Differential-Game-Based Driver Assistance System for Fuel-Optimal Driving

  • Michael FladEmail author
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


Increasing the fuel-efficiency is a current and essential question for all major car manufacturers. Supporting these efforts, the paper presents a shared control driver assistance system that may help the driver to apply a fuel-efficient driving strategy. For the proposed system, both driver and assistance system can apply forces to the acceleration pedal enabling a close cooperation between the two partners. The interaction between driver and such kind of assistance system can be described by means of a differential game. By solving this differential game, the assistance system calculates optimal control outputs. For realization, the assistance system is required to solve different game theoretic problems that are presented in this paper. The assistance system was implemented on a real time system, integrated in a driving simulator and validated in a driving study. The results indicate that the proposed system is able to save in average about 10% fuel in a highway scenario.


Advanced driver assistance system Differential game Cooperative and haptic shared control Increasing fuel efficiency Optimal control in human-machine cooperation 


  1. 1.
    Abbink, D.A.: Neuromuscular analysis of haptic gas pedal feedback during car following. Doctoral Thesis, Delft University of Technology (2006)Google Scholar
  2. 2.
    Automation from driver assistance systems to automated driving. Tech. rep., Verband der Automobilindustrie (2015)Google Scholar
  3. 3.
    Bainbridge, L.: Ironies of automation. Automatica 19, 775–779 (1983)CrossRefGoogle Scholar
  4. 4.
    Borrelli, F., Bemporad, A., Morari, M.: Predictive control for linear and hybrid systems (2014).
  5. 5.
    Braun, D., Ortega, P., Wolpert, D.: Nash equilibria in multi-agent motor interactions. PLoS Comput. Biol. 5(8) (2009). MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chow, C., Jacobson, D.: Studies of human locomotion via optimal programming. Math. Biosci. 10(34), 239–306 (1971)CrossRefGoogle Scholar
  7. 7.
    Engwerda, J.: LQ Dynamic Optimization and Differential Games. Wiley, Chichester (2005)Google Scholar
  8. 8.
    Flad, M.: Kooperative regelungskonzepte auf basis der spieltheorie und deren anwendung auf fahrerassistenzsysteme. Ph.D. Thesis, Karlsruher Institut fr Technologie (KIT) (2016).
  9. 9.
    Flad, M., Trautmann, C., Diehm, G., Hohmann, S.: Experimental validation of a driver steering model based on switching of driver specific primitives. In: 2013 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 214–220 (2013).
  10. 10.
    Flad, M., Otten, J., Schwab, S., Hohmann, S.: Necessary and sufficient conditions for the design of cooperative shared control. In: IEEE International Conference on Systems, Man, and Cybernetics (2014)Google Scholar
  11. 11.
    Flad, M., Otten, J., Schwab, S., Hohmann, S.: Steering driver assistance system: a systematic cooperative shared control design approach. In: IEEE International Conference on Systems, Man, and Cybernetics, pp. 3585–3592 (2014)Google Scholar
  12. 12.
    Flad, M., Rothfuss, S., Diehm, G., Hohmann, S.: Active brake pedal feedback simulator based on electric drive. SAE Int. J. Passeng. Cars Electron. Electr. Syst. 7(1), 189–200 (2014)CrossRefGoogle Scholar
  13. 13.
    Flemisch, F., Kelsch, J., Lper, C., Schieben, A., Schindler, J., Heesen, M.: Cooperative control and active interfaces for vehicle assistance and automation. In: FISITA World automotive Congress, Munich (2008)Google Scholar
  14. 14.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization & Machine Learning. Addison-Wesley, Boston (1989)Google Scholar
  15. 15.
    Gote, C., Flad, M., Hohmann, S.: Driver characterization and driver specific trajectory planning: an inverse optimal control approach. In: 2014 IEEE International Conference on Systems, Man and Cybernetics (SMC), pp. 3014–3021 (2014).
  16. 16.
    Hatze, H.: The complete optimization of a human motion. Math. Biosci. 28(12), 99–135 (1976)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Hayashi, Y.: Study on acceleration and deceleration maneuver guidance for driver by gas pedal reaction force control. In: 13th International IEEE Annual Conference on Intelligent Transportation Systems (2010)Google Scholar
  18. 18.
    Hjaelmdahl, M., Almqvist, S., Varhelyi, A.: Speed regulation by in car active accelerator pedal: effects on speed and speed distribution. IATSS Res. 26(2), 60–66 (2002)CrossRefGoogle Scholar
  19. 19.
    Jagacinski, R., Flach, J.: Control Theory for Humans: Quantitative Approaches to Modeling Performance. Erlbaum, Mahwah (2009)Google Scholar
  20. 20.
    Johnson, M., Aghasadeghi, N., Bretl, T.: Inverse optimal control for deterministic continuous-time nonlinear systems. In: 52nd IEEE Conference on Decision and Control, pp. 2906–2913 (2013).
  21. 21.
    Ludwig, J., Gote, C., Flad, M., Hohmann, S.: Cooperative dynamic vehicle control allocation using time-variant differential games. In: 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 117–122 (2017).
  22. 22.
    MacAdam, C.: Understanding and modeling the human driver. Veh. Syst. Dyn. 40(1–3), 101–134 (2003)CrossRefGoogle Scholar
  23. 23.
    Mombaur, K., Truong, A., Laumond, J.P.: From human to humanoid locomotion an inverse optimal control approach. Auton. Robot. 28(3), 369–383 (2010). CrossRefGoogle Scholar
  24. 24.
    Mosbach, S., Flad, M., Hohmann, S.: Cooperative longitudinal driver assistance system based on shared control. In: 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 1776–1781 (2017).
  25. 25.
    Mulder, M.: Haptic Gas Pedal Feedback for Active Car-Following Support. Delft University of Technology, Doktorarbeit (2007)Google Scholar
  26. 26.
    Mulder, M., Abbink, D., van Paassen, M., Mulder, M.: Design of a haptic gas pedal for active car-following support. IEEE Trans. Intell. Transp. Syst. 12(1), 268–279 (2011)CrossRefGoogle Scholar
  27. 27.
    Na, X., Cole, D.J.: Linear quadratic game and non-cooperative predictive methods for potential application to modelling driverafs interactive steering control. Veh. Syst. Dyn. 51(2), 165–198 (2013)CrossRefGoogle Scholar
  28. 28.
    Na, X., Cole, D.J.: Game theoretic modelling of a human drivers steering interaction with vehicle active steering collision avoidance system. IEEE Trans. Hum.-Mach. Syst. 45(1), 25–38 (2015)CrossRefGoogle Scholar
  29. 29.
    Nash, J.: Non-cooperative games. Ann. Math. 2, 286–295 (1951)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Nelson, W.: Physical principles for economies of skilled movements. Biol. Cybern. 46(2), 135–147 (1983)CrossRefGoogle Scholar
  31. 31.
    Nocedal, J., Wright, S.: Numerical Optimization, 2nd edn. Springer, New York (2006)zbMATHGoogle Scholar
  32. 32.
    Petermeijer, S., Abbink, D., Mulder, M., deWinter, J.: The effect of haptic support systems on driver performance: a literature survey. IEEE Trans. Haptic 8(4), 467–479 (2015)CrossRefGoogle Scholar
  33. 33.
    Rasmussen, J.: Skills, rules, and knowledge; signals, signs, and symbols, and other distinctions in human performance models. IEEE Trans. Syst. Man Cybern. 13(3), 257–266 (1983)CrossRefGoogle Scholar
  34. 34.
    Society of Automotive Engineers (SAE): Stepwise coastdown methodology for measuring tire rolling resistance SAE J 2452 (2008)Google Scholar
  35. 35.
    Tamaddoni, S., Ahmadian, M., Taheri, S.: Optimal vehicle stability control design based on preview game theory concept. In: American Control Conference (ACC), pp. 5249–5254 (2011)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Control SystemsKarlsruhe Institute of TechnologyKarlsruheGermany

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