Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB
Yiu Cheung Shiu,S. Ahmad +1 more
- 01 Feb 1989
- Vol. 5, Iss: 1, pp 16-29
TL;DR: Etalonnage d'un capteur monte sur le poignet d' un robot par resolutions des equations des transformations homogenes de la forme AX=XB.
read more
Abstract: To use a wrist-mounted sensor (such as a camera) for a robot task, the position and orientation of the sensor with respect to the robot wrist frame must be known. The sensor mounting position can be found by moving the robot and observing the resulting motion of the sensor. This yields a homogeneous transform equation of the form AX=XB, where A is the change in the robot wrist position, B is the resulting sensor displacement, and X is the sensor position relative to the robot wrist. The solution to an equation of this form has one degree of rotational freedom and one degree of translation freedom if the angle of rotation of A is neither 0 nor pi radians. To solve for X uniquely, it is necessary to make two arm movements and form a system of two equations of the form: A/sub 1/X=XB/sub 1/ and A/sub 2/X=XB/sub 2/. A closed-form solution to this system of equations is developed and the necessary conditions for uniqueness are stated. >
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Figures
Figure 6.3. Rotational noise sensitivities due to rotational perturbations of robot motion measurements and sensor motion measurements. Errors due to perturbations about the x, y, and z axes are marked by □, O, and A, respectively. 
Figure 3.1. Rotating Rx about ase kA by 9 is equivalent to rotating R^ about •* kB by the same angle. kA is the axis of rotation of A and kB is the axis of rotation of B in the homogeneous transform equation AX — XB. 
Figure 6.1, Translational noise sensitivities due to translational perturbations of robot motion measurements and sensor motion measurements. Errors due to perturbations in x, y, and z directions are marked by □, O, and A, respectively. 
Figure 6.2. Translational noise sensitivities due to rotational perturbations of robot motion measurements and sensor motion measurements. Errors due to perturbations about the x, y, and z axes are marked by □, O, and respectively. 
Figure 1.1. Finding the mounting position of a camera by solving a homogeneous transform equation of the foriii AX=XB, where A is the robot motion, B is the resulting camera motion, and X is the camera mounting position.
Citations
Hand-Eye Calibration Using Dual Quaternions
TL;DR: This paper algebraically prove that if the authors consider the camera and motor transformations as screws, then only the line coefficients of the screw axes are relevant regarding the hand-eye calibration, and shows how a line transformation can be written with the dual-quaternion product.
Robot sensor calibration: solving AX=XB on the Euclidean group
Frank C. Park,B.J. Martin +1 more
- 01 Oct 1994
TL;DR: The authors derive, using methods of Lie theory, a closed-form exact solution that can be visualized geometrically, and aclosed-form least squares solution when A and B are measured in the presence of noise.
568
Hand-eye calibration
Radu Horaud,Fadi Dornaika +1 more
TL;DR: A common mathematical framework is developed to solve for the hand-eye calibration problem using either of the two formulations and the nonlinear optimization method, which solves for rotation and translation simultaneously, seems to be the most robust one with respect to noise and measurement errors.
Optimal Hand-Eye Calibration
Klaus H. Strobl,Gerd Hirzinger +1 more
- 09 Oct 2006
TL;DR: A calibration method for eye-in-hand systems in order to estimate the hand-eye and the robot-world transformations in terms of a parametrization of a stochastic model and a novel metric is proposed for nonlinear optimization.
Simultaneous robot-world and hand-eye calibration
Fadi Dornaika,Radu Horaud +1 more
- 01 Aug 1998
TL;DR: Two new solutions that attempt to solve the homogeneous matrix equation of the for, AX=ZB are presented: a closed-form method which uses quaternion algebra and a positive quadratic error function associated with this representation; and a method based on nonlinear constrained minimization and which simultaneously solves for rotations and translations.
References
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography
TL;DR: New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.
Pattern Classification and Scene Analysis
TL;DR: We provide a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition.
12.5K
A Computational Theory of Human Stereo Vision
David Marr,Tomaso Poggio +1 more
TL;DR: In this paper, an algorithm for solving the stereoscopic matching problem is proposed, which consists of five steps: (1) each image is filtered at different orientations with bar masks of four sizes that increase with eccentricity.
1.7K
Resolved-acceleration control of mechanical manipulators
TL;DR: In this article, the authors present a technique which adopts the idea of "inverse problem" and extends the results of "resolved-motion-rate" controls, which deals directly with the position and orientation of the hand.
1.2K
Related Papers (5)
Frank C. Park,B.J. Martin +1 more
- 01 Oct 1994
[...]
Radu Horaud,Fadi Dornaika +1 more
Fadi Dornaika,Radu Horaud +1 more
- 01 Aug 1998