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.
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 V2/R = V2∙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/s2). 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.