Kinematics-based characterization of the collision course

The problem of collision course between a mobile robot and a moving object is modeled in polar coordinates using the kinematics equations. A model of the relative motion of the moving object as seen by the robot is then derived. This model consists of the relative velocities along and across the visibility line, and gives the range rate and the turning rate of the moving object with respect to the robot. The conditions for the collision course are derived in terms of the robot's and the moving object's states. We define two types of collision course: the exact collision course and the weak collision course. The exact collision course always results in a collision, and is clearly characterized by a given set of equations. The weak collision course may become an exact collision course near collision and allows an early detection of the collision course in various scenarios. Several examples and scenarios illustrating the theory are shown using simulation.