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 8 Issue 1
Jan.  2021

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Xiaoxiang Na and David Cole, "Theoretical and Experimental Investigation of Driver Noncooperative-Game Steering Control Behavior," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 189-205, Jan. 2021. doi: 10.1109/JAS.2020.1003480
Citation: Xiaoxiang Na and David Cole, "Theoretical and Experimental Investigation of Driver Noncooperative-Game Steering Control Behavior," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 189-205, Jan. 2021. doi: 10.1109/JAS.2020.1003480

Theoretical and Experimental Investigation of Driver Noncooperative-Game Steering Control Behavior

doi: 10.1109/JAS.2020.1003480
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  • This paper investigates two noncooperative-game strategies which may be used to represent a human driver’s steering control behavior in response to vehicle automated steering intervention. The first strategy, namely the Nash strategy is derived based on the assumption that a Nash equilibrium is reached in a noncooperative game of vehicle path-following control involving a driver and a vehicle automated steering controller. The second one, namely the Stackelberg strategy is derived based on the assumption that a Stackelberg equilibrium is reached in a similar context. A simulation study is performed to study the differences between the two proposed noncooperative- game strategies. An experiment using a fixed-base driving simulator is carried out to measure six test drivers’ steering behavior in response to vehicle automated steering intervention. The Nash strategy is then fitted to measured driver steering wheel angles following a model identification procedure. Control weight parameters involved in the Nash strategy are identified. It is found that the proposed Nash strategy with the identified control weights is capable of representing the trend of measured driver steering behavior and vehicle lateral responses. It is also found that the proposed Nash strategy is superior to the classic driver steering control strategy which has widely been used for modeling driver steering control over the past. A discussion on improving automated steering control using the gained knowledge of driver noncooperative-game steering control behavior was made.


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  • [1]
    D. J. Cole, “Occupant-vehicle dynamics and the role of the internal model,” Veh. Syst. Dyn., vol. 56, no. 5, pp. 661–688, Dec. 2017.
    R. B. Myerson. Game Theory: Analysis of Conflict. Cambridge, MA, USA: Harvard Univ. Press, 1991, ch. 1.
    T. Başar and G. J. Olsder. Dynamic Noncooperative Game Theory, 2nd ed., New York, NY, USA: Academic, 1995, ch. 1.
    J. Engwerda, LQ Dynamic Optimization and Differential Games. Sussex, UK: Wiley, 2005, ch. 1.
    Y. Shoham and K. Leyton-Brown, Multiagent Systems: Algorithmic, Game-theoretic, and Logical Foundations. Cambridge, UK: Cambridge Univ. Press, 2009, ch. 3.
    E. J. Dockner and R. Neck, “Time consistency, subgame perfectness, solution concepts and information patterns in dynamic models of stabilization policies,” Adv. Comput. Econ., vol. 22, pp. 51–101, 2008.
    I. K. Geckil and P. L. Anderson. Applied Game Theory and Strategic Behavior. Boca Raton, FL, USA: CRC Press, 2010, ch. 2.
    C. I. Chen and J. B. Cruz, “Stackelberg solution for two-person games with biased information patterns,” IEEE Trans. Autom. Control, vol. 17, no. 6, pp. 791–798, Dec. 1972. doi: 10.1109/TAC.1972.1100179
    D. A. Braun, P. A. Ortega, and D. M. Wolpert, “Nash Equilibria in multi-agent Motor Interactions,” PLOS Computational Biology, vol. 5, no. 8, pp. 1–8, 2009.
    X. 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
    R. Isermann, R. Mannale, and K. Schmitt, “Collision-avoidance systems PRORETA: situation analysis and intervention control,” J. Control. Eng. Pract., vol. 20, no. 11, pp. 1236–1246, Nov. 2012. doi: 10.1016/j.conengprac.2012.06.003
    X. X. Na and D. 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, Sep. 2019. doi: 10.1109/JAS.2019.1911675
    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. W. Ji, Y. L. Liu, X. X. Na, and Y. H. 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. W. Ji, K. M. Yang, X. X. Na, C. Lv, and Y. H. 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
    E. E. Tsiropoulou, G. K. Katsinis, A. Filios, and S. Papavassiliou, “On the problem of optimal cell selection and uplink power control in open access multi-service two-tier femtocell networks,” in Proc. Int. Conf. Ad-Hoc Networks and Wireless, Benidorm, Spain, 2014.
    K. A. Yau, P. Komisarczuk, and P. D. Teal, “Reinforcement learning for context awareness and intelligence in wireless networks: review, new features and open issues,” J. Network and Computer Applications, vol. 35, no. 1, pp. 253–267, 2012. doi: 10.1016/j.jnca.2011.08.007
    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
    C. Lv, H. J. Wang, D. P. Cao, Y. F. Zhao, D. J. Auger, M. Sullman, R. Matthias, L. Skrypchuk, and A. Mouzakitis, “Characterization of driver neuromuscular dynamics for human-automation collaboration design of automated vehicles,” IEEE/ASME Trans. Mechatronics, vol. 23, no. 6, Dec. 2018.
    H. Y. Guo, L. H. Song, J. Liu, F.-Y. Wang, D. P. 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
    L. Chen, X. M. Hu, W. Tian, H. Wang, D. P. Cao, and F.-Y. 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
    H. Y. Guo, D. P. Cao, H. Chen, C. Lv, H. J. Wang, and S. Q. 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
    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
    R. J. Li, Y. N. Li, S. E. Li, E. Burdet, and B. Cheng, “Driver-automation indirect shared control of highly automated vehicles with intention-aware authority transition,” in Proc. IEEE Intelligent Vehicles Symp., Redondo Beach, CA, USA, 2017.
    C. J. Nash and D. J. Cole, “Identification and validation of a driver steering control model incorporating human sensory dynamics,” Veh. Syst. Dyn., vol. 58, no. 4, pp. 1259–1263, Apr. 2020.
    C. MacAdam, “Application of an optimal preview control for simulation of closed-loop automobile driving,” IEEE Trans. Syst.,Man,Cybern., vol. SMC-11, no. 6, pp. 393–399, Jun. 1981.
    A. Y. Ungoren and H. Peng, “An adaptive lateral preview driver model,” Veh. Syst. Dyn., vol. 43, no. 4, pp. 245–260, Apr. 2005. doi: 10.1080/00423110412331290419
    J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and Design. New York: NY, USA: Nob Hill, 2009, ch. 6.
    J. C. Liu, P. Jayakumar, J. L. Stein, and T. Ersal, “A study on model fidelity for model predictive control-based obstacle avoidance in high-speed autonomous ground vehicles,” Veh. Syst. Dyn., vol. 54, no. 11, pp. 1629–1650, 2016. doi: 10.1080/00423114.2016.1223863
    Y. Q. Gao, “Model predictive control for autonomous and semiautonomous vehicles”, Ph.D. dissertation, Dept. Mechanical Eng., Univ. California, Berkeley, Berkeley, CA, USA, 2014.
    P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat, “Predictive active steering control for autonomous vehicle systems,” IEEE Trans. Control Syst. Technol., vol. 15, no. 3, pp. 566–580, May 2007. doi: 10.1109/TCST.2007.894653
    J. M. Maciejowski, Predictive Control: With Constraints. London, UK: Prentice-Hall, 2002, ch. 3.
    J. Bonnefon, A. Shariff, and I. Rahwan, “The social dilemma of autonomous vehicles,” Science, vol. 352, pp. 1573–1576, Jun. 2016. doi: 10.1126/science.aaf2654
    A. M. C. Odhams and D. J. Cole, “Identification of preview steering control models using data from a driving simulator and a randomly curved road path,” Int. J. Veh. Auton. Syst., vol. 12, no. 1, pp. 44–46, Jan. 2014. doi: 10.1504/IJVAS.2014.057863
    X. X. Na, “Game theoretic modelling of a driver’s steering interaction with active steering”, Ph.D. dissertation, Dept. Eng., Univ. Cambridge, Cambridge, UK, 2014.
    L. Ljung, System Identification Theory for the User, 2nd ed., London, UK: Prentice-Hall, 1999, ch. 13.
    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


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    • Two noncooperative-game driver steering control strategies were investigated
    • The two strategies are derived based on Nash and Stackelberg equilibria, respectively
    • The two strategies are found represent distinct driver steering control behavior
    • The Nash strategy is found capable of representing measured driver steering control
    • The Nash strategy is found superior to a classic strategy in representing driver steering control


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