Catchability of a moving object by a robot

Catching a moving object by a robot is studied in the framework of a pursuer-evader problem. The models of the robot and the moving object in the world coordinate system are assumed to be linear, after feedback linearization, and discrete in time. A performance criterion for the system is quadratic and contains a measure of the distance between the robot and the object. The problem is then to minimize the performance criterion with respect to the robot control and maximize it with respect to the object control subject to the dynamics of the robot and the moving object. The definition of the catchability of the moving object by the robot is then introduced. It is based on the existence of the inverse matrix obtained as the solution to the discrete-time Riccati equation. The catchability condition thus established can be viewed as the difference of the reduced controllability matrices of the robot and the moving object.