Adaptive Identification on the Group of Rigid Body Rotations

This paper reports a novel stable adaptive identifier on the group of rigid body rotations, and its application to a sensor calibration problem arising in underwater vehicle navigation. The problem addressed is the identification of a rigid-body rotation map from input-output data. General least-square and adaptive identification techniques are commonly employed to identify general linear maps from input-output data, but do not guarantee that the resulting identified map is a rigid body rotation. At present, a least-square singular value decomposition approach is the standard method for identification constrained to the group of rigid body rotations. This paper reports the first exact adaptive identifier on the group of rigid body rotations, together with a proof of stability. The performance of this adaptive identifier is evaluated on actual experimental data and found to compare favorably with results obtained via previously reported least-squares techniques. The methodology reported herein is of broader interest because of its applicability to general problems in the identification, dynamics, and control on the group of rigid body motions.