Skip to main content
Log in

Smooth longitudinal driving strategy with adjustable nonlinear reference model for autonomous vehicles

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

Comfort in Autonomous Vehicles (AVs) is a decisive aspect and plays an essential role in their advanced driving systems. As the comfort is directly influenced by the amount of acceleration and deceleration, a smooth longitudinal driving strategy can significantly improve the passenger’s acceptance level. Although some safe longitudinal strategies such as time-headway are introduced for AVs, the breakpoints in their speed generation models when approaching the front vehicle made discomfort behavior. In this paper, we proposed a continuous and differentiable reference speed model with a single equation to cover all possible relative distances. This model is constructed based on the well-known attributes of a hyperbolic tangent curve to smoothly change the speed of the host vehicle at the corner points. Moreover, the adjustable variables in our reference speed generator make it possible to choose between low and high-accelerate driving strategies. The experiments are performed based on several driving scenarios such as stop-and-go, hard-stop, and normal driving, and the results are compared with different reference speed models. The maximum improvement is obtained in the stop-and-go scenario, and on average, about 7.29 and 12.47% are achieved in terms of the magnitude of acceleration and jerk, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data availability

Data available on request.

Code availability

Code available on request.

References

  1. Li L, Liang H, Wang J, Yang J, Li Y (2022) Online routing for autonomous vehicle cruise systems with fuel constraints. J Intell Rob Syst 104:1–16

    Article  Google Scholar 

  2. Zhao S, Wang X, Chen H, Wang Y (2020) Cooperative path following control of fixed-wing unmanned aerial vehicles with collision avoidance. J Intell Rob Syst 100:1569–1581

    Article  Google Scholar 

  3. Nguyen AT, Sentouh C, Popieul JC (2018) Fuzzy steering control for autonomous vehicles under actuator saturation: design and experiments. J Franklin Inst 355:9374–9395

    Article  MathSciNet  MATH  Google Scholar 

  4. Osman K, Ghommam J, Saad M (2020) Guidance based lane-changing control in high-speed vehicle for the overtaking maneuver. J Intell Rob Syst 98:643–665

    Article  Google Scholar 

  5. Petrović Đ, Mijailović R, Pešić D (2020) Traffic accidents with autonomous vehicles: type of collisions, manoeuvres and errors of conventional vehicles’ drivers. Transpo Res Proc 45:161–168

    Article  Google Scholar 

  6. Makridis M, Mattas K, Ciuffo B (2019) Response time and time headway of an adaptive cruise control. An empirical characterization and potential impacts on road capacity. IEEE Trans Intell Transp Syst 21:1677–1686

    Article  Google Scholar 

  7. Campbell S, O'Mahony N, Krpalcova L, Riordan D, Walsh J, Murphy A and Ryan C. (2018) Sensor technology in autonomous vehicles: a review. In: IEEE 29th Irish Signals and Systems Conference (ISSC), pp 1–4

  8. Zhao X, Wang Z, Xu Z, Wang Y, Li X, Qu X (2020) Field experiments on longitudinal characteristics of human driver behavior following an autonomous vehicle. Transp Res Part C: Emerg Technol 114:205–224

    Article  Google Scholar 

  9. Lu C, Gong J, Lv C, Chen X, Cao D, Chen Y (2019) A personalized behavior learning system for human-like longitudinal speed control of autonomous vehicles. Sensors 19:3672

    Article  Google Scholar 

  10. Guo L, Ge P and Sun D (2020) Variable time headway autonomous emergency braking control algorithm based on model predictive control. Chinese Automation Congress (CAC), pp 1794–1798

  11. Goodall NJ, Lan CL (2020) Car-following characteristics of adaptive cruise control from empirical data. J Transp Eng, Part A: Syst 146:04020097

    Article  Google Scholar 

  12. Wang W, Xi J, Zhao D (2018) Learning and inferring a driver’s braking action in car-following scenarios. IEEE Trans Veh Technol 67:3887–3899

    Article  Google Scholar 

  13. Milanés V, Pérez J, Godoy J, Onieva E (2012) A fuzzy aid rear-end collision warning/avoidance system. Expert Syst Appl 39:9097–9107

    Article  Google Scholar 

  14. Wang X, Chen M, Zhu M, Tremont P (2016) Development of a kinematic-based forward collision warning algorithm using an advanced driving simulator. IEEE Trans Intell Transp Syst 17:2583–2591

    Article  Google Scholar 

  15. Ahmed HU, Huang Y, Lu P (2021) A review of car-following models and modeling tools for human and autonomous-ready driving behaviors in micro-simulation. Smart Cities 4:314–335

    Article  Google Scholar 

  16. Martinez JJ, Canudas-de-Wit C (2007) A safe longitudinal control for adaptive cruise control and stop-and-go scenarios. IEEE Trans Control Syst Technol 15:246–258

    Article  Google Scholar 

  17. Mohtavipour SM, Jafari H and Shahhoseini HS (2017) A novel design for adaptive cruise control based on extended reference model. In: IEEE 4th international conference on knowledge-based engineering and innovation (KBEI), pp 0822–0827

  18. Mohtavipour SM, Mollajafari M, Naseri A (2019) A guaranteed-comfort and safe adaptive cruise control by considering driver’s acceptance level. Int J Dyn Control 7:966–980

    Article  MathSciNet  Google Scholar 

  19. Mohtavipour SM, Mollajafari M (2021) An analytically derived reference signal to guarantee safety and comfort in adaptive cruise control systems. J Intell Transp Syst 25:1–20

    Article  Google Scholar 

  20. Chaturvedi S, Kumar N (2021) Design and implementation of an optimized PID controller for the adaptive cruise control system. IETE J Res. 1–8. https://doi.org/10.1080/03772063.2021.2012282

  21. Pradhan R, Majhi SK, Pradhan JK, Pati BB (2018) Antlion optimizer tuned PID controller based on Bode ideal transfer function for automobile cruise control system. J Ind Inf Integr 9:45–52

    Google Scholar 

  22. Rout MK, Sain D, Swain SK and Mishra SK (2016) PID controller design for cruise control system using genetic algorithm. In: International conference on electrical, electronics, and optimization techniques (ICEEOT), pp 4170–4174

  23. Lin Y, McPhee J, Azad NL (2020) Comparison of deep reinforcement learning and model predictive control for adaptive cruise control. IEEE Trans Intell Veh 6:221–231

    Article  Google Scholar 

  24. Zhao D, Xia Z, Zhang Q (2017) Model-free optimal control based intelligent cruise control with hardware-in-the-loop demonstration. IEEE Comput Intell Mag 12:56–69

    Article  Google Scholar 

  25. Chen X, Zhai Y, Lu C, Gong J and Wang G (2017) A learning model for personalized adaptive cruise control. In: IEEE intelligent vehicles symposium (IV), pp 379–384

  26. Åström KJ, Hägglund T and Astrom KJ (2006) Advanced PID control. Research Triangle Park: ISA-the instrumentation, systems, and automation society, Vol 461

  27. Milanés V, Villagrá J, Godoy J, González C (2011) Comparing fuzzy and intelligent PI controllers in stop-and-go manoeuvres. IEEE Trans Control Syst Technol 20:770–778

    Article  Google Scholar 

  28. Nagesh I, Edwards C (2014) A multivariable super-twisting sliding mode approach. Automatica 50:984–988

    Article  MathSciNet  MATH  Google Scholar 

  29. Siebert FW, Oehl M, Pfister HR (2014) The influence of time headway on subjective driver states in adaptive cruise control. Transp Res F: Traffic Psychol Behav 25:65–73

    Article  Google Scholar 

  30. Zegelaar PWA, Gong S and Pacejka HB (2021) Tyre models for the study of in-plane dynamics. In: The Dynamics of Vehicles on Roads and on Tracks, 1st edn, CRC Press, pp 578–590

Download references

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

Authors

Contributions

Method and Model Analysis SMM and TZE, Simulation and Reviewing: HJA, Writing: M. M.

Corresponding author

Correspondence to Seyed Mehdi Mohtavipour.

Ethics declarations

Competing interests

The authors have no relevant financial or non-financial interests to disclose.

Consent to participate

This research does not involved human subjects.

Consent for publication

The manuscript does not contain any individual person’s data.

Ethics approval

This research does not involved human or animal subjects.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohtavipour, S.M., Ehsan, T.Z., Abeshoori, H.J. et al. Smooth longitudinal driving strategy with adjustable nonlinear reference model for autonomous vehicles. Int. J. Dynam. Control 11, 2320–2334 (2023). https://doi.org/10.1007/s40435-023-01142-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-023-01142-4

Keywords

Navigation