A sufficient condition for capturing an object in the plane with disc-shaped robots

Abstract

An object is captured when it is restricted to stay within a bounded region of the workspace. In this paper, we present a sufficient condition for a team of disc-shaped robots to capture a two dimensional rigid object in the plane by enclosing it in a capturing formation. This condition is defined in terms of the robots' positions and a certain geometric property of the object. We do not assume any particular geometry, therefore the condition immediately holds for all object shapes. We also sketch an application of the capturing formation to the problem of object manipulation.