An Evaluation of the Dual Vectors Based Solutions for Robot-World/Hand-Eye Calibration

The hand-eye calibration problem represents a major challenge in robotics, arising from the widespread usage of robotic systems along with robot-mounted sensors. Briefly, consisting of estimating the position and orientation of a visual sensor (usually a camera attached to the robot’s end-effector) with respect to the robot itself, calibration is critical in tracking rigid bodies—a common task within mixed reality applications. Hand-eye calibration implies solving the problem formulated as AX = XB or AX = YB equations. The solution lies in computing the unknown homogeneous transformation matrices X and Y, given the A and B parameterizations of rigid body motions. We present the dual vectors based approaches for AX = XB and AX = YB calibration problems, making use of the isomorphism between the special Euclidean group and the orthogonal dual tensor group. Comparisons with state-of-the-art algorithms are used to assess our obtained results.