Hand-Eye Calibration with a Remote Centre of Motion

Abstract

In the eye-in-hand robot configuration, hand-eye calibration plays a vital role in completing the link between the robot and camera coordinate systems. Calibration algorithms are mature and provide accurate transformation estimations for an effective camera-robot link but rely on a sufficiently wide range of calibration data to avoid errors and degenerate configurations. This can be difficult in the context of keyhole surgical robots because they are mechanically constrained to move around a remote centre of motion (RCM) which is located at the trocar port. The trocar limits the range of feasible calibration poses that can be obtained and results in ill-conditioned hand-eye constraints. In this paper, we propose a new approach to deal with this problem by incorporating the RCM constraints into the hand-eye formulation. We show that this not only avoids ill-conditioned constraints but is also more accurate than classic hand-eye calibration with a free 6DoF motion, due to solving simpler equations that take advantage of the reduced DoF. We validate our method using simulation to test numerical stability and a physical implementation on an RCM constrained KUKA LBR iiwa 14 R820 equipped with a NanEye stereo camera.