A new approach is described for geometric calibration of Cartesian robots. This is part of a set of procedures for real-time 3-D robotics eye, eye-to-hand, and hand calibration which uses a common setup and calibration object, common coordinate systems, matrices, vectors, symbols, and operations and is especially suited to machine vision systems. The robot makes a series of automatically planned movement with a camera rigidly mounted at the gripper. At the end of each move, it takes a total of 90 ms to grab an image, extract image feature coordinates, and perform camera-extrinsic calibration. After the robot finishes all the movements, it takes only a few milliseconds to do the calibration. The key of this technique is that only one rotary joint is moving for each movement. This allows the calibration parameters to be fully decoupled, and converts a multidimensional problem into a series of one-dimensional problems. Another key is that eye-to-hand transformation is not needed at all during the computation.>

The authors describe a novel technique for computing position and orientation of a camera relative to the last joint of a robot manipulator in an eye-on-hand configuration. It takes only about 100+64N arithmetic operations to compute the hand/eye relationship after the robot finishes the movement, and incurs only additional 64 arithmetic operations for each additional station. The robot makes a series of automatically planned movements with a camera rigidly mounted at the gripper. At the end of each move, it takes a total of 90 ms to grab an image, extract image feature coordinates, and perform camera extrinsic calibration. After the robot finishes all the movements, it takes only a few milliseconds to do the calibration. A series of generic geometric properties or lemmas are presented, leading to the derivation of the final algorithms, which are aimed at simplicity, efficiency, and accuracy while giving ample geometric and algebraic insights. Critical factors influencing the accuracy are analyzed, and procedures for improving accuracy are introduced. Test results of both simulation and real experiments on an IBM Cartesian robot are reported and analyzed.>

A novel approach is described to geometric calibration of Cartesian robots. This is one-third of an overall approach to real-time 3-D robotics eye, eye-to-hand, and hand calibration, which uses a common setup and calibration object, and is especially suited to machine vision community. The robot makes a series of automatically planned movements with a camera rigidly mounted at the gripper. At the end of each move, it takes a total of 90 ms to grab an image, extract image feature coordinates, and perform camera extrinsic calibration. After the robot finishes all the movements, it takes only a few milliseconds to do the calibration. Only one single rotary joint is moving for each movement while the robot motion can still be planned such that the calibration object remains within the field of view. This allows the calibration parameters to be fully decoupled, and converts a multidimensional problem into a series of one-dimensional problems. Eye-to-hand transformation is not needed at all during the computation.>

A technique is described for computing 3-D position and orientation of a camera relative to the last joint of a robot manipulator in an eye-on-hand configuration. The calibration can be done within a fraction of a millisecond after the robot finishes the movement. The setup is simple (a planar set of calibration points arbitrarily placed on the work table, in addition to robot and camera) and is the same as that for a common camera calibration. This method is claimed to be faster, simpler, and more accurate than any existing technique for hand/eye calibration. Generic geometric properties of lemmas are presented, leading to the derivation of the final algorithms, which are aimed at simplicity, efficiency, and accuracy while giving ample geometric and algebraic insights. Besides describing the technique, critical factors influencing the accuracy are analysed, and procedures for improving accuracy are introduced. Tests results of both simulation and real experiments on an IBM Cartesian robot are reported.>

Techniques are described for calibrating certain intrinsic camera parameters for machine vision. The parameters to be calibrated are the horizontal scale factor, and the image center. The scale factor calibration uses a one-dimensional fast Fourier transform and is accurate and efficient. It also permits the use of only one coplanar set of calibration points for general camera calibration. Three groups of techniques for center calibration are presented: Group I requires using a laser and a four-degree-of-freedom adjustment of its orientation, but is simplest in concept and is accurate and reproducible; Group II is simple to perform, but is less accurate than the other two; and the most general, Group II, is accurate and efficient, but requires a good calibration plate and accurate image feature extraction of calibration points. Group II is recommended most highly for machine vision applications. Results of experiments are presented and compared with theoretical predictions. Accuracy and reproducibility of the calibrated parameters are reported, as well as the improvement in actual 3-D measurement due to center calibration.>

This paper describes techniques for calibrating certain intrinsic camera parameters for machine vision. The parameters to be calibrated are the horizontal scale factor, i.e. the factor that relates the sensor element spacing of a discrete array camera to the picture element spacing after sampling by the image acquisition circuitry, and the image center, i.e. the intersection of the optical axis with the camera sensor. The scale factor calibration uses a 1D-FFT and is accurate and efficient. It also permits the use of only one coplanar set of calibration points for general camera calibration. Three groups of techniques for center calibration are presented: Group I requires using a laser and a four-degree of freedom adjustment of its orientation, but is simplest in concept, and is accurate and reproducible. Group II is simple to perform, but is less accurate than the other two. The most general Group III is accurate and efficient, but requires accurate image feature extraction of calibration points with known 3D coordinates. A feasible setup is described. Results of real experiments are presented and compared with theoretical predictions. Accuracy and reproducibility of the calibrated parameters are reported, as well as the improvement in actual 3D measurement due to center calibration.