C²-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion

Table 5

The third B-spline curve is mapped to unit quaternions (data partly).

SN	Variable	Position of B-spline in Cartesian space			Rotation angle	Vector of rotation axis			Unit quaternion
									Real part		Imaginary part
	u	x	y	z	θ	a	b	c	q0	q1	q2	q3
1	0	1.571	0	0	1.571	1	0	0	0.707	0.707	0	0
2	0.2	1.553	0.045	0.181	1.564	0.993	0.029	0.115	0.710	0.700	0.020	0.081
3	0.5	1.246	0.315	0.556	1.400	0.890	0.225	0.397	0.765	0.573	0.145	0.256
4	0.8	0.782	0.689	0.940	1.403	0.557	0.491	0.670	0.764	0.360	0.317	0.432
5	1	0.468	0.937	1.171	1.571	0.298	0.596	0.745	0.707	0.211	0.422	0.527