Modified parallel navigation for ball interception by a wheeled mobile robot goalkeeper

This paper deals with the design of a control strategy for a wheeled mobile robot goalkeeper whose task is to intercept the ball before it goes inside the goal. The control law is based on the parallel navigation guidance law where the goalkeeper moves on lines which are parallel to the initial line of sight that joins the robot and the ball. A relative kinematics model in polar coordinates is derived. Two approaches based on two different versions of parallel navigation are used. In the first approach, we introduce a new version for parallel navigation which is adapted to the case of the goalkeeper. In this formulation, the robot is controlled in the linear velocity and moves along a predefined path that covers the goal. The particular case where the goalkeeper moves on the goal line is considered in more detail and important quantities such as the interception time are derived in closed form in some particular cases. In the second approach the robot is controlled in the orientation angle, giving more flexibility for the robot motion. The robot path depends on the ball path, the linear velocities of the robot and the ball, and their initial positions. Ball interception by the goalkeeper is proven in this case also. Our control strategies are illustrated using an extensive simulation.