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Identification of tire forces using Dual Unscented Kalman Filter algorithm

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An Erratum to this article was published on 07 November 2014

Abstract

Nowadays, application of active control systems in vehicles has been developed in order to increase safety and steerability. In these systems, using an appropriate dynamic model can be very effective in increasing the accuracy of simulations and analysis. Tire-road forces are crucial in vehicle dynamics and control since they are the only forces that a vehicle experiences from the ground and have maximum uncertainty on vehicle dynamic model. In order to simulate the non-linear regimes of vehicle motion, the ‘Pacejka’ tire model is being utilized. In this paper, a dynamic model with Dual Unscented Kalman Filter algorithm has been utilized to identify the lateral forces, side slip angle, and normal forces of tires. In order to solve the non-linear least squares problem, these parameters were given as input to the hybrid Levenberg–Marquardt and quasi Newton algorithm to find the Pacejka tire model coefficients in the offline mode. Four degrees of freedom vehicle model combined with Pacejka tire model are used for simulation in various maneuvers. Results show appropriate compatibility with CarSim software.

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Abbreviations

\(a_x \) :

Longitudinal acceleration

\(a_y \) :

Lateral acceleration

m:

Vehicle mass

\(m_s\) :

Sprung mass

\(I_z\) :

Moment of inertia about z axis

\(I_x\) :

Moment of inertia about x axis

\(I_{xz}\) :

Product of moment of inertia

a:

Distance of vehicle C.G from front axle

b:

Distance of vehicle C.G from rear axle

l:

Distance between two axle

h:

Height of C.G

\(h_s\) :

Height of roll center

T:

Track

\(\rho \) :

Density of air

\(C_d\) :

Drag coefficient

\(A_p\) :

Frontal area projection

\(\mu _R\) :

Rolling resistance coefficient

\(K_\phi \) :

Roll stiffness

\(D_\phi \) :

Roll damping

\(\delta \) :

Wheel steer angle

\(\alpha \) :

Tire side slip angle

\(F_z\) :

Tire normal load

\(F_y\) :

Lateral tire force

\(\sigma \) :

Relaxation length

BCD:

Tire lateral stiffness

C:

Shape factor

D:

Peak factor

B:

Stiffness factor

E:

Curvature factor

\(S_h\) :

Horizontal shift

\(S_v\) :

Vertical shift

\(a_0 ,\ldots ,a_{13}\) :

Parameters of Pacejka -tire model

\(\gamma \) :

Camber angle

\(\tau \) :

Step size

u:

Longitudinal velocity

v:

Lateral velocity

r:

Yaw rate

\(\phi \) :

Roll angle

p:

Roll rate

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Authors and Affiliations

  1. Department of Automotive Engineering, Iran University of Science & Technology, Tehran, Iran

    Iraj Davoodabadi, Ali Asghar Ramezani & Pouyan Ahmadizadeh

  2. Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Parand, Iran

    Mehdi Mahmoodi-k

Authors
  1. Iraj Davoodabadi
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  2. Ali Asghar Ramezani
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  3. Mehdi Mahmoodi-k
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  4. Pouyan Ahmadizadeh
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Correspondence to Mehdi Mahmoodi-k.

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Davoodabadi, I., Ramezani, A.A., Mahmoodi-k, M. et al. Identification of tire forces using Dual Unscented Kalman Filter algorithm. Nonlinear Dyn 78, 1907–1919 (2014). https://doi.org/10.1007/s11071-014-1566-z

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  • DOI: https://doi.org/10.1007/s11071-014-1566-z

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