A Group Theoretic Approach to Assembly Planning

high-level robotic assembly planning. An assembly is a collection of bodies that are spatially related. When two bodies in an assembly are related, they do not make contact over their whole surface; rather, features of each body are in contact. For the moment, let us think of a feature as some part of the surface of a body. Thus, for example, a journal on a shaft fits a bearing, the teeth of gears mesh, the threaded portion of the shank of a bolt fits a hole tapped in some body. All these relationships between bodies can be described as liaisons (Bourtjault 1984, De Fazio, and Whitney 1987). For the purpose of automatic generation of assembly plans, it is necessary to represent the shapes of assembly components, locations of components, and the spatial relations between bodies in a systematic computational form. One of the important aspects of shape representation that is relevant to assembly planning and mechanical design is the symmetry of shapes and their features. A symmetry of a feature is simply a rotation or translation that maps this feature to itself.1 In assembly planning, the symmetry of features is usually more important than the symmetry of the bodies to which the features belong because bodies are mated through their features. For example, consider a cylindrical hole in a block. This feature is mapped into itself by We treat robotic assembly planning on two distinct conceptual levels. Planning at the higher level involves deriving nominal trajectories along which the bodies to be assembled are to be moved. These trajectories are nominal in the sense that they would accomplish the assembly were we to have a perfect robot manipulating bodies whose shapes were perfectly accurate. Planning at the lower level transforms such a high-level specification into an assembly plan that takes account of uncertainty. In this article, we are primarily Articles