Noise Effects on Quaternion and Axis-Angle Representations in Robotics

This letter provides a methodology to analyze noise sensitivity of quaternion and axis-angle representations in the presence of joint measurement noise. A general formulation based on the trace of the rotation matrix is proposed, enabling to compute noise sensitivity as a function of robot postures and noise variances. Additionally, noise sensitivity as a function of the orientation angle is derived, enabling to identify regions with different sensitivities. The theoretical findings are general and are not associated to any particular noise distribution. Simulation results with zero-mean Gaussian noise and real experiments are provided corroborating the theoretical findings.