**Dickmanns and Zapp 1986**: An efficient method for guiding high speed land vehicles
along roadways by computer vision has been developed and demonstrated with
image sequence processing hardware in a real-time simulation loop. The approach
is tailored to a well structured highway environment with good lane markings.
Contour correlation and high order world models are the basic elements of the
method, realized in a special multi-microprocessor (on board) computer system.
Perspective projection and dynamical models (Kalman filter) are used in an
integrated approach for the design of the visual feedback control system.

By determining road curvature explicitly from the visual input, previously
encountered steady state errors in curves are eliminated. The performance of
the system will be demonstrated by a video film. The operation of the image
sequence processing system has been tested on a typical Autobahn scene at
velocities up to 100 km/h.

__1. Introduction __

The term ‘mobile’ in the class title “mobile robots” refers to the fact that
the system base can perform locomotion, i.e. translatory displacements. If the
freedom for controllable motion is along one axis, this is called 1D-motion,
even though the trajectory described is a curve in 3D-space, the shape of which
cannot be altered (e.g. a roller-coaster trajectory). The curvature of the
guiding rails in connection with the vehicle speed determines the transversal
accelerations encountered.

Correspondingly, a 2D-motion is defined as a motion in which a vehicle is able
to move on a surface, like ships and ground vehicles. Driving through hilly
terrain in these terms is a 2D-motion, although in Cartesian coordinates the
third motion component is nonzero. Gravity prohibits controllable motion in the
third dimension except along the surface tangent. This determines the gravity
vector, its direction defining the vertical, the tangent slope relative to the
horizontal and the surface curvature as natural metric units. 3D-motion only
occurs in free space, either submarine, in atmospheric flight or in outer
space.

In this type of 2D or 3D-motion the turning of the velocity vector requires
transversal accelerations (or forces); these accelerations are balanced by the
counteracting centrifugal acceleration V^{2}/R = V^{2}∙C,
where V is the velocity magnitude, R the radius of curvature and C = 1/R the ‘curvature’.
It is immediately seen that limited forces for generating transversal
accelerations, for given speed V result in limited curvatures of the
trajectory. In 2D ground surface motion, to which we restrict our attention in
the sequel, lateral forces are generally generated by surface friction and/or
by 3D micro-shape in connection with pressure or shear due to profile / ground
interaction. For conventional road vehicles, depending on the surface
conditions, lateral accelerations are usually limited to the order of magnitude
1 g, for more agreeable riding comfort to about 0.1 g ≈ 1 m/s^{2}).
This means that at V = 10 m/s (36 km/h or 22 mph) the maximal permissible
curvature C_max_10) = 0.01 (R_min_10 = 100 m); for V ≈ 30 m/s (≈ 100
km/h), C_max_30 ≈ 0.001 (R_min_30 = 1 km).

In the usual design of road vehicles lateral control is achieved by
‘steering’, a controlled rotation of the front wheels essentially around a
vertical axis. The steering angle is directly related to the curvature of the
trajectory driven, at least in normal situations; this also suggests that
curvature is a natural parameter for road design. Roads for high speed driving
reflect these facts in that the shape of the transition curves is based on a
linear curvature law (see below) which guarantees continuous curvature changes.
The resulting curves are called “clothoids”, which together with circular arcs
(C = const) and straight line segments (C = 0) are basic elements of well built
roads.