J-function based geometric reasoning for robotics. I. A new distance measure for collision detection and grasping

This paper presents the J-function (Junction) approach to denoting a pseudo distance measure, which can be applied to collision detection, navigation, find space problem and find path problem. Unlike other distance measure, the Junction describes both qualitative and quantative relationships of the spatial locations between two objects A and B. The developed Junction algorithm solves the problems in real world space, configuration space and screw space. At one hand, the Junction´s value represents how far is it between the two objects; at the other hand, its solution will give the geometric and topological relationship between them. In the case of A∩B=Φ, the solution will indicate the nearest point pair