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Inverse-dynamics observer design for a linear single-track vehicle model with distributed tire dynamics

Luigi Romano, Ole Morten Aamo, Jan Åslund, Erik Frisk

Abstract

Accurate estimation of the vehicle's sideslip angle and tire forces is essential for enhancing safety and handling performances in unknown driving scenarios. To this end, the present paper proposes an innovative observer that combines a linear single-track model with a distributed representation of the tires and information collected from standard sensors. In particular, by adopting a comprehensive representation of the tires in terms of hyperbolic partial differential equations (PDEs), the proposed estimation strategy exploits dynamical inversion to reconstruct the lumped and distributed vehicle states solely from yaw rate and lateral acceleration measurements. Simulation results demonstrate the effectiveness of the observer in estimating the sideslip angle and tire forces even in the presence of noise and model uncertainties.

Inverse-dynamics observer design for a linear single-track vehicle model with distributed tire dynamics

Abstract

Accurate estimation of the vehicle's sideslip angle and tire forces is essential for enhancing safety and handling performances in unknown driving scenarios. To this end, the present paper proposes an innovative observer that combines a linear single-track model with a distributed representation of the tires and information collected from standard sensors. In particular, by adopting a comprehensive representation of the tires in terms of hyperbolic partial differential equations (PDEs), the proposed estimation strategy exploits dynamical inversion to reconstruct the lumped and distributed vehicle states solely from yaw rate and lateral acceleration measurements. Simulation results demonstrate the effectiveness of the observer in estimating the sideslip angle and tire forces even in the presence of noise and model uncertainties.
Paper Structure (11 sections, 6 theorems, 29 equations, 5 figures, 1 table)

This paper contains 11 sections, 6 theorems, 29 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Notation
  3. Problem statement
  4. Structure of the considered ODE-PDE system
  5. Observer design
  6. Observer structure
  7. Frequency-domain analysis
  8. Gain injection design and output-feedback control law
  9. Simulation results
  10. Conclusions
  11. Proof of Lemma \ref{['lemma:stablePoles']}

Key Result

Theorem II.1

The ODE-PDE system eq:originalSystems admits a unique mild solution$(\bm{X},\bm{z}) \in C^0([0,T];\mathcal{X})$ for all initial conditions (ICs) $(\bm{X}_0,\bm{z}_0) \triangleq (\bm{X}(0), \bm{z}(\cdot,0)) \in \mathcal{X}$ and inputs $\bm{\delta} \in L^p((0,T);\mathbb{R}^2)$, $p\geq 1$. If, in addit

Figures (5)

  • Figure 1: Schematic of the single track model.
  • Figure 2: Schematic representation of the ODE-PDE interconnection \ref{['eq:originalSystems']}.
  • Figure 3: Behavior of the lumped states and steering inputs, for $\eta=1$ and $\gamma = 500$: (a) kinematic variables; (b) axle forces; (c) steering inputs.
  • Figure 4: Dynamics of $\norm{(\bm{X}(t),\bm{z}(\cdot,t))}_{\mathcal{X}}$, $\norm{(\hat{\bm{X}}(t),\hat{\bm{z}}(\cdot,t))}_{\mathcal{X}}$, and $\norm{(\tilde{\bm{X}}(t),\tilde{\bm{z}}(\cdot,t))}_{\mathcal{X}}$ for $\eta=1$ and $\gamma = 500$.
  • Figure 5: Evolution of the PDE state $\tilde{z}_1(\xi,t)$, along with its IC (blue line) and BC (orange line).

Theorems & Definitions (12)

  • Theorem II.1: Global existence and uniqueness of solutions
  • proof
  • Lemma III.1
  • proof
  • Lemma III.2
  • proof
  • Theorem III.1
  • proof
  • Theorem III.2
  • Lemma 1.1: Shinozaki and Mori LambertAutomatica
  • ...and 2 more