Roads are usually built from elements of circles, clothoids with intermediate connections, and straight lines; see RAA (2008). Curves have curvatures which develop steadily, such that driving without lateral jerk is possible. The vehicle has to follow the road lane in a straight direction or has to follow the curvatures by cornering with a constant or steadily changing radius. Lateral vehicle control is required for driving maneuvers like cornering, lane change, and parking; see Fig. 19.1.As shown in Fig. 19.2, the vehicle has to follow a lane, ideally in the center of the lane. The geometric form of the lane then defines the vehicle's path. The distance of the center of gravity of the vehicle to the right lane marking is noted by the lateral distance D y . (Also the distance of the front axle or of the right front wheel to the right lane marking may be used.)In the case of circles, the curvature κ = 1/R is inverse proportional to the radius, and clothoids have a curvature which is proportional to the path length L, κ = c cl L.The control of vehicles along a straight or bending lane means that the driver or an automatic controller has to follow a certain path: y = f (x). If this can be performed without time condition, it is called path control. The state variables for the position are x and y and for the orientation of the vehicle, the yaw angle ψ or the course angle ν = ψ + β; see Fig. 20.1. The manipulated variable is the steering wheel angle δ f for a car with front steering. If the position y(x) has to be reached at a certain time t, such that y = f (x, t), this a called trajectory control. Hence, for path control, the lateral motion has to be controlled and for trajectory control, the lateral and longitudinal motion; see Sect. 18.2.The lane markers are usually detected with cameras located behind the windscreen for forward looking. Monocular cameras provide, for example, a ±20 • field of view and ranges up to 80 m. Corresponding image processing then provides the distance to line crossing (DLC) or time to line crossing (TLC) in front of the vehicle and based on a lane marking approximation with polynomials or clothoid functions with the curvature κ and its first derivative dκ/dx in a distance x τ ahead. For more details, see Winner et al. (2016) andSchmitt (2012).