Planning motion in contact to achieve parts mating

Abstract

The research presented in this thesis focuses on planning a parts mating task by formulating a plan for a motion in contact. Specifically, it deals with the problem of moving a 3-dimensional polyhedral object while maintaining contact with a set of stationary obstacles. An algorithm has been developed and implemented which derives a motion plan as as sequence of contacts that have to be established during a motion from some initial to some final contact state.

A configuration space approach to motion planning has been adopted. In planning a motion in contact, a subset of the configuration space, the contact space, is of relevance. The contact space is decomposed into faces of various dimensions and adjacency relations between the faces are determined. For a path-connected contact space, if the 0-dimensional faces (vertices) are connected by 1-dimensional faces (edges), then the motion planning problem is reduced to the problem of searching for a path in the graph of vertices and edges.

The algorithm has two stages. In the first stage, the graph of the surfaces of various dimensions, on which the faces of the contact space lie, is found, and in the second stage, the vertices and edges are determined. The implemented algorithm makes use of a spatial reasoning system for finding the intersections of surfaces and a solid modeller for checking physical interference.

Spatial relationships are used to represent the constraints on the relative location of objects imposed by contacts. Using a spatial reasoning system based on the RAPT inference engine, it is possible to associate a spatial relationship with every contact state. The spatial relationship is arrived at by considering conjunctions of 5 degree of freedom spatial relationships which describe the basic types of contact among polyhedral objects.

The plan for a motion in contact is thus formulated in terms of the interactions between features of objects. A method for transforming the plan into a sequence of motions with sensory involvement could follow naturally from such a formulation of the problem.