A robust and singular-free analytical solution for the hand-eye calibration of a novel surgical robot

For the hand-eye calibration of the robot-assisted minimally invasive surgery with an endoscopic camera, the closed-form solutions should be considered primarily by taking the time occupancy and security of the surgery into account. Although all the existing analytical solutions are widely used, at least one of them (i.e., the analytical solution based on Lie Group theory) may be singular. According to the polar decomposition of a matrix, the singularity of the Lie Group-based solution is firstly pointed out. For avoiding the above singularity, a singular-free analytical solution based on singular value decomposition is put forward. In addition, simulation and real-data experiments are conducted for the proposed and another two classical solutions of the hand-eye calibration, which can demonstrate the feasibility and accuracy of the proposed closed-form solution.