1
Observers With Unknown Inputs to Estimate
Contact Forces and Road Profile
A. Rabhi1, H. Imine1, N. M’ Sirdi1 and Y. Delanne2
1LRV, FRE 2659 CNRS, Universit´e de Versailles St Quentin
10, avenue de l’Europe 78140 V´elizy, FRANCE. nkms@free.fr
2 LCPC: Division ESAR BP 44341 44 Bouguenais cedex
Abstract—This paper presents sliding mode observers
designed to estimate tire forces and road profile.
Tire forces aect the vehicle dynamic performance and
behavior properties. The tire forces and road friction
are dicult to measure and their modelling is rather
complex. In this work we deal with a simple model
of vehicle combined with sliding mode approach to
develop robust observers.
Index Terms—Nonlinear observers, Sliding Modes,
Vehicle-Road Interaction Models, State Estimation,
Tire Forces, Road Profile.
I. Introduction
Knowledge of tire forces is essential for systems such as
antilock braking systems (ABS), traction control systems
(TCS) and electronic stability program (ESP). Vehicle
dynamics depend largely on the tire forces which are
nonlinear functions of wheel slip and slip angles and
depend on some factors such as tire wear, pressure, normal
load tire road interface properties [1][2][3]. Recently, many
analytical and experimental studies have been performed
on estimation of the frictions and contact forces between
tires and road [4][5][6]. The tire forces aect the vehicle
dynamic performance and behavior properties. Thus for
vehicles and road safety analysis, it is necessary to take
into account the contact force characteristics. However,
tire forces and road friction are dicult to measure directly
and complex to be precisely represented by some
deterministic equations. Vehicle dynamics depends largely
on the tire forces represented by the nonlinear functions
of wheel slip. The tire models encountered are complex
and depend on several factors (as load, tire pressure,
environmental characteristics, etc.). This makes on line
estimation of forces and parameters dicult for vehicle
control applications like detection and diagnosis for driving
monitoring and surveillance. In this paper, modelling of
the contact forces and interactions between a vehicle and
road is revisited in the objective of on line force estimation
using robust observers coupled with a robust and adaptive
estimation of contact forces. We propose a robust observer
to estimate the vehicle state and an adaptive estimator for
tire forces identification[7]. The designed observer is based
on the sliding mode approach. The main contribution
is on-line estimation of inputs (the tire forces and road
profile) needed for control. In this work, we deal with a
simple vehicle model coupled with an appropriate wheelroad
contact model in order to estimate contact forces.
Then, we develop a method to observe tire forces and road
profile.
This paper is organized as follows. Section 2 deals with
the vehicle description and modelling for estimation of
contact forces. The design of an observer and an adaptive
tire force estimation is presented in section 3. Section 4 is
devoted to develop an observer with unknown inputs to
estimate the road profile. Some results about the states
observations and estimation of the two kinds of unknown
inputs are presented in section 5. Finally, some remarks
and perspectives are given in a concluding section.
II. VEHICLE MODELLING
In the literature, many studies deal with vehicle modelling
[8][9][10]. The objective may be either analysis for
better design and features enhancement or increase of
safety and maniability. The vehicle is a complex mechanical
system that exhibits nonlinear behaviors. Commonly,
the proposed and used models are not very complicated
and give partial representation of the system dynamics.
It would be relatively dicult and intricacy to involve
more complete models and to define the size of dierent
parameters. Several models have been considered in
literature for analysis of the road - vehicle interaction
and its consequence on the behavior (see eg Figures 1
and 2). The motions (longitudinal, lateral, and vertical)
depend on interaction between the wheels and the road,
the disruptions and the gravity.
Fig. 1. Half Vehicle Longitudinal and Vertical Model (x, z, ')
We generally we can distinguish three types of vehicle
models:
- Longitudinal (Figures 1)
- Lateral
- longitudinal + lateral (Figure 2).
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