  Robot-world, hand-eye calibration is the problem of determining the
transformation between the robot end-effector and a camera, as well as the
transformation between the robot base and the world coordinate system. This
relationship has been modeled as $\mathbf{AX}=\mathbf{ZB}$, where $\mathbf{X}$
and $\mathbf{Z}$ are unknown homogeneous transformation matrices. The
successful execution of many robot manipulation tasks depends on determining
these matrices accurately, and we are particularly interested in the use of
calibration for use in vision tasks. In this work, we describe a collection of
methods consisting of two cost function classes, three different
parameterizations of rotation components, and separable versus simultaneous
formulations. We explore the behavior of this collection of methods on real
datasets and simulated datasets, and compare to seven other state-of-the-art
methods. Our collection of methods return greater accuracy on many metrics as
compared to the state-of-the-art. The collection of methods is extended to the
problem of robot-world hand-multiple-eye calibration, and results are shown
with two and three cameras mounted on the same robot.
