Fused-like angles:replacement for roll-pitch-yaw angles for a six-degree-of-freedom grating interferometer

Representation of orientation is important in a six-degree-of-freedom grating interferometer but only a few studies have focused on this topic.Roll-pitch-yaw angles,widely used in aviation,navigation,and robotics,are now being brought to the field of multi-degree-of-freedom interferometric measurement.However,the roll-pitch-yaw angles are not the exact definitions the metrologists expected in interferometry,because they require a certain sequential order of rotations and may cause errors in describing complicated rotations.The errors increase as the tip and tilt angles of the grating increase.Therefore,a replacement based on fused angles in robotics is proposed and named“fused-like angles.”The fused-like angles are error-free,so they are more in line with the definitions in grating interferometry and more suitable for six-degree-of-freedom measurements.Fused-like angles have already been used in research on the kinematic model and decoupling algorithm of the six-degree-of-freedom grating interferometer.