Rotation matrix optimization with quaternion

Abstract

This paper shows that the representation with the quaternions improves the efficiency in optimization of rotation matrix. The effects of vibration caused by oscillating objects can be suppressed if the object is fixed with the adequate attitude. In general, Euler angles are widely known as a representation of rotation matrices, however it is difficult to optimize the attitude angle by using Euler angles. This is because Euler angles have trigonometric functions. Contrarily, rotation matrices described by the quaternions do not include trigonometric functions and the effectiveness of the quaternions has already recognized in the field such as computer vision and robotics. This paper demonstrates the effectiveness of the quaternions representation for optimization problems through a numerical example.