Tyre-Road Adherence Conditions Estimation for Intelligent Vehicle Safety Applications

Abstract

It is well recognized in the automotive research community that knowledge of the real-time tyre-road friction conditions can be extremely valuable for intelligent safety applications, including design of braking, traction, and stability control systems. This paper presents a new development of an on-line tyre-road adherence estimation methodology and its implementation using both Burckhardt and LuGre tyre-road friction models. The proposed strategy first employs the recursive least squares to identify the linear parameterization (LP) form of Burckhardt model. The identified parameters provide through a Takagi-Sugeno (T-S) fuzzy system the initial values for the LuGre model. Then, it is presented a new large-scale optimization based estimation algorithm using the steady state solution of the partial differential equation (PDE) form of LuGre to obtain its parameters. Finally, real-time simulations in various conditions are provided to demonstrate the efficacy of the algorithm.

Appendix

Vehicle nominal parameters are listed below [6, 10].

$R_w$: Radius of the wheel = 0.3 [m]	$J_w$: Rotation inertia of the wheel = 1 [kg.m$^2$]
$l_f$: Distance from CG to front axles = 1.3 [m]	$l_r$: Distance from CG to rear axles = 1.4 [m]
$d_f,d_r$: Distances between front/rear wheels = 0.9 [m]	h: Height of CG = 0.5 [m]
$M_v$: Mass of the vehicle at CG = 900 [kg]	L: Road/tyre patch length = 0.2 [m]
$\omega _{rot}$: Model parameter of EMB dynamic = 70 [rad/s]	$\mu _c$: Normalized coulomb friction = 0.8
$\sigma _0$: Rubber longitudinal lumped stiffness = 181.54 [1/m]	$\mu _s$: Normalized static friction = 1.55 [m]
$\sigma _1$: Rubber longitudinal lumped damping = 4.94 [s/m]	$\sigma _2$: Viscous relative damping = 0.0018 [s/m]
$\tau _M$: Delay parameter of EMB dynamic = 10 [ms]	$v_0$: Stribeck relative velocity = 6.57 [m/s]
$c_1$: Maximum value of friction curve = [0.19, 1.28]	$c_3$: $\mu (\lambda _{opt})-\mu (1)$ = [6.46, 94.13]
$c_2$: Maximum value of friction curve shape = [0.06, 0.67]