Shared control scheme improves the driving performance while having an impact on driver behavior, drivers would constantly adapt their steering behavior mechanism in interaction with a shared controller. This paper proposes a novel data-driven model-based shared control strategy which is capable of considering drivers’ adaptive behaviors in driver-automation interaction to improve safety. The Koopman operator theory, which is a pure data-driven modeling technology, is adopted to yield an explicit control-oriented driver-vehicle model for shared controller design. Besides, a weighted online extended dynamic mode decomposition (WOEDMD) algorithm is proposed to update the Koopman driver model online for better capturing the driver’s adaptive behavior in driver-automation interaction, which settles the problem of driver’s potential behavior mechanism variations in practice. Based on the Koopman driver-vehicle model, a model-based shared controller is proposed in the model predictive control (MPC) framework, and the potential fields are incorporated in the optimization objectives to ensure safety. A group of human-in-the-loop experiments are conducted on a driving simulator to demonstrate the effectiveness of the modeling and shared control methods. The results show that the Koopman operator theory can be exploited for modeling the dynamics of the driver-vehicle integrated system, and the drivers’ adaptive behavior can be captured by the WOEDMD algorithm. Moreover, the shared controller considering the driver’s adaptive behavior improves the driving safety in the collision avoidance task.
WangHHuangYKhajepourA, et al. Ethical decision-making platform in autonomous vehicles with lexicographic optimization based model predictive controller. IEEE Trans Vehicular Technol2020; 69(8): 8164–8175.
2.
MartiEde MiguelMAGarciaF, et al. A review of sensor technologies for perception in automated driving. IEEE Intell Transp Syst Mag2019; 11(4): 94–108.
3.
DoganEHonnêtVMasfrandS, et al. Effects of non-drivingrelated tasks on takeover performance in different takeover situations in conditionally automated driving. Transp Res F Traffic Psychol Behaviour2019; 62: 494–504.
4.
ErcanZCarvalhoATsengHE, et al. A predictive control framework for torque-based steering assistance to improve safety in highway driving. Veh Syst Dyn2018; 56(5): 810–831.
5.
YangKLiuYNaX, et al. Preview-scheduled steering assistance control for co-piloting vehicle: a human-like methodology. Veh Syst Dyn2020; 58(4): 518–544.
6.
ZhangZZhangHZhaoW.A human-vehicle game stability control strategy considering drivers’ steering characteristics. IEEE Trans Intell Transp Syst2021; 22: 7306–7316.
7.
MarcanoMDiazSPerezJ, et al. A review of shared control for automated vehicles: Theory and applications. IEEE Trans Human-Mach Syst2020; 50: 475–491.
8.
WangJZhangGWangR, et al. A gain-scheduling driver assistance trajectory-following algorithm considering different driver steering characteristics. IEEE Trans Intell Transp Syst2017; 18(5): 1097–1108.
9.
ChenYZhangXWangJ.Robust vehicle driver assistance control for handover scenarios considering driving performances. IEEE Trans Syst Man Cybern Syst2019; 51(7): 4160–4170.
10.
LazcanoAMNiuTCarrera AkutainX, et al. MPC-based haptic shared steering system: a driver modeling approach for symbiotic driving. IEEE/ASME Trans Mechatron2021; 26: 1201–1211.
11.
ChenKYamaguchiTOkudaH, et al. Realization and evaluation of an instructor-like assistance system for collision avoidance. IEEE Trans Intell Transp Syst2021; 22(5): 2751–2760.
12.
LiRLiYLiSE, et al. Indirect shared control for cooperative driving between driver and automation in steer-bywire vehicles. IEEE Trans Intell Transp Syst2021; 22: 7826–7836.
13.
WangWZhaoDHanW, et al. A learning-based approach for lane departure warning systems with a personalized driver model. IEEE Trans Vehicular Technol2018; 67(10): 9145–9157.
14.
XingYLvCMoX, et al. Toward safe and smart mobility: Energy-aware deep learning for driving behavior analysis and prediction of connected vehicles. IEEE Trans Intell Transp Syst2021; 22: 4267–4280.
15.
ShahverdyMFathyMBerangiR, et al. Driver behavior detection and classification using deep convolutional neural networks. Expert Syst Appl2020; 149: 113240.
16.
OkamotoKTsiotrasP.Data-driven human driver lateral control models for developing haptic-shared control advanced driver assist systems. Robot Auton Syst2019; 114: 155–171.
17.
LuCWangHLvC, et al. Learning driver-specific behavior for overtaking: a combined learning framework. IEEE Trans Vehicular Technol2018; 67(8): 6788–6802.
18.
MezićI.Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dyn2005; 41(1–3): 309–325.
19.
KordaMMezićI.Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control. Automatica2018; 93: 149–160.
20.
WilliamsMOKevrekidisIGRowleyCW.A data–driven approximation of the Koopman operator: extending dynamic mode decomposition. J Nonlinear Sci2015; 25(6): 1307–1346.
21.
NarasingamAKwonJSI. Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation. J Process Control2020; 91: 25–36.
22.
NarasingamAKwonJS.Koopman Lyapunov-based model predictive control of nonlinear chemical process systems. AIChE J2019; 65(11): e16743.
23.
HuangXZhouWLiX, et al. Online Koopman operator learning to identify cross-coupling effect of piezoelectric tube scanners in atomic force microscopes. IEEE Trans Ind Inform2022; 18: 1111–1120.
24.
LiMCaoHLiG, et al. A two-layer potential-field-driven model predictive shared control towards driver-automation cooperation. IEEE Trans Intell Transp Syst2022; 23: 4415–4431.
25.
ZhangZWangCZhaoW, et al. Driving authority allocation strategy based on driving authority real-time allocation domain. IEEE Trans Intell Transp Syst2021; 1–16.
26.
LiXWangY.Shared steering control for human–machine co-driving system with multiple factors. Appl Math Model2021; 100: 471–490.
27.
YueMFangCZhangH, et al. Adaptive authority allocation-based driver-automation shared control for autonomous vehicles. Accid Anal Prev2021; 160: 106301.
28.
ZhangWZhaoYZhangX, et al. Shared control for lane keeping assistance system based on multiple-phase handling inverse dynamics. Control Eng Pract2019; 93: 104182.
29.
LiQDietrichFBolltEM, et al. Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator. Chaos2017; 27(10): 103111.
30.
ShermanJMorrisonWJ.Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Ann Math Stat1950; 21(1): 124–127.
31.
WangJWuJLiY.The driving safety field based on driver–vehicle–road interactions. IEEE Trans Intell Transp Syst2015; 16(4): 2203–2214.
32.
LiMSongXCaoH, et al. Shared control with a novel dynamic authority allocation strategy based on game theory and driving safety field. Mech Syst Signal Process2019; 124: 199–216.
33.
RasekhipourYKhajepourAChenSK, et al. A potential field-based model predictive path-planning controller for autonomous road vehicles. IEEE Trans Intell Transp Syst2017; 18(5): 1255–1267.
34.
LiRLiYLiSE, et al. Driver-automation indirect shared control of highly automated vehicles with intention-aware authority transition. In: 2017 IEEE intelligent vehicles symposium (IV), Los Angeles, CA, 11–14 June 2017, pp.26–32. New York, NY: IEEE.
35.
GuoHShenCZhangH, et al. Simultaneous trajectory planning and tracking using an MPC method for cyber-physical systems: a case study of obstacle avoidance for an intelligent vehicle. IEEE Trans Ind Inform2018; 14(9): 4273–4283.
36.
OjedaLLHanJSciarrettaA, et al. A real-time eco-driving strategy for automated electric vehicles. In: 2017 IEEE 56th annual conference on decision and control (CDC), Melbourne, VIC, 12–15 December 2017, pp.2768–2774. New York, NY: IEEE.
37.
XiaoYZhangXXuX, et al. A deep learning framework based on koopman operator for data-driven modeling of vehicle dynamics. arXiv preprint arXiv:200702219, 2020.
38.
BedouiSLtaïefMAbderrahimK.Online identification of multivariable discrete time delay systems using a recursive least square algorithm. Math Probl Eng2013; 2013: 1–18.
39.
CaoHZhaoSSongX, et al. An optimal hierarchical framework of the trajectory following by convex optimisation for highly automated driving vehicles. Veh Syst Dyn2019; 57(9): 1287–1317.
40.
LiMCaoHSongX, et al. Shared control driver assistance system based on driving intention and situation assessment. IEEE Trans Ind Inform2018; 14(11): 4982–4994.
41.
SongXCaoHHuangJ.Vehicle path planning in various driving situations based on the elastic band theory for highway collision avoidance. Proc IMechE Part D: J Automobile Engineering2013; 227(12): 1706–1722.
42.
NaXColeDJ.Game-theoretic modeling of the steering interaction between a human driver and a vehicle collision avoidance controller. IEEE Trans Human-Mach Syst2015; 45(1): 25–38.
43.
CaoHSongXHuangZ, et al. Simulation research on emergency path planning of an active collision avoidance system combined with longitudinal control for an autonomous vehicle. Proc IMechE Part D: J Automobile Engineering2016; 230(12): 1624–1653.
