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.
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