Workpiece localization : theory, algorithms and implementation
by Yunxian Chu
THESIS
1999
Ph.D. Electrical and Electronic Engineering
xiv, 135 leaves : ill. (some col.) ; 30 cm
Abstract
Workpiece localization refers to the following problem: assuming a rigid workpiece is arbitrarily fixtured to a work table, determine the position and orientation of the workpiece frame relative to some known world reference frame. In this dissertation, we develop a unified geometric theory for localization of all three types of workpieces: (1) general 3-dimensional workpieces where points from the finished surfaces fully constrain the rigid motions of the workpieces; (2) symmetric workpieces where rigid motions along the symmetry directions of the workpiece can not be determined; and (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, refixturi...[ Read more ]
Workpiece localization refers to the following problem: assuming a rigid workpiece is arbitrarily fixtured to a work table, determine the position and orientation of the workpiece frame relative to some known world reference frame. In this dissertation, we develop a unified geometric theory for localization of all three types of workpieces: (1) general 3-dimensional workpieces where points from the finished surfaces fully constrain the rigid motions of the workpieces; (2) symmetric workpieces where rigid motions along the symmetry directions of the workpiece can not be determined; and (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. The contributions of the dissertation are as follows:
First, we formulate the general 3-dimensional localization problem as a least squares problem (LSP) on the Euclidean group, SE(3). The mathematics of LSP is analyzed in detail where necessary conditions are derived for the optimal Euclidean transformation and the optimal home surface points. We describe an iterative method for solving LSP and show how different considerations in updating the Euclidean transformations lead to different algorithms. We show the local convergence of three localization algorithms and present a method to improve the performance of these algorithms. We give simulation results showing convergence, accuracy and computational efficiency of the various geometric algorithms.
Second, we discuss the factors affecting the accuracy and reliability of the localization results. Using the F-test method in statistics, we provide an effective algorithm to analyze the reliability of workpiece localization. This allows the localization method to be applied effectively to real manufacturing tasks.
Third, we formulate the hybrid localization/envelopment problem (HLEP) as a symmetric localization problem on the homogeneous space SE(3)/G0 of the Euclidean group and a minimization problem on G0 subject to inequality constraints, where G0 [is a subset of] SE(3) is the symmetry subgroup formed by the finished surfaces of the workpiece. We solve the envelopment problem by solving a sequence of linear programming problems where the solution from the symmetric localization problem is used as an initial condition. We also address the issue of hybrid localization/ inspection/machinability. We develop a methodology for treating localization, on-line inspection and machinability of workpieces simultaneously using the geomet-ric properties of the homogeneous space. We also analyze the localization problem of a class of workpieces with special shapes and discuss their configuration spaces. We show that this kind of localization problem can be transformed into a two-dimension problem, thus, a set of simpler algorithms can be obtained.
Finally, making use of these algorithms, we propose a computer aided setup (CAS) system and implement the system on an open architecture machining tool environment. The experimental results show the validation of the developed localization algorithms and the CAS system. Availability of the CAS system eliminates the need of having an operator fixture workpiece accurately, thus simplifying and accelerating greatly the machining cycle.
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