2005
DOI: 10.1002/rob.20082
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Abstract: In this paper, the matrix equation AX = XB used for hand to sensor calibration of robotmounted sensors is analyzed using a geometrical approach. The analysis leads to an original way to describe the properties of the equation and to find all of its solutions. It will also be highlighted why, when multiple instances A i X = XB i ͑i =1,2, . . .͒ of the equation are to be solved simultaneously, the system is overconstrained. Finally, singular cases are also discussed.

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Cited by 75 publications
(40 citation statements)
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“…There are several papers addressing the computation of AX= XB [37,38]. In our case, we have acquired 10 views of a calibrating pattern and the X matrix is estimated by using the algorithm of Shiu [38].…”
Section: Qualitative Evaluationmentioning
confidence: 99%
“…There are several papers addressing the computation of AX= XB [37,38]. In our case, we have acquired 10 views of a calibrating pattern and the X matrix is estimated by using the algorithm of Shiu [38].…”
Section: Qualitative Evaluationmentioning
confidence: 99%
“…Different techniques were proposed to solve the classic AX =XB problem. Depending on the outcome, the proposed techniques can be divided into: separable [1,2], simultaneous [3] or iterative [4][5][6]. Any method used to solve the sensor calibration problem presents its own advantages and disadvantages [7].…”
Section: Introductionmentioning
confidence: 99%
“…If an external sensor, e.g., an optical localizer, is used, the calibration procedure estimates the geometrical transformation between its CF and the robot's CF. Such calibration [14] can be performed with closed form solutions [15] or with iterative optimization approaches [16][17][18]. In robotic surgery, external sensors can also allow the definition of the task in the robot's coordinate frame and can also check the accuracy of the task during its execution.…”
Section: Introductionmentioning
confidence: 99%