Study and application of geometric concepts in the movement of a vehicle using cartesian coordinates

Abstract

Autonomous vehicles are already a reality in many contexts. Most of them need sensors to move around their environment, which increases the complexity and cost of the project. This study uses the coordinates of the Cartesian plane to orient a prototype vehicle in relation to its geographic space, allowing it to move to predefined coordinates without the use of any sensors. For the steering system of the prototype, concepts of point, line, and vectors were used. The initial position of the vehicle is represented by a vector, which informs its direction in the plane, having as final destination any point in the Cartesian system. From this information, a displacement vector is created, which leads the prototype to the reference point, and indicates the angle it must rotate. Regarding the direction of rotation, the concept of parallel lines between the prototype's vector and the destination point was used, where the analysis of their y-intercept determines if the vehicle rotates to the left or right. So, with the use of vectors and the Cartesian plane, it was possible to determine fundamental information for the locomotion of the prototype, such as angle and direction of rotation, although there was some difficulty in determining the graphic location of the vector.