Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB

Abstract

In order 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. We can find the sensor mounting position by impying 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 translational freedom if the angle of rotation of A is neither 0 nor tt radians. To solve for X uniquely, it is necessary to make two arm movements and form a system of two equations of the form: A1X=XB1 and A2X=XB2. A closed-form solution to this system of equations is developed and the necessary conditions for uniqueness is stated.

A new hand-eye calibration approach for fracture reduction robot

“…To determine the spatial relationship between the robot end-effector and the camera, the conventional approach is to use a homogeneous transformation equation AX ¼ XB; The equation is solved to obtain the rotational and translational terms either individually or simultaneously [1,14]. Moreover, some extension studies based on AX ¼ XB are also in progress, such as transforming the equation to AX ¼ YB [15].…”

“…The spatial relation is usually represented by a homogeneous matrix, which consists of a rotational component and a translational component; the robot analyses the matrix to know the exact position of end-effector in camera space. In general, a homogenous transform equation of the form AX ¼ XB can be established when the robot moves once [1]. In this equation, A is the transform matrix of the tool coordinate system (TCS) in the robot; B is the transform matrix of the camera, and X is the transform matrix that extends from the TCS of the robot to the camera.…”

“…Numerous methods were proposed to solve this equation. Shiu et al [1] solved the equation by decoupling the rotational part from the translational part (equation 1, 2); the afterprocessed formulations were simple, fast but errorprone. Chen [3] solved the equation without decoupling the rotational and translational parts for the first time; the solution was based on the concept of screw motion.…”

Pose-relay videometrics based ship deformation measurement system and sea trials

“…(1) and (2), the attitude and position of the target relative to the reference base can be calculated as long as the attitude and position of each relay station are obtained [18][19][20][21][22][23] via measurement or calibration. Because each relay station is a rigid body, neither the rotation nor the translation of the stations as a whole brought by the installation deformation will affect the final measurement results.…”

Hand-Eye Calibration from Image Derivatives

“…[10,11,2,4]. The standard approach relies on (i) a known reference object (calibration object) and (ii) the possibility to reliably track points on this reference object in order to obtain corresponding points between pairs of images.…”