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A Method for Calculating Angle-Axis Vector at Singular Points and a Proposal of Extended Angle-Axis Vector

Angle-axis vector, which is also called axis-angle representation or rotation vector, can be applied to represent an orientation or orientation error with minimal three parameters. However, it has a problem about singular points. Therefore, this paper shows a method for calculating angle-axis vector at singular points. In addition, this paper proposes an extended angle-axis vector. Conventional angle-axis vector cannot represent an orientation error that is greater than π due to the range of inverse trigonometric function. The extended angle-axis vector can express the orientation that cannot be represented by the conventional method. The results of this study are expected to give a new method for expressing an orientation error which is needed for numerical solution of inverse kinematics or some attitude controls.