A Method for Inverse Robot Calibration

J. S. Shamma; D. E. Whitney

doi:10.1115/1.3143817

A Method for Inverse Robot Calibration

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3143817 ◽

1987 ◽

Vol 109 (1) ◽

pp. 36-43 ◽

Cited By ~ 41

Author(s):

J. S. Shamma ◽

D. E. Whitney

Keyword(s):

Internal Model ◽

Location Error ◽

Joint Angles ◽

Robot Calibration ◽

Third Order ◽

Error Sources ◽

Six Dof ◽

General Drive ◽

Inverse Calibration ◽

Model Inverse

A method is described for the inverse calibration of a manipulator or robot. Inverse calibration is defined to be finding the joint angles necessary to drive a robot to a desired endpoint location. The joint angles recommended by the robot controller’s internal model will not, in general, drive the robot to the desired location because of inaccuracies in this model. Inverse calibration seeks to reduce the error. Unlike previous work in calibration, the method reported here does not require modeling any specific phenomena that may cause the error; hence it is not limited in accuracy by inability to identify all the error sources. The method consists of finding approximation functions by which corrections are made to the encoder readings recommended by the robot’s internal model. These functions are found by measuring the error at discrete locations throughout a region of the robot’s workspace and then least-squares fitting third order trivariate polynomials to the error samples. A forward calibration (one which reports actual tool location from given encoder readings) based on the above method is also described. The inverse calibration is tested on a six DOF PUMA simulation. Results show that the endpoint location error can be reduced from an average of about 1.2 mm down to an average of about 0.12 mm.

Download Full-text

Including Geophysical Data in Ground Water Model Inverse Calibration

Ground Water ◽

10.1111/j.1745-6584.2003.tb02581.x ◽

2003 ◽

Vol 41 (2) ◽

pp. 178-189 ◽

Cited By ~ 15

Author(s):

Dorte Dam ◽

Steen Christensen

Keyword(s):

Ground Water ◽

Geophysical Data ◽

Water Model ◽

Inverse Calibration ◽

Model Inverse

Download Full-text

Prediction of Workpiece Location Error Due to Fixture Geometric Errors and Fixture-Workpiece Compliance

Manufacturing ◽

10.1115/imece2003-42126 ◽

2003 ◽

Cited By ~ 1

Author(s):

Anand Raghu ◽

Shreyes N. Melkote

Keyword(s):

Geometric Error ◽

Influence Coefficient ◽

Geometric Errors ◽

Location Error ◽

Error Sources ◽

Linear Elastic ◽

Part Quality ◽

Contact Points ◽

Influence Coefficient Method ◽

Coefficient Method

Workpiece location relative to the cutting tool is affected by the accuracy of part placement in the fixture. A number of error sources are known to contribute to the resulting workpiece location error, which can lead to poor part quality. The major sources include fixture geometric error and elastic deformation of the fixture and workpiece due to fixturing forces. In this paper, workpiece location error is predicted by modeling the process of part loading (given fixture geometric variations) and clamping (given deformations at the contact points) in a machining fixture. Linear elastic models for the fixture elements, contact mechanics models at the region of contact, and the flexibility influence coefficient method for the bulk elasticity of the workpiece have been used to model the compliance of the entire fixture-workpiece system. The deformations at the contact points are obtained by solving a constrained optimization model. The effect of geometric errors and compliance on workpiece location error is examined using part response points as a measure of quality, through examples involving a 3-2-1 machining fixture.

Download Full-text

Astigmatism correction of convex aspheres using the subaperture stitching Hindle test

Measurement Science and Technology ◽

10.1088/1361-6501/ac47be ◽

2022 ◽

Author(s):

Goeun Kim ◽

In-Ung Song ◽

Hagyong Kihm ◽

Ho-Soon Yang

Keyword(s):

Measurement Data ◽

Correction Method ◽

Test Surface ◽

Test Results ◽

Third Order ◽

Error Sources ◽

Surface Error ◽

Astigmatism Correction ◽

Subaperture Stitching ◽

System Errors

Abstract We propose an astigmatism correction method for the subaperture stitching Hindle test to measure hyperbolic convex aspheres. Astigmatic wavefront errors arise from misaligned Hindle setups, mechanical runout errors of the rotational motion for stitching, and the surface error of the target itself. Because these errors are combined, they cannot be separated in the conventional subaperture stitching Hindle tests. We exploited the rotational periodicity of each error to distinguish the surface figure error from other astigmatic error sources and rectified the Hindle test results with a third-order astigmatism. Using the subaperture stitching Hindle test, we averaged two sets of measurement data with a 180° rotational phase difference between them to calculate the astigmatic surface error. The proposed method was verified experimentally by comparing it with the results from a commercial stitching interferometer from QED Technologies; only subnanometer differences in the root-mean-square values were obtained. Therefore, the proposed method calibrated the system errors from the test surface wedge and the rotational decenter easily, thereby reducing the mechanical costs and alignment efforts and making it more accessible than a sophisticated mechanism.

Download Full-text

Modeling of Workpiece Location Error Due to Fixture Geometric Error and Fixture-Workpiece Compliance

Journal of Manufacturing Science and Engineering ◽

10.1115/1.1828052 ◽

2005 ◽

Vol 127 (1) ◽

pp. 75-83 ◽

Cited By ~ 45

Author(s):

Anand Raghu ◽

Shreyes N. Melkote

Keyword(s):

Cutting Tool ◽

Geometric Error ◽

Location Error ◽

Error Sources ◽

Linear Elastic ◽

Contact Points ◽

Influence Coefficients ◽

Machining System ◽

Bulk Elasticity

Several fixture-related error sources contribute to workpiece location error in a machining system. Inaccurate part placement in the fixture relative to the cutting tool, for example, can negatively affect the quality of the part. In this paper, the following major sources of error are considered: fixture geometric error and elastic deformation of the fixture and workpiece due to fixturing forces. The workpiece location error is predicted by modeling the process of part loading (given fixture geometric variations) and clamping (given deformations at the contact points) in a machining fixture. Linear elastic models for the fixture elements, contact mechanics models for the contact regions, and flexibility influence coefficients to capture the bulk elasticity of the workpiece have been used to model the compliance of the entire fixture-workpiece system. The deformations at the contact points are obtained by solving a constrained optimization model. The effect of geometric errors and compliance on workpiece location error is examined using part response points as a measure of quality. Experimental validation is also provided for several fixture-workpiece variable levels using a 3-2-1 machining fixture.

Download Full-text

Probe size and 5th-order aberration

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125609 ◽

1987 ◽

Vol 45 ◽

pp. 134-135 ◽

Cited By ~ 1

Author(s):

Zhifeng Shao

Keyword(s):

Electron Probe ◽

Spherical Aberration ◽

Wave Length ◽

Cylindrical Symmetry ◽

Electron Wave ◽

Third Order ◽

The Third ◽

Probe Radius ◽

Small Probe ◽

Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Download Full-text

Children’s Recall of Approximations to English

Journal of Speech and Hearing Research ◽

10.1044/jshr.1602.201 ◽

1973 ◽

Vol 16 (2) ◽

pp. 201-212 ◽

Cited By ~ 3

Author(s):

Elizabeth Carrow ◽

Michael Mauldin

Keyword(s):

Language Development ◽

Fourth Order ◽

Third Order ◽

Memory Processes ◽

The Third ◽

General Index ◽

General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

Download Full-text