A Group Theoretic Approach to Assembly Planning

Abstract

HIGH LEVEL ROBOTIC ASSEMBLY PLANNING IS CONCERNED WITH HOW BODIES FIT TOGETHER AND HOW SPATIAL RELATIONSHIPS AMONG BODIES ARE ESTABLISHED OVER TIME. IN ORDER TO GENERATE AN ASSEMBLY TASK SPECIFICATION FOR ROBOTS, IT IS NECESSARY TO REPRESENT THE GEOMETRIC SHAPES OF THE ASSEMBLY COMPONENTS IN A COMPUTATIONAL FORM. ONE OF THE PRINCIPAL ASPECTS OF SHAPE REPRESENTA- TION THAT IS RELEVANT FOR ASSEMBLY TASKS IS THE SYMMETRY OF THE SHAPE. GROUP THEORY IS THE STANDARD MATHEMATICAL TOOL FOR DESCRIBING SYMMETRY. THE INTERACTION BETWEEN ALGEBRA AND GEOMETRY WITHIN A GROUP THEORETIC FRAMEWORK HAS PROVIDED US WITH A UNIFIED COMPUTATIONAL TREATMENT OF REASON- ING ABOUT HOW PARTS WITH MULTIPLE CONTACTING FEATURES FIT TOGETHER.