. Mag. 58 (12), 27–33. https://doi.org/10.1109/MCOM.001.2000382 (2020).

    Google Scholar 

  13. Mirzaeinejad, H. & Mirzaei, M. A novel method for non-linear control of wheel slip in anti-lock braking systems. Control Eng. Pract. 18, 918–926. https://doi.org/10.1016/j.conengprac.2010.03.015 (2010).

    Google Scholar 

  14. Deng, G. & Li, D. Safety Distance Analysis of Automatic Emergency Braking System. In Selected Contributions of 2024 2nd International Conference on Electric Vehicle and Vehicle Engineering (eds Wong, P. K. & Xu, J.) Lecture Notes in Electrical Engineering, vol. 1424, 452–458Springer, Singapore, https://doi.org/10.1007/978-981-96-6827-4_47 (2025).

  15. Gounis, K. & Bassiliades, N. Intelligent momentary assisted control for autonomous emergency braking. Simul. Model. Pract. Theory. 115, 102450. https://doi.org/10.1016/j.simpat.2021.102450 (2022).

    Google Scholar 

  16. Zhang, R. & Pourkand, A. Emergency-braking Distance Prediction using Deep Learning. arXiv preprint arXiv 2112.01708 https://doi.org/10.48550/arXiv.2112.01708 (2021).

  17. Shewale, N. S. & Deivanathan, R. Modelling and simulation of anti-lock braking system. Inter. J. Eng. Tech. Res. 7(1) (2017).

  18. García, C. E., Prett, D. M. & Morari, M. Model predictive control: Theory and practice—a survey. Automatica 25, 335–348. https://doi.org/10.1016/0005-1098(89)90002-2 (1989).

    Google Scholar 

  19. Rumelhart, D., Hinton, G. & Williams, R. Learning representations by back-propagating errors. Nature 323, 533–536. https://doi.org/10.1038/323533a0 (1986).

    Google Scholar 

  20. Rakotondrasoa, H. M., Bucher, M. & Sinayskiy, I. Quantitative comparison of nearest neighbor search algorithms. arXiv preprint arXiv (2023).

  21. Parseh, M., Nybacka, M. & Asplund, F. Motion planning for autonomous vehicles with the inclusion of post-impact motions for minimising collision risk. Veh. Syst. Dyn. 61, 1707–1733. https://doi.org/10.1080/00423114.2022.2088396 (2023).

    Google Scholar 

  22. Qasem, G. A. A., Abdullah, M. F., Farid, M. & Bakhuraisa, Y. A. Enhancing anti-lock braking system performance using fuzzy logic control under variable friction conditions. Symmetry 17, 1692. https://doi.org/10.3390/sym17101692 (2025).

    Google Scholar 

  23. Labh, S. K., Khanal, R. & Dahal, C. Comparative analysis of performance of antilock braking system using PID and fuzzy controllers. OODBODHAN 8, 135–142. https://doi.org/10.3126/oodbodhan.v8i1.81260 (2025).

    Google Scholar 

  24. Zulhilmi, I. M., Peeie, M. H., Asyraf, S. M., Sollehudin, I. M. & Ishak, I. M. Experimental study on the effect of emergency braking without anti-lock braking system on vehicle dynamics behaviour. Int. J. Automot. Mech. Eng. 17, 7832–7841. https://doi.org/10.15282/ijame.17.2.2020.02.0583 (2020).

    Google Scholar 

  25. Wang, X., Li, W., Li, Z. & Li, L. Effect of braking torque on vehicle nonlinear dynamics. Meccanica 58, 1267–1289. https://doi.org/10.1007/s11012-023-01683-0 (2023).

    Google Scholar 

  26. Eberhart, M., Plöchl, M., Unterreiner, M. & Edelmann, J. Insights into stability and control of the powerslide motion with variable drive torque distribution applied to a driver assistance system. Veh. Syst. Dyn. 1–21. https://doi.org/10.1080/00423114.2025.2457433 (2025).

  27. Saraiev, O. & Gorb, Y. A mathematical model of the braking dynamics of a car. SAE Tech. Pap. https://doi.org/10.4271/2018-01-1893 (2018).

    Google Scholar 

  28. Rajesh, N., Zheng, Y. & Shyrokau, B. Comfort-oriented motion planning for automated vehicles using deep reinforcement learning. IEEE Open. J. Intell. Transp. Syst. 4, 348–359. https://doi.org/10.1109/OJITS.2023.3275275 (2023).

    Google Scholar 

  29. Lee, M. An analysis of the effects of artificial intelligence on electric vehicle technology innovation using patent data. World Pat. Inf. 63, 102002. https://doi.org/10.1016/j.wpi.2020.102002 (2020).

    Google Scholar 

  30. Stefanidou, A., Politi, E. & Dimitrakopoulos, G. Foundation models in autonomous driving: A review of current tasks and applications. IEEE Open. J. Intell. Transp. Syst. 6, 1522–1538. https://doi.org/10.1109/OJITS.2025.3633871 (2025).

    Google Scholar 

  31. Basso, F., Pezoa, R., Varas, M. & Villalobos, M. A deep learning approach for real-time crash prediction using vehicle-by-vehicle data. Accid. Anal. Prev. 162, 106409. https://doi.org/10.1016/j.aap.2021.106409 (2021).

    Google Scholar 

  32. Teng, X. et al. Time-to-collision estimation with autonomous emergency braking using multi-scale transformer network. IEEE Trans. Mob. Comput. 23, 14903–14917. https://doi.org/10.1109/TMC.2024.3454122 (2024).

    Google Scholar 

  33. Folkers, A., Rick, M. & Büskens, C. Controlling an autonomous vehicle with deep reinforcement learning. Proc. IEEE Intell. Veh. Symp. 2025-2031 https://doi.org/10.1109/IVS.2019.8814124 (2019).

  34. Chen, D., Gong, Y. & Yang, X. Advanced longitudinal control and collision avoidance for high-risk edge cases in autonomous driving. arXiv preprint (2025).

  35. Guerrero-Ibáñez, J., Zeadally, S. & Contreras-Castillo, J. Sensor technologies for intelligent transportation systems. Sensors 18, 1212. https://doi.org/10.3390/s18041212 (2018).

    Google Scholar 

  36. Chen, J., Xu, X. & Yang, J. Adaptive model predictive control for autonomous vehicle trajectory tracking. Vehicles 7, 114. https://doi.org/10.3390/vehicles7040114 (2025).

    Google Scholar 

  37. Kudarauskas, N. Analysis of emergency braking of a vehicle. Transport 22 (3), 154–159. https://doi.org/10.3846/16484142.2007.9638118 (2007).

    Google Scholar 

  38. Sun, W. & Wang, S. Research on lateral acceleration of lane changing. In Frontier Computing (eds Hung, J., Yen, N. & Hui, L.) Lecture Notes in Electrical Engineering, vol. 542, 950–960 Springer, Singapore, https://doi.org/10.1007/978-981-13-3648-5_120 (2019).

  39. Seo, M., Yoo, C., Park, S. S. & Nam, K. Development of wheel pressure control algorithm for electronic stability control (ESC) system of commercial trucks. Sensors 18, 2317. https://doi.org/10.3390/s18072317 (2018).

    Google Scholar 

  40. Han, K., Lee, B. & Choi, S. B. Development of an antilock brake system for electric vehicles without wheel slip and road friction information. IEEE Trans. Veh. Technol. 68, 5506–5517. https://doi.org/10.1109/TVT.2019.2911687 (2019).

    Google Scholar 

  41. Hotelling, H. Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24 (6), 417–441. https://doi.org/10.1037/h0071325 (1933).

    Google Scholar 

  42. Nair, V. & Hinton, G. E. Rectified Linear Units Improve Restricted Boltzmann Machines. Proc. 27th Int. Conf. Mach. Learn. 807–814. (2010).

  43. He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. Proc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR). 770–778. https://doi.org/10.1109/CVPR.2016.90 (2016).

  44. Solis, C. U., Clempner, J. B. & Poznyak, A. S. Continuous-time gradient-like descent algorithm for constrained convex unknown functions: Penalty method application. J. Comput. Appl. Math. 355, 268–282. https://doi.org/10.1016/j.cam.2019.01.023 (2019).

    Google Scholar 

  45. Ning, Z., Iradukunda, H. N., Zhang, Q. & Zhu, T. Benchmarking machine learning: how fast can your algorithms go? arXiv preprint arXiv 2101.03219 (2021).

  46. Pedregosa, F. et al. Nearest Neighbors — scikit-learn: Machine Learning in Python.Retrieved from https://scikit-learn.org/stable/modules/neighbors.html (2011).

Download references

Funding

This work was partially supported by the National Natural Science Foundation of China (62171285), Natural Science Foundation of Shanghai Municipality (20ZR1440500) and General Research Fund of Shanghai Normal University (KF2021100 and Sk201220).

Author information

Authors and Affiliations

  1. College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai, China

    Rui Xu, Shijie Xu, Peng Jiang, Xiangfen Zhang, Feiniu Yuan, Xiqiang Guan, Ruifeng Zhai, Yixuan Wang & Tianyi Lu

  2. King’s University College, University of Western Ontario, London, Canada

    Ziyou Chen

  3. Department of Electrical and Computer Engineering, University of Alberta, Alberta, Canada

    Wenhao Lu

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Contributions

Rui Xu, Shijie Xu contributed to the conception and design of this study. Rui Xu, Xiangfen Zhang and Feiniu Yuan performed the experiment and evaluated the model performance. Peng Jiang, Rui Xu collected and processed the datasets. Xiqiang Guan, Tianyi Lu, Ruifeng Zhai, Yixuan Wang contributed to the theoretical research. Xiangfen Zhang, Rui Xu, Ziyou Che and Wenhao Lu contributed significantly to result analysis and manuscript preparation. Figures 1, 2 and 3 were drawn by Rui Xu and Xiangfen Zhang. Fig. 4 was drawn by Shijie Xu. Rui Xu, Xiangfen Zhang and Feiniu Yuan contributed to the manuscript revision.

Corresponding authors

Correspondence to Xiangfen Zhang or Xiqiang Guan.

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Cite this article

Xu, R., Xu, S., Jiang, P. et al. Constraint optimization and key factor analysis based vehicle emergency braking strategy generator. Sci Rep (2026). https://doi.org/10.1038/s41598-026-41679-w

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  • Received: 26 December 2025

  • Accepted: 23 February 2026

  • Published: 27 February 2026

  • DOI: https://doi.org/10.1038/s41598-026-41679-w

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Keywords

  • constraint optimization
  • emergency braking
  • key factor analysis
  • model predictive control
  • nearest neighbor search
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