Mathematical Simulation and Research of Optimal Configurations of a Triangulation Optoelectronic System when Backlighting the Object Space with a Single Strip

Abstract

The article discusses the theoretical research of triangulation optoelectronic systems consisting of a video camera and a source of structured illumination in the form of a single straight strip. Such optoelectronic systems can be used for solving various problems of three-dimensional modeling, for example, in the problem of detecting obstacles in front of an autonomous mobile robot. The aim of this work is to identify the optimal configuration of such systems to achieve the best accuracy in determining the size of the observed objects, as well as the distances to them. Using the apparatus of analytical geometry, linear algebra and mathematical analysis, a mathematical model of such a system has been developed, taking into account various internal parameters and technical characteristics of the video camera and the structured light source, as well as the relative position and orientation of the camera and the source. Using the constructed mathematical model, equations were obtained allowing estimating the error in calculating the distances to the detected objects. The question of the optimal configuration of such optoelectronic systems is examined, as well as optimality criteria: minimization of errors in determining the distance, the smallest height of the detected objects. The obtained theoretical results can be used in control systems for unmanned vehicles, in systems for non-destructive testing of industrial products, and in further studies of optoelectronic systems of this type