Robot-world and hand–eye calibration based on motion tensor with applications in uncalibrated robot

Abstract

Accurate estimation of robot-world and hand–eye transformations is crucial for robotic vision system. Although as existing methods provide accurate calibration results, which method is best for uncalibrated robot remains a challenging question. This study applied the motion tensor to the dual equations as an operator that performs coordinate frame change, resulting in the most efficient and elegant representation of dual equations. The analytical solution and the numerical solution were given, respectively. The analytical solution requires only four independent variables involving the screw axis, since the pitch and magnitude of a general screw motion are coordinate invariants. The numerical solution used the closed-form rotation solution based on the Kronecker product as an initial value, and followed the optimization with Gauss–Newton algorithm. The superiority with applications in uncalibrated robot was further tested through simulated and experimental tests compared to the existing methods.