  The need to relate measurements made by a camera to a different known
coordinate system arises in many engineering applications. Historically, it
appeared for the first time in the connection with cameras mounted on robotic
systems. This problem is commonly known as hand-eye calibration. In this paper,
we present several formulations of hand-eye calibration that lead to
multivariate polynomial optimization problems. We show that the method of
convex linear matrix inequality (LMI) relaxations can be used to effectively
solve these problems and to obtain globally optimal solutions. Further, we show
that the same approach can be used for the simultaneous hand-eye and
robot-world calibration. Finally, we validate the proposed solutions using both
synthetic and real datasets.
