Position and orientation calibration of a 2D laser line sensor using closed-form least-squares solution

Abstract

Abstract Laser line sensors are used for inspecting, positioning and scanning 3D objects. They are often mounted on the flange of an industrial robot. The laser line sensor provides 2D measurement values, in the x and z direction with respect to the sensor coordinate frame. In order to transform the measured values into the robot coordinate frame and therefore expand the 2D measured values into 3D coordinates, the position and orientation of the sensor coordinate frame with respect to the flange coordinate system must be determined by solving a kinematic equation in terms of transformation matrices. This article provides a complete solution for solving this problem. A unique solution is derived based on the separable closed-form solution after two movements of the robot flange under satisfying constraints [Shiu & Ahmad (2014)]. Robotic applications are usually implemented with the presence of noise. Therefore, a least-squares solution is determined after performing several measurements [Park & Martin (1994)].