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

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.

First-order friction models with bristle dynamics: lumped and distributed formulations

Dynamic models, particularly rate-dependent models, have proven effective in capturing the key phenomenological features of frictional processes, whilst also possessing important mathematical properties that facilitate the design of control and estimation algorithms. However, many rate-dependent formulations are built on empirical considerations, whereas physical derivations may offer greater interpretability. In this context, starting from fundamental physical principles, this paper introduces a novel class of first-order dynamic friction models that approximate the dynamics of a bristle element by inverting the friction characteristic. Amongst the developed models, a specific formulation closely resembling the LuGre model is derived using a simple rheological equation for the bristle element. This model is rigorously analyzed in terms of stability and passivity -- important properties that support the synthesis of observers and controllers. Furthermore, a distributed version, formulated as a hyperbolic partial differential equation (PDE), is presented, which enables the modeling of frictional processes commonly encountered in rolling contact phenomena. The tribological behavior of the proposed description is evaluated through classical experiments and validated against the response predicted by the LuGre model, revealing both notable similarities and key differences.

Semilinear single-track vehicle models with distributed tyre friction dynamics

This paper introduces a novel family of single-track vehicle models that incorporate a distributed representation of transient tyre dynamics, whilst simultaneously accounting for nonlinear effects induced by friction. The core of the proposed framework is represented by the distributed Friction with Bristle Dynamics (FrBD) model, which unifies and extends classical formulations such as Dahl and LuGre by describing the rolling contact process as a spatially distributed system governed by semilinear partial differential equations (PDEs). This model is systematically integrated into a single-track vehicle framework, where the resulting semilinear ODE-PDE interconnection captures the interaction between lateral vehicle motion and tyre deformation. Two main variants are considered: one with rigid tyre carcass and another with flexible carcass, each admitting a compact state-space representation. Local and global well-posedness properties for the coupled system are established rigorously, highlighting the dissipative and physically consistent properties of the distributed FrBD model. A linearisation procedure is also presented, enabling spectral analysis and transfer function derivation, and potentially facilitating the synthesis of controllers and observers. Numerical simulations demonstrate the model's capability to capture micro-shimmy oscillations and transient lateral responses to advanced steering manoeuvres. The proposed formulation advances the state-of-the-art in vehicle dynamics modelling by providing a physically grounded, mathematically rigorous, and computationally tractable approach to incorporating transient tyre behaviour in lateral vehicle dynamics, when accounting for the effect of limited friction.