Knowledge of tire–road friction coefficient (TRFC) is valuable for autonomous vehicle control and design of active safety systems. This paper investigates TRFC estimation on the basis of longitudinal vehicle dynamics. A two-stage TRFC estimation scheme is proposed that limits the disturbances to the vehicle motion. A sequence of braking pressure pulses is designed in the first stage to identify desired minimal pulse pressure for reliable estimation of TRFC with minimal interference with the vehicle motion. This stage also provides a qualitative estimate of TRFC. In the second stage, tire normal force and slip ratio are directly calculated from the measured signals, a modified force observer based on the wheel rotational dynamics is developed for estimating the tire braking force. A constrained unscented Kalman filter (CUKF) algorithm is subsequently proposed to identify the TRFC for achieving rapid convergence and enhanced estimation accuracy. The effectiveness of the proposed methodology is evaluated through CarSim™-MATLAB/Simulink™ co-simulations considering vehicle motions on high-, medium-, and low-friction roads at different speeds. The results suggest that the proposed two-stage methodology can yield an accurate estimation of the road friction with a relatively lower effect on the vehicle speed.
WangJAlexanderLRajamaniR.Friction estimation on highway vehicles using longitudinal measurements. J Dyn Syst Meas Control2004; 126(2): 265–275.
2.
AhnCPengHTsengHE.Robust estimation of road frictional coefficient. IEEE Trans Control Syst Technol2013; 21(1): 1–13.
3.
JalalmaabMPiraniMFidanB, et al. Cooperative estimation of road condition based on dynamic consensus and vehicular communication. IEEE Trans Intell Veh2018; 4(1): 90–100.
4.
SinghKBTaheriS.Estimation of tire–road friction coefficient and its application in chassis control systems. Syst Sci Control Eng2015; 3(1): 39–61.
5.
ZhangXGöhlichD.A hierarchical estimator development for estimation of tire–road friction coefficient. PloS ONE2017; 12(2): e0171085.
6.
PendletonSDAndersenHDuX, et al. Perception, planning, control, and coordination for autonomous vehicles. Machines2017; 5(1): 6.
7.
BagloeeSATavanaMAsadiM, et al. Autonomous vehicles: challenges, opportunities, and future implications for transportation policies. J Mod Transp2016; 24(4): 284–303.
8.
HussainRZeadallyS.Autonomous cars: research results, issues, and future challenges. IEEE Commun Surv Tutor2018; 21(2): 1275–1313.
9.
YamadaMUedaKHoribaI, et al. Discrimination of the road condition toward understanding of vehicle driving environments. IEEE Trans Intell Trans Syst2001; 2(1): 26–31.
10.
NiskanenATuononenA.Three three-axis IEPE accelerometers on the inner liner of a tire for finding the tire–road friction potential indicators. Sensors2015; 15(8): 19251–19263.
11.
DoganDBoyrazP.Smart traction control systems for electric vehicles using acoustic road-type estimation. IEEE Trans Intell Veh2019; 4(3): 486–496.
12.
AhnCPengHTsengHE.Robust estimation of road friction coefficient using lateral and longitudinal vehicle dynamics. Veh Syst Dyn2012; 50(6): 961–985.
13.
RajamaniRPhanomchoengGPiyabongkarnD, et al. Algorithms for real-time estimation of individual wheel tire–road friction coefficients. IEEE ASME Trans Mechatron2012; 17(6): 1183–1195.
14.
LiBDuHLiW.Comparative study of vehicle tyre-road friction coefficient estimation with a novel cost-effective method. Veh Syst Dyn2014; 52(8): 1066–1098.
15.
LeeCHedrickKYiK.Real-time slip-based estimation of maximum tire–road friction coefficient. IEEE ASME Trans Mechatron2004; 9(2): 454–458.
16.
ErdoganGAlexanderLRajamaniR.Estimation of tire–road friction coefficient using a novel wireless piezoelectric tire sensor. IEEE Sens J2011; 11(2): 267–279.
17.
KimCSHahnJOHongKS, et al. Estimation of tire–road friction based on onboard 6-DoF acceleration measurement. IEEE Trans Veh Technol2015; 64(8): 3368–3377.
18.
MadhusudhananAKCornoMAratMA, et al. Load sensing bearing based road-tyre friction estimation considering combined tyre slip. Mechatronics2016; 39: 136–146.
19.
ZhaoJZhangJZhuB.Coordinative traction control of vehicles based on identification of the tyre-road friction coefficient. Proc IMechE, Part D: J Automobile Engineering2016; 230(12): 1585–1604.
20.
KimTLeeJYiK. Enhanced maximum tire–road friction coefficient estimation based advanced emergency braking algorithm. In: 2015 IEEE intelligent vehicles symposium (IV), Seoul, South Korea, 28 June–1 July 2015, pp.883–888. IEEE.
21.
HuCWangRWangZ, et al. Integrated optimal dynamics control of 4WS4WD electric ground vehicles with tire–road frictional coefficient estimation. In: 2015 American control conference (ACC), Chicago, IL, 1–3 July 2015, pp.5426–5431. IEEE.
22.
WangRWangJ. Tire–road friction coefficient and tire cornering stiffness estimation based on longitudinal tire force difference generation. Control Eng Pract2013; 21(1): 65–75.
23.
ShaoLJinCLexC, et al. Robust road friction estimation during vehicle steering. Veh Syst Dyn2019; 57(4): 493–519.
24.
ZongCFSongPHuD. Estimation of vehicle states and tire–road friction using parallel extended Kalman filtering. J Zhejiang Univ Sci A2011; 12(6): 446–452.
25.
EniszKSzalayIKohlruszG, et al. Tyre-road friction coefficient estimation based on the discrete-time extended Kalman filter. Proc IMechE, Part D: J Automobile Engineering2015; 229(9): 1158–1168.
26.
ZhaoJZhangJZhuB. Development and verification of the tire/road friction estimation algorithm for antilock braking system. Math Probl Eng2014; 2014: 1–15.
27.
ChoiMOhJJChoiSB. Linearized recursive least squares methods for real-time identification of tire–road friction coefficient. IEEE Trans Veh Technol2013; 62(7): 2906–2918.
28.
QiZTaheriSWangB, et al. Estimation of the tyre-road maximum friction coefficient and slip slope based on a novel tyre model. Veh Syst Dyn 015; 53(4): 506–525.
29.
RenHChenSShimT, et al. Effective assessment of tyre-road friction coefficient using a hybrid estimator. Veh Syst Dyn2014; 52(8): 1047–1065.
30.
ChenLBianMLuoY, et al. Estimation of road-tire friction with unscented Kalman filter and MSE-weighted fusion based on a modified Dugoff tire model. SAE technical paper 2015-01-1601, 2015.
31.
PaulDVelenisEHumbertF, et al. Tyre-road friction -estimation based on braking force distribution. Proc IMechE, Part D: J Automobile Engineering2019; 233(8): 2030–2047.
32.
VillagraJD’Andréa-NovelBFliessM, et al. A diagnosis-based approach for tire–road forces and maximum friction estimation. Control Eng Pract2011; 19(2): 174–184.
33.
ChenWTanDZhaoL. Vehicle sideslip angle and road friction estimation using online gradient descent algorithm. IEEE Trans Veh Technol2018; 67(12): 11475–11485.
34.
YoonJHLiSEAhnC. Estimation of vehicle sideslip angle and tire–road friction coefficient based on magnetometer with GPS. Int J Automot Technol2016; 17(3): 427–435.
35.
HuJRakhejaSZhangY. Real-time estimation of tire–road friction coefficient based on lateral vehicle dynamics. Proc IMechE, Part D: J Automobile Engineering2020; 234(10–11): 2444–2457.
36.
CabreraJACastilloJJPérezJ, et al. A procedure for determining tire–road friction characteristics using a modification of the magic formula based on experimental results. Sensors2018; 18(3): 896.
37.
OrtizACabreraJGuerraA, et al. An easy procedure to determine magic formula parameters: a comparative study between the starting value optimization technique and the imma optimization algorithm. Veh Syst Dyn2006; 44(9): 689–718.
38.
WongJY. Theory of ground vehicles. New York: John Wiley & Sons, 2008.
39.
WangRWangJ. Fault diagnosis method utilizing actuator redundancy and identicalness with applications to electric vehicles. In: Proceedings of the 2012 ASME dynamic systems and control conference, Fort Lauderdale, FL, 17–19 October 2012, pp.111–118. ASME.
40.
RezaeianAZarringhalamRFallahS, et al. Novel tire force estimation strategy for real-time implementation on vehicle applications. IEEE Trans Veh Technol2015; 64(6): 2231–2241.
41.
WanEAVan Der MerweR. The unscented Kalman filter for nonlinear estimation. In: Proceedings of the IEEE 2000 adaptive systems for signal processing, communications, and control symposium (AS-SPCC), Lake Louise, Alberta, 4 October 2000, pp.153–158. IEEE.
42.
HaykinS. Kalman filtering and neural networks. New York: John Wiley & Sons, 2004.
43.
SimonD. Optimal state estimation: Kalman, H∞, and nonlinear approaches. New York, NY: John Wiley & Sons, 2006.
