### Unit Quaternions to Express Orientations in Robotics

In the lesson about the Exponential Coordinate Representation of the orientation, we saw that the logarithm could be numerically sensitive to small rotation angles ฮธ because of the division by sinฮธ. We also saw that all other three-parameter representations of SO(3), like Euler angles and roll-pitch-yaw angles, suffer from similar singularities in representation, and this means that the solution will not always exist for the inverse problem where we want to find a set of parameters for a given orientation. Therefore, an alternative representation of the orientation named Unit Quaternion is used that alleviates the singularity at the cost of…