+ Game Theory for Automotive Control

The focus of the ongoing research has been on developing game theoretic techniques for vehicle energy management and for automated/autonomous driving.

Game theory for energy management

A game-theoretic framework has been defined for developing controllers that improve fuel efficiency and reduce emissions by considering powertrain-driver interaction as a multi-stage leader-follower game. The controller is generated off-line as a feedback Stackelberg equilibrium policy and is implemented online in the form of look-up tables. Recently, this approach was demonstrated to lead to a successful solution to HEV energy management problem that was confirmed with extensive vehicle validation results. The calibration process, while it involved some iterations between offline and in-vehicle tuning steps, was relatively straightforward. Ancillary parts of the controller, augmented to handle real-world drivability requirements, were also developed. Based on the results, the game theory controller was adopted as an integral part of the future Jaguar Land Rover hybrid vehicle line.

The paper [1] defines the basic framework and demonstrates applications to fuel economy and emissions optimization of stratified charge direct injection engines with Lean NOx Trap.

The application to energy management of an advanced Hybrid Electric Vehicle is the subject of [2]-[5] written with Clement Dextreit. The results of experimental implementation are found in [5].

[1] I. Kolmanovsky and I.F. Siverguina, "Feasibility assessment and operating policy optimization of automotive powertrains with uncertainties using game theory," Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposition, New York, NY, November 11-16, 2001, Paper IMECE2001/DSC-24530 .

[2] C. Dextreit F. Assadian, I. Kolmanovsky, J. Mahtani, and K. Burnham, "Approaches to optimisation of energy management in a hybrid electric vehicle," Proceedings of the 16th International Conference on Systems Science, Vol. 3, pp. 67-78, Editor: Adam Grzech, 4-6 September, 2007.

[3] C. Dextreit, F. Assadian, I. Kolmanovsky, J. Mahtani, and K. Burnham, "Hybrid Electric Vehicle energy management using game theory," Proceedings of 2008 SAE World Congress, Detroit, Michigan, April, 2008, SAE Paper 2008-01-1317.

[4] C. Dextreit and I. Kolmanovsky, “Approaches to energy management of Hybrid Electric Vehicles: Experimental comparison,” Proceedings of UKACC International Conference on CONTROL 2010, Coventry, September, 2010, UK.

[5] C. Dextreit and I. Kolmanovsky, "Game theory controller for Hybrid Electric Vehicles," IEEE Transactions on Control Systems Technology, vol. 22, no. 2, pp. 652-663, 2014.

Game Theory for Autonomous/Automated Driving

To facilitate the testing, validation and verification of autonomous/automated vehicles, a game theory based simulation environment to inform traffic relevant trajectories has been developed. Such an environment is interactive, that is other vehicles in the simulation react, in a representative way, to the actions taken by the autonomous vehicles thereby facilitating the discovery of faults, i.e., incorrect decisions made by the automated vehicle leading to safety or comfort related issues. The proposed game theoretic policies can also be used directly for automated driving. The attached video discusses the approach and the results which are also found in references [6], [7], [8]

References

[6] Oyler, D.W., Yildiz, Y., Girard, A., Li, N., and Kolmanovsky, I.V., “A game theoretical model of traffic with multiple interacting drivers for use in autonomous vehicle development,” Proceedings of 2016 American Control Conference (ACC), Boston, MA, 2016, pp. 1705-1710, doi: 10.1109/ACC.2016.7525162.

[7] Li, N., Oyler, D., Zhang, M., Yildiz, Y., Girard, A., and Kolmanovsky, I.V., “Hierarchical reasoning game theory based approach for evaluation and testing of autonomous vehicle control systems,” Proceedings of 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, pp. 727-733, doi: 10.1109/CDC.2016.7798354, 2016.

[8] Li, N., Oyler, D., Zhang., M., Yildiz, Y., Kolmanovsky, I.V., and Girard, A., "Game-theoretic modeling of driver and vehicle interactions for verification and validation of autonomous vehicle control systems," IEEE Transactions on Control Systems Technology, vol. 26, no. 5, pp. 1782-1797, Sept. 2018, doi: 10.1109/TCST.2017.2723574.