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

Table 4

The second 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	0	0.785	0	0.785	0	1	0	0.924	0	0.383	0
2	0.2	0.269	0.697	−0.120	0.757	0.355	0.921	−0.159	0.929	0.131	0.340	−0.059
3	0.5	0.849	0.401	−0.207	0.962	0.883	0.417	−0.216	0.887	0.409	0.193	−0.100
4	0.8	1.373	0.101	−0.145	1.384	0.992	0.073	−0.105	0.770	0.633	0.046	−0.067
5	1	1.571	0	0	1.571	1	0	0	0.707	0.707	0	0