In visual servoing applications using a position-based approach and an end-effector-mounted camera, the position and orientation of the camera with respect to the end-effector must be known. This information is frequently represented in the form of a Homogeneous Transformation Matrix (HTM). For special "noise-free" cases, a closed-form solution for this calibration problem can be determined. However, in the real world, such a solution is not adequate and a least-squares approach or an adaptive algorithm must be used. In this paper, we describe a new algorithm that can simultaneously calculate the Base-World, and the Hand-Eye (camera to end-effector) HTMs. This method is robust to noise, and converges to a valid solution very quickly.

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