Algorithms and techniques for manufacturing

This dissertation investigates the application of computer science techniques to tasks in manufacturing. Many of these techniques are founded upon three underlying approaches: machine vision techniques, generate and test techniques, and classical algebraic geometry techniques. The ten main algorithms presented in this thesis are: recognizing and localizing prismatic parts using a crossbeam sensor, recognizing and localizing prismatic parts using a scanning beam sensor, constructing complete indexing tables to recognize objects from crossbeam sensor data and scanning beam sensor data, localizing features of dissimilar types, enumerating all fixture configurations capable of immobilizing a given prismatic polyhedral object, enumerating all fixture configurations capable of immobilizing a given prismatic generalized polyhedral object, reducing the problem of enumerating modular fixture designs to the problem of constructing complete indexing tables, constructing complete indexing tables for generic systems, using tree grid structures to compact indexing tables, calibrating point probe and line probe sensors, and calibrating the end effector arm of high precision manipulators. We discuss the implementation of these algorithms and their performance on a number of examples. These techniques are also applicable to other problems in computer vision, and robotics. The thesis consists of twelve chapters. Each chapter has been organized independently. Chapter 1 gives a brief overview of the thesis. In Chapter 2 we present the algorithm for recognizing and localizing prismatic parts using a crossbeam sensor, and discuss its implementation and performance. Chapter 3 describes the algorithm for recognizing and localizing parts using a scanning beam sensor and provide performance measurements. In Chapter 4, we present an exact algorithm for localizing features of dissimilar types by reducing it to a nonlinear least squares problem which is solved using a combination of algebraic and numerical techniques. In Chapter 5, we discuss a complete modular fixture design algorithm which efficiently enumerates all fixture configurations for immobilizing a given prismatic polyhedral workpiece. In Chapter 6, we extend this algorithm to handle prismatic generalized polyhedral workpieces. In Chapter 7, we discuss the duality between modular fixturing and scanning which provides a generic algorithm for designing fixtures for arbitrary workpieces and arbitrary minimal fixture toolkits. In Chapter 8, we describe a technique for constructing complete indexing tables, thereby enabling indexing techniques to be used for systems which do not exhibit invariants. In Chapter 9, we describe the tree grid indexing mechanism which reduces the size of indexing tables, and also provides for coherent searches. In Chapters 10 and 11, we discuss calibration issues which are prerequisites for exploiting the high precisions achieved by the sensing strategies. Finally, in Chapter 12 we conclude the thesis and discuss problem areas for future research.