A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 6 Issue 5
Sep.  2019

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 11.8, Top 4% (SCI Q1)
    CiteScore: 17.6, Top 3% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Xiaoxiang Na and David J. Cole, "Modelling of a Human Driver’s Interaction with Vehicle Automated Steering Using Cooperative Game Theory," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1095-1107, Sept. 2019. doi: 10.1109/JAS.2019.1911675
Citation: Xiaoxiang Na and David J. Cole, "Modelling of a Human Driver’s Interaction with Vehicle Automated Steering Using Cooperative Game Theory," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1095-1107, Sept. 2019. doi: 10.1109/JAS.2019.1911675

Modelling of a Human Driver’s Interaction with Vehicle Automated Steering Using Cooperative Game Theory

doi: 10.1109/JAS.2019.1911675
More Information
  • The introduction of automated driving systems raised questions about how the human driver interacts with the automated system. Non-cooperative game theory is increasingly used for modelling and understanding such interaction, while its counterpart, cooperative game theory is rarely discussed for similar applications despite it may be potentially more suitable. This paper describes the modelling of a human driver’s steering interaction with an automated steering system using cooperative game theory. The distributed Model Predictive Control approach is adopted to derive the driver’s and the automated steering system’s strategies in a Pareto equilibrium sense, namely their cooperative Pareto steering strategies. Two separate numerical studies are carried out to study the influence of strategy parameters, and the influence of strategy types on the driver’s and the automated system’s steering performance. It is found that when a driver interacts with an automated steering system using a cooperative Pareto steering strategy, the driver can improve his/her performance in following a target path through increasing his/her effort in pursuing his/her own interest under the driver-automation cooperative control goal. It is also found that a driver’s adoption of cooperative Pareto steering strategy leads to a reinforcement in the driver’s steering angle control, compared to the driver’s adoption of non-cooperative Nash strategy. This in turn enables the vehicle to return from a lane-change maneuver to straight-line driving swifter.


  • loading
  • [1]
    T. J. Gordon and M. Lidberg, " Automated driving and autonomous functions on road vehicles,” Veh. Syst. Dyn., vol. 53, no. 7, pp. 958–994, Jul. 2015. doi: 10.1080/00423114.2015.1037774
    D. J. Fagnant and K. Kockelman, " Preparing a nation for autonomous vehicles: Opportunities, barriers and policy recommendations,” Transp. Res. Part A:Policy Pract., vol. 77, pp. 167–181, Jul. 2015. doi: 10.1016/j.tra.2015.04.003
    A. Nunes, B. Reimer, and J. F. Coughlin, " People must retain control of autonomous vehicles,” Nature, vol. 556, pp. 169–171, Apr. 2018. doi: 10.1038/d41586-018-04158-5
    W. Klier, G. Relmann, and W. Reinelt, " Concept and functionality of the Active Front Steering system, ” Soc. Automotive Eng., Warrendale, PA, USA, SAE Technical Paper 2004-21-0073, Oct. 2004.
    H. Guo, L. Song, J. Liu, F. Wang, D. Cao, H. Chen, C. Lv, and P. C. Luk, " Hazard-evaluation-oriented moving horizon parallel steering control for driver-automation collaboration during automated driving,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1062–1073, Nov. 2018. doi: 10.1109/JAS.2018.7511225
    D. A. Abbink, T. Carlson, M. Mulder, J. C. F. de Winter, F. Aminravan, T. L. Gibo, and E. R. Boer, " A topology of shared control systems–finding common ground in diversity,” IEEE Trans. Human-Mach. Syst., vol. 48, no. 5, pp. 509–525, Oct. 2018. doi: 10.1109/THMS.2018.2791570
    G. Guo and Q. Wang, " Fuel-efficient en route speed planning and tracking control of truck platoons, ” IEEE Trans. Intell. Transp. Syst., to be published.
    L. Chen, X. Hu, W. Tian, H. Wang, D. Cao, and F. Wang, " Parallel planning: a new planning framework for autonomous driving,” IEEE/CAA J. Autom. Sinica., vol. 6, no. 1, pp. 236–246, Jan. 2019. doi: 10.1109/JAS.2018.7511186
    T. Başar and G. J. Olsder. Dynamic Noncooperative Game Theory, 2nd ed. New York, NY, USA: Academic, 1995, ch. 1.
    Y. Shoham and K. Leyton-Brown, Multiagent Systems: Algorithmic, Game-theoretic, and Logical Foundations. Cambridge, U.K.: Cambridge Univ. Press, 2009, ch. 3.
    W. Ma and H. Peng, " Worst-case vehicle evaluation methodology–examples on truck rollover/jackknifing and active yaw control systems,” Veh. Syst. Dyn., vol. 32, no. 4–5, pp. 389–408, May 1999. doi: 10.1076/vesd.32.4.389.2076
    S. H. Tamaddoni, S. Taheri, and M. Ahmadian, " Optimal preview game theory approach to vehicle stability controller design,” Veh. Syst. Dyn., vol. 49, no. 12, pp. 1967–1979, Dec. 2011. doi: 10.1080/00423114.2011.565778
    C. Dextreit and I. V. Kolmanovsky, " Game theory controller for hybrid electric vehicles,” IEEE Trans. Control Syst. Technol., vol. 22, no. 2, pp. 652–663, Mar. 2014. doi: 10.1109/TCST.2013.2254597
    M. Flad, L. Fröhlich, and S. Hohmann, " Cooperative shared control driver assistance systems based on motion primitives and differential games,” IEEE Trans. Human-Mach. Syst., vol. 47, no. 5, pp. 711–722, Oct. 2017. doi: 10.1109/THMS.2017.2700435
    X. Na and D.J. Cole, " Application of open-loop Stackelberg equilibrium to modelling a driver’s interaction with vehicle active steering control in obstacle avoidance,” IEEE Trans. Human-Mach. Syst., vol. 47, no. 5, pp. 673–685, Oct. 2017. doi: 10.1109/THMS.2017.2700541
    X. Ji, Y. Liu, X. Na, and Y. Liu, " Research on interactive steering control strategy between driver and AFS in different game equilibrium strategies and information patterns,” Veh. Syst. Dyn., vol. 56, no. 9, pp. 1344–1374, Feb. 2018. doi: 10.1080/00423114.2018.1435890
    X. Ji, K. Yang, X. Na, C. Lv, and Y. Liu, " Shared steering torque for lane change assistance: a stochastic game-theoretic approach,” IEEE Trans. Ind. Electron., vol. 66, no. 4, pp. 3093–3105, Apr. 2019. doi: 10.1109/TIE.2018.2844784
    X. Na and D. J. Cole, " Game-theoretic modeling of the steering interaction between a human driver and a vehicle collision avoidance controller,” IEEE Trans. Human-Mach. Syst., vol. 45, no. 1, pp. 25–38, Feb. 2015. doi: 10.1109/THMS.2014.2363124
    C. W. Rosier and D. J. Cole, " Model predictive control to represent interaction of driver and active accelerator pedal, ” presented at the Int. Symp. Advanced Vehicle Control, Munich, Germany, 2016.
    H. Guo, D. Cao, H. Chen, C. Lv. H. Wang, and S. Yang, " Vehicle dynamic state estimation: state of the art schemes and perspectives,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 418–431, Mar. 2018. doi: 10.1109/JAS.2017.7510811
    Y., Xing, C. Lv, H. Wang, D. Cao, E. Velenis, and F. Wang, " Driver activity recognition for intelligent vehicles, ” IEEE Trans. Veh. Tech., in press, 2019.
    J. F. Nash., " Non-cooperative games,” Ann. Math., vol. 54, pp. 286–295, 1951. doi: 10.2307/1969529
    D. J. Cole, " Occupant-vehicle dynamics and the role of the internal model,” Veh. Syst. Dyn., vol. 56, no. 5, pp. 661–688, Dec. 2018. doi: 10.1080/00423114.2017.1398342
    A. Y. Ungoren and H. Peng, " An adaptive lateral preview driver model,” Veh. Syst. Dyn., vol. 43, no. 4, pp. 245–259, Apr. 2005. doi: 10.1080/00423110412331290419
    S. D. Keen and D. J. Cole, " Bias-free identification of a linear model-predictive steering controller from measured drier steering behaviour,” IEEE Trans. Syst.,Man,Cybern. B,Cybern., vol. 42, no. 2, pp. 434–443, Apr. 2012. doi: 10.1109/TSMCB.2011.2167509
    J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and Design. New York: NY, USA: Nob Hill, 2009, ch. 6.
    X. Na, " Game theoretic modelling of a driver’s steering interaction with active steering”, Ph.D. dissertation, Dept. Eng., Univ. Cambridge, Cambridge, U.K., 2014.
    J. M. Maciejowski, Predictive Control: With Constraints. London, U.K.: Prentice-Hall, 2002, ch. 1.
    A. Odhams, " Identification of driver steering and speed control”, Ph.D. dissertation, Dept. Eng., Univ. Cambridge, Cambridge, U.K., 2006.
    S. J. Anderson, J. M. Walker, and K. Iagnemma, " Experimental performance analysis of a homotopy-based shared autonomy framework,” IEEE Trans. Human-Mach. Syst., vol. 44, no. 2, pp. 190–199, Apr. 2014. doi: 10.1109/TSMC.2014.2298383
    S. M. Erlien, S. Fujita, and J. C. Gerdes, " Shared steering control using safe envelopes for obstacle avoidance and vehicle stability,” IEEE Trans. Intell. Transp. Syst., vol. 17, no. 2, pp. 441–451, Feb. 2016. doi: 10.1109/TITS.2015.2453404
    J. M. Hoc, " Towards a cognitive approach to human-machine cooperation in dynamic situations,” Int. J. Human-Computer Studies, vol. 54, no. 4, pp. 509–540, 2001. doi: 10.1006/ijhc.2000.0454


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(3)  / Tables(3)

    Article Metrics

    Article views (2526) PDF downloads(141) Cited by()


    DownLoad:  Full-Size Img  PowerPoint