Numerical optimization on the Euclidean group with applications to camera calibration

We present the cyclic coordinate descent (CCD) algorithm for optimizing quadratic objective functions on SE(3), and apply it to a class of robot sensor calibration problems. Exploiting the fact that SE(3) is the semidirect product of SO(3) and ℜ³, we show that by cyclically optimizing between these two spaces, global convergence can be assured under a mild set of assumptions. The CCD algorithm is also invariant with respect to choice of fixed reference frame (i.e., left invariant, as required by the principle of objectivity). Examples from camera calibration confirm the simplicity, efficiency, and robustness of the CCD algorithm on SE(3), and its wide applicability to problems of practical interest in robotics.