Collision course by transformation of coordinates and plane decomposition

Abstract

This paper deals with the problem of collision course checking in a dynamic environment for mobile robotics applications. Our method is based on the relative kinematic equations between moving objects. These kinematic equations are written under polar form. A transformation of coordinates is derived. Under this transformation, collision between two moving objects is reduced to collision between a stationary object and a virtual moving object. In addition to the direct collision course, we define the indirect collision course, which is more critical and difficult to detect. Under this formulation, the collision course problem is simplified, and complex scenarios are reduced to simple scenarios. In three-dimensional (3D) settings, the working space is decomposed into two planes: the horizontal plane and the vertical plane. The collision course detection in 3D is studied in the vertical and horizontal planes using 2D techniques. This formulation brings important simplifications to the collision course detection problem even in the most critical and difficult scenarios. An extensive simulation is used to illustrate the method in 2D and 3D working spaces.