Lateral tracking control of all-wheel steering vehicles with intelligent tires

TL;DR

This paper tackles the challenge of robust lateral tracking for all-wheel-steering vehicles equipped with intelligent tires by formulating a coupled ODE-PDE model that captures rigid-body dynamics and distributed tire deformation. It proposes a model-based, output-feedback controller with an observer, leveraging PDE stability to decouple estimation from control and to suppress micro-shimmy while achieving accurate path tracking via force control. Key contributions include a rigorous ODE-PDE stability framework, a backstepping-style output-feedback controller, and an observer that ensures exponential convergence of state estimates, all validated on a nonlinear double-track vehicle with distributed tires. The work offers a pathway toward safer, energy-efficient autonomous driving using smart-tire sensing, with future directions in adaptive estimation and real-vehicle validation, particularly near nonlinear handling limits.

Abstract

The accurate characterization of tire dynamics is critical for advancing control strategies in autonomous road vehicles, as tire behavior significantly influences handling and stability through the generation of forces and moments at the tire-road interface. Smart tire technologies have emerged as a promising tool for sensing key variables such as road friction, tire pressure, and wear states, and for estimating kinematic and dynamic states like vehicle speed and tire forces. However, most existing estimation and control algorithms rely on empirical correlations or machine learning approaches, which require extensive calibration and can be sensitive to variations in operating conditions. In contrast, model-based techniques, which leverage infinite-dimensional representations of tire dynamics using partial differential equations (PDEs), offer a more robust approach. This paper proposes a novel model-based, output-feedback lateral tracking control strategy for all-wheel steering vehicles that integrates distributed tire dynamics with smart tire technologies. The primary contributions include the suppression of micro-shimmy phenomena at low speeds and path-following via force control, achieved through the estimation of tire slip angles, vehicle kinematics, and lateral tire forces. The proposed controller and observer are based on formulations using ODE-PDE systems, representing rigid body dynamics and distributed tire behavior. This work marks the first rigorous control strategy for vehicular systems equipped with distributed tire representations in conjunction with smart tire technologies.

Figures (12)

• Figure 1: Single-track vehicle model with four-wheel steering. The kinematic variables are depicted in blue, whereas the dynamic ones in red.
• Figure 2: Schematic representation of the ODE-PDE interconnection \ref{['eq:ssOriginal']}-\ref{['eq:B1Origin']}, with $\mathbb{R}^2\ni \bm{U}_1(t) \triangleq \mathbf{A}_2\bm{Y}(t)$, $\mathbb{R}^2 \ni \bm{U}_2(t) \triangleq \mathbf{A}_3\bm{x}(t) + \mathbf{B}\bm{\delta}(t)$, and $\bm{Y}(t)$ given according to \ref{['eq:tireForce']}.
• Figure 3: Stability charts for the single-track model with distributed tires, as described by \ref{['eq:ssOriginal']}, for different values of the ratio $\chi \triangleq C_1l_1/(C_2l_2)$ and longitudinal speed $v_x$. The unstable regions (shaded) correspond to combinations of parameters for which $\det(A(s))$ has two roots with positive real part. Model parameter values as in Table \ref{['table:Param1']}.
• Figure 4: Typical shimmy behavior of an understeer vehicle traveling at low speed ($v_x = 0.4$$\text{m}\,\text{s}^{-1}$). Model parameter values as in Table \ref{['table:Param1']}.
• Figure 5: True (solid blue line) and estimated (dashed orange line) states for the nonlinear double-track model operating in an unstable parameter region associated with micro-shimmy oscillations, and subjected to the control input \ref{['eq:controlInputYFeed']} with $\bm{x}_\textnormal{ref}(t) = \bm{x}^\star = \bm{0}$, after $t = 2$ s.

Theorems & Definitions (19)

• Remark 2.1
• Lemma 2.1: Stability of the linear single-track model with distributed tires
• proof
• Lemma 2.2
• proof
• Proposition 3.1: Stabilizability of the ODE systems \ref{['eq:ssOriginalODE']} and \ref{['eq:Yref']}
• proof
• Lemma 3.1
• proof
• Lemma 3.2