Longitudinal control For Nonlinear
Vehicle’s Dynamics
M. El Adel, M. Ouladsine and C.Urrea
LSIS CNRS UMR 6168
Domaine Universitaire de Saint Jérôme
Av. Escadrille Normandie Niémen 13397 Marseille Cedex 20
Tél. :0491056062, Fax : 0491056033
Email : mustapha.ouladsine@lsis.org
Abstract-In this paper, a longitudinal control for a nonlinear vehicle’s dynamics is presented. A platoon of vehicles following a lead car is considered. The proposed control law is established in order to avoid the collisions in a file of cars in a motorway. Simulation results are presented to illustrate the effectiveness of the presented approach.
Keywords- Non linear systems, orthogonal Laguerre basis, longitudinal vehicle control.
I- Introduction
Due to increasing traffic congestion, there has been a renewed interest in the development of an AHS in which high traffic flow rates may be safely achieved. Since the many of today’s automobile accidents are caused by human error, automating the driving process may actually increase the safety of the highway. Vehicles will be driven automatically with onboard lateral and longitudinal controllers. The lateral controllers will be used to steer the vehicles around corners, make lane changes, and perform additional steering tasks. The longitudinal controllers will be used to maintain a steady velocity if a vehicle is traveling alone, follow a lead vehicle at a safe distance (car following, see Fig.1), or perform other speed/tracking tasks. Many works have been considered this problem of car following [3], [12] and references therein. The main problem in this situation is the loss of communication between the lead vehicle and the other vehicles in a platoon. In this paper, the interaction terms are considered to be unknown, and are predicted by using the orthogonal Laguerre basis of functions. Such basis has proved to be useful for dealing with this situation of the interconnection terms [6-8]. The paper is organized as follows:
In section 2, a problem statement is presented. The proposed control law is given in section 3. In section 4, simulation results are presented. A fundamental Laguerre functions is presented in appendix.
II- Problem statement
Consider a platoon of vehicles described by figure 1 where each car is represented by the abscissa with respect to a fixed point O. It is considered that the dynamics of the i vehicle is described by the state vector such that: thi?Tiiif?X][=
1--=iiixx? (1)
)1(-icar)(icar)1(+icar1-ixix1+ixiLii++s??Fig.1 Car following within an automated lane
ix(-i denotes the position of the i vehicle and denotes the position of the lead vehicle.th1-ixi? is the inter-vehicle spacing between the i and the thth)1 vehicle
i? is the ivehicle’s velocity and is the driving / braking force applied to the longitudinal dynamics of the ivehicle. thifth
The simple model used to describe the engine dynamics [12] is considered as follows:
)(1iiiuff+-=t& (2)
Assuming that the ivehicle is modeled as a particle of mass, one has: thm
) (12iipifdKm+--=??& (3)
where and denote respectively the aerodynamic and mechanical drag coefficients. pKd
The longitudinal dynamics may be expressed [3] by the following nonlinear equations:
)(1) (121iiiiiiiiiufffdAm+-=+--=-=-t??????&&& (4)
where is the control input (if u, then it represents the throttle input, and if u it represents a brake input). The vehicle parameters are summarized in the following table: iu0>i0<i

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