MODELING AND SIMULATING A NARROW TILTING CAR
Salim Maakaroun, Wisama Khalil, Maxime Gautier and Philippe Chevrel
Institut de Recherche en Communication et Cybernétique de Nantes, 1 rue de la Noe, Nantes 44321, France
Keywords: Intelligent Transportation Systems, Modelling, Simulator, Robotics, Tilting car.
Abstract: The use of an electrical narrow tilting car instead of a large gasoline car should significantly decrease traffic
congestion, pollution and parking problem. The aim of this paper is to give an approach to develop a
dynamic model for narrow cars. This model can be used to simulate their behaviours and evaluate tilt
control systems. The approach is based on considering the vehicle as a multi-body poly-articulated system
and the modelling is carried out using the robotics formalism based on the modified Denavit-Hartenberg
geometric description.
1 INTRODUCTION
The idea behind narrow tilting car research is to
develop a vehicle used in urban transportation
having the advantages of motorcycle and passenger
car. This will reduce the size of the vehicle such that
it can be operated on reduced size lanes thereby
increasing the effective capacity of highways. In
order to maintain its stability, the vehicle should tilt
while cornering, to compensate the effect of lateral
acceleration and remain in its trajectory. Moreover
the use of electric motors with a group of batteries is
the most earth friendly technology.
In the literature, many works have been
published on the topic of tilting narrow vehicle.
Karnopp and Fang (Karnopp, 1992) were the first to
suggest a leaning into the turn similar like
motorcyclist’s one. Karnopp, Hibbard and So
(Hibbard, 1992. So, 1997) studied the tilt angle
required and the dynamics of such a vehicle. But
few people talked about the global dynamic model
of a four wheel tilting car. Rajamani, Gohl and
Alexander (Gohl, 2006) developed a dynamic model
of a three wheel vehicle which has four degrees of
freedom including lateral and tilt dynamics. All
these models don’t take into account the dynamics
of the suspensions, the vertical dynamic and the
study was on a simplified model called bicycle
model. Therefore to model a complex system in 3D
motion, many methods can be used. Kiencke
described his model with 4 individual co-ordinate
systems (Kiencke, 2000) while Rajamani with 6 co-
ordinate system (Rajamani, 2006). We claim that it
is preferable to proceed in a systematic method of
geometrical description, based on the modified
Denavit-Hartenberg parameterization (Khalil, 1986).
The last was applied on a two wheeled vehicle
model with suspensions (Maakaroun, 2011). This
description allows to automatically calculate the
symbolic expression of the geometric, kinematic and
dynamic models by using a symbolic software
package SYMORO+ (Symbolic Modelling of
Robots) (Khalil, 1997). Moreover, the dynamical
model can be calculated numerically using
programming software as Matlab, C++. This
formulation leads to a minimum set of equations
where the constraint equations for the mechanical
system are automatically eliminated.
This paper concentrates on developing a global
dynamic model for a narrow tilting car “Lumeneo
Smera “ (Lumeneo, 2003) by applying methods used
in robotics. Since the structure of the Smera is
complex and contains loops, this approach can
elaborate systematically the symbolic equations of
motion and makes the implementation of the
dynamic model very easy. This method is described
and applied on the car in section 2. Then Kinematics
and dynamics models are given in section 3 and 4.
Finally, simulation results are illustrated and
commented and conclusions are done.
2 GEOMETRIC DESCRIPTION
OF THE CAR
2.1 Robotic Representation of a
Multi-body System
The car is considered as a mobile tree-structured
229
Maakaroun S., Khalil W., Gautier M. and Chevrel P..
MODELING AND SIMULATING A NARROW TILTING CAR.
DOI: 10.5220/0003538102290235
In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 229-235
ISBN: 978-989-8425-75-1
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)