Jianbo Gou

Geometric algorithms for workpiece localization

We present a unified geometric theory for localization of three types of workpieces: 1) general three-dimensional (3D) workpieces where points from the finished surfaces fully constrain the rigid motions of the workpieces; 2) symmetric workpieces; 3) partially machined workpieces where points from the finished surfaces are inadequate to fully constrain the rigid motions of the workpieces. Applications of the study include workpiece setup, refixturing and dimensional inspections in a flexible manufacturing environment. First, we formulate the localization problem for a general 3D workpiece and study the mathematical properties of the underlying problem. We discuss an iterative approach for solving the general localization problem and show how different considerations in updating the Euclidean transformation lead to various geometric algorithms. Then, we extend the localization techniques to symmetric workpieces and partially machined workpieces and present a simple algorithm for each of the problems. Finally, we present simulation results showing convergence and robustness properties of the various geometric algorithms.

Performance analysis of localization algorithms

Workpiece localization, with novel applications such as workpiece setup, refixturing and dimensional inspections, is a problem of permanent importance in manufacturing. Using the popular least square formulation, several geometric algorithms have been developed for workpiece localization over the last few years. In this paper, we analyze and compare the performance of three localization algorithms based on the following criteria: (a) robustness with respect to variations in initial conditions; (b) accuracy of computed results; and (c) computational efficiency. We develop an approach for improving the robustness of the algorithms for workpieces with sculptured surfaces for which the region of convergence is typically small. Based on simulation results, we also discuss sensitivity of the algorithms with respect to the number of measurement points and give a lower bound on this number for recovering a Euclidean transformation with certain accuracy.

Workpiece localization algorithms: Performance evaluation and reliability analysis

Abstract Workpiece localization plays an important role in automation of many manufacturing processes, such as workpiece setup, refixturing, dimensional inspection, and robotic assembly/manipulation. This paper provides unified treatment of three geometric algorithms for workpiece localization. Local convergence of these localization algorithms is shown, and new techniques are developed to make these local algorithms globally convergent. A method is presented for analyzing the reliability of localization solutions. Along with extensive simulation results, the performance of the algorithms is studied and analyzed in terms of accuracy, convergence, and computational efficiency. The Hong-Tan algorithm has better accuracy and computational efficiency than two other algorithms tested. Finally, the experimental implementation of the algorithms is performed, and the experimental results are presented to confirm the proposed global convergence method and the reliability analysis method.

Localization algorithms: performance evaluation and reliability analysis

Workpiece localization plays a vital role in automation of many important manufacturing processes, such as workpiece setup, refixturing and dimensional inspection. In this paper, we provide a unified treatment of three geometric algorithms for workpiece localization, and develop new techniques to make these local algorithms globally convergent. We also study and analyze, along with extensive simulation results, their performance with respect to convergence and computational efficiency. Finally, we present a method for analyzing reliability of localization solutions and give a lower bound on the number of measurement points needed for reliable recovering of Euclidean transformations.

On the Hybrid Localization/Envelopment Problem

The problem of aligning the CAD model of a workpiece such that all points measured on the finished surfaces of the workpiece match closely to corresponding surfaces on the model while all unmachined surfaces lie outside the model is referred to as the hybrid localization/envelopment problem. The hybrid problem has important applications in setting up for machining of partially finished workpieces. This paper gives a formulation of the hybrid localization/envelopment problem, and presents a simple algorithm for computing its solutions. First, we show that when the finished surfaces of a workpiece are inadequate to fully constrain the rigid motions of the workpiece, then the set of free motions remaining must form a subgroup G0 of the Euclidean group SE(3). This allows us to decompose the hybrid problem into a (symmetric) localization problem on the homogeneous space SE(3)/G0 and an envelopment problem on G0. While the symmetric localization problem is solved using the fast symmetric localization (FSL) algorithm developed in one of our earlier papers, the envelopment problem is solved by computing the solutions of a sequence of linear programming (LP) problems. We derive explicitly the LP problems, and apply standard linear programming techniques to solve the LP problems. We present simulation results to demonstrate the effectiveness of our method for the hybrid problem.

On the hybrid workpiece localization/envelopment problems

This paper defines a hybrid localization/envelopment problem, develops a formulation of the hybrid localization/envelopment problem, and presents a simple algorithm for computing its solutions. First, we show that when the finished surfaces of a workpiece are inadequate to fully constrain the rigid motions of the workpiece, then the remaining set of free motions must form a subgroup G/sub 0/ of the Euclidean group SE(3). This allows us to decompose the hybrid problem into a (symmetric) localization problem on the homogeneous space SE(3)/G/sub 0/ and an envelopment problem on G/sub 0/. The geometric properties of SE(S)/G/sub 0/ are used to convert the envelopment problem into a nonlinear programming problem with a convex objective function, which is then solved using techniques from nonlinear programming. Finally, we present simulation results to illustrate the effectiveness of our method for the hybrid problem.

A CAD-based probing and localisation method for arbitrarily fixed workpiece

In this paper an efficient method for automatic probing and localisation of 3D workpiece arbitrarily fixed to the machine table of a five-axis milling machine is presented. First, by formulating localisation problem as minimizing a least-square question an explicit solution is obtained. Based upon this solution and sensitivity analysis, we present some guidelines and develop a CAD-based automatic probing strategy. By means of the knowledge about the approximate location of workpiece computed by 3D localisation algorithm as estimator, together with the CAD model of workpiece, we then generate online a new collision free probing trajectory to probe additional point on a neighbourhood of the previous sampling point. Utilizing the newly measurement point, we improve the Euclidean transformation which in turn is used together With the CAD model, to generate another collision free probing path to probe more points on the surfaces of workpiece. This process continuous until the workpiece is accurately located. Experimental results show that this algorithm overcomes the need of home surface identification process and is thus suitable for real-time implementation in manufacturing or inspection process.

A geometric approach to establishment of datum reference frames

A datum reference frame is a coordinate system used to locate and orient port features. Constructing a datum reference frame from a set of features is a complicated process involving: 1) specifying a valid combination and the precedence of the datum features which define the datum reference frame; 2) developing from datum features of the part; and 3) determining the position and orientation of the datum reference frame from the data. In this paper, we develop a geometric theory for establishing datum reference frames, and present a sequential procedure that transforms the primary, secondary and tertiary datum problems as a minimization or a constrained minimization problem. We develop simple algorithms to solve these problems, and give simulation results illustrating efficiency and simplicity of the approach.

A geometric algorithm for hybrid localization/inspection/machinability problem

We first propose a hybrid localization/inspection/machinability problem. Next, we formulate the hybrid problem using differential geometric theory and the minimax method. Then, we develop a methodology for treating localization, online inspection and machinability of workpieces simultaneously. Using the geometric properties of the hybrid problem, the hybrid problem is decoupled into a (symmetric) localization/inspection problem and a machinability problem. Then both problems are formulated as constrained optimization problems and are solved by a sequence of linear programming problems. Finally, we present simulation results to demonstrate the efficiency of our method for the hybrid problem.

A geometric theory for formulation and evaluation of form and profile tolerances

Abstract This paper develops a geometric theory which unities the formulation and computation of form and profile tolerances stipulated in ANSI Y14.5M standard. The theory rests on an important observation that the configuration space of a toleranced feature can be identified with the homogeneous space SE (3)/ G 0 of the Euclidean group, where G 0 is the symmetry group of the underlying feature. We show that all cases of form and profile tolerances can be formulated as a minimization or constrained minimization problem in the Space SE (3)/ G 0 . Using properties of SE (3)/ G 0 we develop a simple geometric algorithm, called the Symmetric Minimum Zone (SMZ) algorithm to unify the computation of form and profile tolerances.