Singularities of Euler and Roll-Pitch-Yaw Representations

Euler and roll-pitch-yaw angles are routinely used to represent the orientation of rigid bodies in aerospace, navigation, and robotics because they minimize the dimensionality of the control problem.Both representations, however, introduce unwarranted mathematical singularities which are identified in this paper.Trajectory-tracking algorithms break down at singularities and cause loss of control. Since mathematical singularities do not reflect physical limitations of orientation, remedial measures can beimplemented in the controller.