There is uncertainty in the friction coefficient during on-road driving due to road conditions, external tire conditions, and other factors, which may lead to vehicle instability when driven in a critical state under extreme conditions. To solve this problem, the stochastic phase plane induced by the randomness of tire-road friction coefficient is analyzed, and a stability control scheme is proposed to improve vehicle handling and stability. First, the tire-road friction coefficient uncertainty is described using the polynomial chaos method. The stochastic phase plane under the influence of friction uncertainty, as well as the vehicle velocity and front wheel steering angle is analyzed. The transition region induced by the friction uncertainty can be observed, and a stability index is designed based on the position of the vehicle state relative to the transition region and the movement trend of the vehicle state in the phase plane. Then, a sliding mode controller (SMC) is designed to track the desired vehicle state calculated by a two-degree-of-freedom (2-DoF) vehicle model, with the stability index serving as a weighting factor for stability control. Finally, the CarSim-Simulink co-simulation results demonstrate that the proposed control scheme is robust to road friction uncertainty and optimizes tire-road adhesion, promoting vehicle maneuverability and stability.
KuuttiSBowdenRJinY, et al. A survey of deep learning applications to autonomous vehicle control. IEEE Trans Intell Transp Syst2020; 22(2): 712–733.
2.
XiongLYangXLengB, et al. Integrated longitudinal and lateral control for autonomous vehicles with active load transfer strategy at the handling limits. Proc IMechE, Part D: J Automobile Engineering2021; 235(4): 961–974.
3.
SinghASPNishiharaO. Nondimensionalized univariate equation characterizing optimal state feedback control for collision avoidance. IEEE Trans Intell Transp Syst2018; 19(10): 3344–3359.
4.
HayashiRIsogaiJRaksincharoensakP, et al. Autonomous collision avoidance system by combined control of steering and braking using geometrically optimised vehicular trajectory. Veh Syst Dyn2012; 50(sup1): 151–168.
5.
NilssonJÖdblomACFredrikssonJ.Worst-case analysis of automotive collision avoidance systems. IEEE Trans Veh Technol2015; 65(4): 1899–1911.
6.
WeiSZouYZhangX, et al. An integrated longitudinal and lateral vehicle following control system with radar and vehicle-to-vehicle communication. IEEE Trans Veh Technol2019; 68(2): 1116–1127.
7.
ChenYChenSRenH, et al. Path tracking and handling stability control strategy with collision avoidance for the autonomous vehicle under extreme conditions. IEEE Trans Veh Technol2020; 69(12): 14602–14617.
8.
JohnsonDHustonJ.Nonlinear lateral stability analysis of road vehicles using Lyapunov’s second method. SAE Trans1984; 93: 798–805.
9.
SadriSWuCQ. Lateral stability analysis of on-road vehicles using Lyapunov’s direct method. In: 2012 IEEE intelligent vehicles symposium, Madrid, Spain, 3–7 June 2012, pp.821–826. New York: IEEE.
10.
SadriSWuC.Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents. Veh Syst Dyn2013; 51(6): 906–924.
11.
RossaFDMastinuGPiccardiC.Bifurcation analysis of an automobile model negotiating a curve. Veh Syst Dyn2012; 50(10): 1539–1562.
12.
BobierCGGerdesJC.Staying within the nullcline boundary for vehicle envelope control using a sliding surface. Veh Syst Dyn2013; 51(2): 199–217.
13.
FarroniFRussoMRussoR, et al. A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability. Veh Syst Dyn2013; 51(8): 1265–1285.
14.
LiawDCChiangHHLeeTT. A bifurcation study of vehicle’s steering dynamics. In: IEEE proceedings. Intelligent vehicles symposium, 2005, Las Vegas, NV, USA, 6–8 June 2005, pp.388–393. New York: IEEE.
15.
HashemiEPiraniMKhajepourA, et al. A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models. Veh Syst Dyn2016; 54(12): 1736–1761.
16.
GoodarziANaghibianMChoodanD, et al. Vehicle dynamics control by using a three-dimensional stabilizer pendulum system. Veh Syst Dyn2016; 54(12): 1671–1687.
17.
Bobier-TiuCGBealCEKegelmanJC, et al. Vehicle control synthesis using phase portraits of planar dynamics. Veh Syst Dyn2019; 57(9): 1318–1337.
18.
InagakiSKushiroIYamamotoM.Analysis on vehicle stability in critical cornering using phase-plane method. JSAE Rev1995; 2(16): 216.
19.
ZhaiLSunTWangJ.Electronic stability control based on motor driving and braking torque distribution for a four in-wheel motor drive electric vehicle. IEEE Trans Veh Technol2016; 65(6): 4726–4739.
20.
HanZXuNChenH, et al. Energy-efficient control of electric vehicles based on linear quadratic regulator and phase plane analysis. Appl Energy2018; 213: 639–657.
21.
LiuJZhuangWZhongH, et al. Integrated energy-oriented lateral stability control of a four-wheel-independent-drive electric vehicle. Sci China Technol Sci2019; 62(12): 2170–2183.
22.
LiangYLiYYuY, et al. Integrated lateral control for 4WID/4WIS vehicle in high-speed condition considering the magnitude of steering. Veh Syst Dyn2020; 58(11): 1711–1735.
23.
ZhouCLiuXXuF.Intervention criterion and control strategy of active front steering system for emergency rescue vehicle. Mech Syst Signal Process2021; 148: 107160.
24.
HeJCrollaDALevesleyM, et al. Coordination of active steering, driveline, and braking for integrated vehicle dynamics control. Proc IMechE, Part D: J Automobile Engineering2006; 220(10): 1401–1420.
25.
ChungTYiK.Design and evaluation of side slip angle-based vehicle stability control scheme on a virtual test track. IEEE Trans Control Syst Technol2006; 14(2): 224–234.
26.
ShenSWangJShiP, et al. Nonlinear dynamics and stability analysis of vehicle plane motions. Veh Syst Dyn2007; 45(1): 15–35.
27.
HaoZXian-shengLShu-mingS, et al. Phase plane analysis for vehicle handling and stability. Int J Comput Intell Syst2011; 4(6): 1179–1186.
28.
BealCEBobierCGGerdesJC.Controlling vehicle instability through stable handling envelopes. In: Dynamic systems and control conference, Arlington, VA, USA, 31 October–2 November 2011, vol. 54761, pp.861–868. New York: ASME.
29.
BealCEGerdesJC.Model predictive control for vehicle stabilization at the limits of handling. IEEE Trans Control Syst Technol2012; 21(4): 1258–1269.
30.
LiangXWangQChenW, et al. Coordinated control of distributed drive electric vehicle by TVC and ESC based on function allocation. Proc IMechE, Part D: J Automobile Engineering2022; 236(4): 606–620.
31.
PacejkaHB.Non-linearities in road vehicle dynamics. Veh Syst Dyn1986; 15(5): 237–254.
32.
Di CairanoSTsengHEBernardiniD, et al. Vehicle yaw stability control by coordinated active front steering and differential braking in the tire sideslip angles domain. IEEE Trans Control Syst Technol2012; 21(4): 1236–1248.
33.
LiXXuNGuoK, et al. An adaptive SMC controller for EVs with four IWMs handling and stability enhancement based on a stability index. Veh Syst Dyn2021; 59(10): 1509–1532.
34.
SanduCSanduALiL.Stochastic modeling of terrain profiles and soil parameters. SAE Trans2005; 114: 211–220.
35.
LiLSanduCSanduA. Modeling and simulation of a full vehicle with parametric and external uncertainties. In: ASME international mechanical engineering congress and exposition, Orlando, FL, USA, 5–11 November 2005, vol. 42150, pp.209–214. New York: ASME.
36.
MashadiBAhmadizadehPMajidiM, et al. Integrated robust controller for vehicle path following. Multibody Syst Dyn2015; 33(2): 207–228.
37.
GuoKLuDChenS, et al. The UniTire model: a nonlinear and non-steady-state tyre model for vehicle dynamics simulation. Veh Syst Dyn2005; 43(sup1): 341–358.
38.
GuoKXuNLuD, et al. A model for combined tire cornering and braking forces with anisotropic tread and carcass stiffness. SAE Int J Commer Veh2011; 4: 84–95.
39.
SchoutensW.Stochastic processes and orthogonal polynomials. New York, NY: Springer, 2000.
40.
EldredMWebsterCConstantineP. Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos. In: 4th AIAA multidisciplinary design optimization specialists conference, Schaumburg, IL, USA, 7–10 April 2008, p.1892. Reston, VA: AIAA.
41.
SanduASanduCAhmadianM.Modeling multibody systems with uncertainties. Part II theoretical and computational aspects. Multibody Syst Dyn2006; 15(4): 369–391.
42.
HuangSMahadevanSRebbaR.Collocation-based stochastic finite element analysis for random field problems. Probabilistic Eng Mech2007; 22(2): 194–205.
43.
GhikeCShimT. 14 degree-of-freedom vehicle model for roll dynamics study. SAE technical paper 2006-01-1277, 2006.
44.
ChuW.State estimation and coordinated control for distributed electric vehicles. Berlin, Germany: Springer, 2016.
45.
YaoXGuXJiangP.Coordination control of active front steering and direct yaw moment control based on stability judgment for AVs stability enhancement. Proc IMechE, Part D: J Automobile Engineering2022; 236(1): 59–74.
46.
MokhiamarOAbeM.Simultaneous optimal distribution of lateral and longitudinal tire forces for the model following control. J Dyn Syst Meas Control2004; 126(4): 753–763.
47.
DingHGuoKLiF, et al. Arbitrary path and speed following driver model based on vehicle acceleration feedback. Chin J Mech Eng2010; 46(10): 116–120.
