Plane collision course detection between moving objects by transformation of coordinates

This paper deals with the problem of collision course checking between objects moving in a two-dimensional working space. A relative kinematics system is derived, and a transformation of coordinates is applied to simplify the problem. Under this formulation, the collision course checking problem is studied in an equivalent virtual plane, where the collision course problem between two moving objects is reduced to the collision course problem between a virtual moving object and a stationary object. This approach reduces complex scenarios to simple equivalent scenarios. We define two types of collision course, namely the direct collision course and the indirect collision course. Various simulation examples are used to illustrate the method and show the equivalence between the real plane and the virtual plane.