Calibration-Free Robot-Sensor Calibration approach based on Second-Order Cone Programming

Abstract

In order to overcome the restrictions of traditional robot-sensor calibration method which solve the tool-camera transformation and robot-world transformation rely on calibration target, a calibration-free approach that solve the robot-sensor calibration problem of the form AX = YB based on Second-Order Cone Programming is proposed. First, a Structure-From-Motion approach was used to recover the camera motion matrix up to scaling. Then rotation and translation matrix in calibration equation were parameterized by dual quaternion theory. Finally, the Second-Order Cone Programming method was used to simultaneously solve the optimal solution of camera motion matrix scale factor, the robot-world and hand-eye relation. The experimental results indicate that the calibration precision of rotation relative error is 3.998% and the translation relative error is 0.117% in defect of calibration target as 3D benchmark. Compared with similar methods, the proposed method can effectively improve the calibration accuracy of the robot-world and hand-eye relation, and extend the application field of robot-sensor calibration method.

Globally Optimal Multi-Scale Monocular Hand-Eye Calibration Using Dual Quaternions

“…In this section, we evaluate our proposed algorithms and discuss the results. Additionally, the FAST and the GLOBAL algorithm are compared to other state-of-the-art approaches for monocular hand-eye calibration [18,23,24]. First, the influence of noise is evaluated on simulated data [24].…”

“…All compared approaches are implemented in Python using either SciPy [22] or CVXPY [1,6] for optimization. We have implemented the cost function for HMs and DQs of Schmidt et al [18] and the DQ approach of Wei et al [23]. The HM approach of Wise et al [24] is evaluated using their provided source code.…”

“…The usual derivations for HMs or DQs lead to two equations: the first is constraining the rotation only, and the second is jointly constraining rotation, translation, and scale. A common approximation for reducing the complexity of the resulting optimization problem is to estimate the rotation from the first equation only and afterwards the translation and scale from the second equation [9,10,23]. However, as already observed by Horaud et al [11], for noisy measurements, this approximation leads to a greater error than a simultaneous estimation of all parameters.…”

“…In addition to the fast local approach, both optimization problems (13) or (23) can also be solved in a global manner. The respective Lagrangian dual problems have been derived in Section 3.…”

“…Given the optimization problem (13) or (23), a Sequential Quadratic Programming (SQP) solver is used for a fast local optimization. In [12], this was proven to be better suited than Interior Point (IP) methods due to the quadratic form of the problem.…”