An observer-based approach for the projection onto a 2d-curve under movement

Standard path control laws of autonomous vehicles use the shortest distance between the vehicle’s position and the path as a control error. In order to determine this distance, the projection point onto the path needs to be determined continuously. This requires fast algorithms that feature high numerical reliability in the field of vehicle application.This paper presents two different observer-based approaches for the projection problem. The identity observer reconstructs all states of interest for path control. The second one, a reduced observer, only possesses the curve parameter as a state and calculates the other values by algebraic formulas. Both algorithms consider the continuous movement of the vehicle, the run of the curve, and work without any approximation of the curve. Furthermore, they are applicable for arbitrary parameterized smooth curves, guarantee the required numerical stability, have short calculating time, and show good statistical properties. The performance is shown in several simulations as well as under real conditions.

Research highlights
► Continuous orthogonal projection of a moving point onto a 2d curve.
► Well-tested observer-based approach which guarantees high numerical stability.
► The problem is reduced to solving basically one differential equation.
► No approximation of the arbitrary parametrable curve needed.
► The kinematics of the moving point are considered.