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

Table 3

The first 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	1.047	`1.047	0	0	1	0.866	0	0	0.5
2	0.2	−0.079	0.175	0.885	0.905	−0.088	0.193	0.977	0.899	−0.038	0.085	0.427
3	0.5	−0.194	0.503	0.550	0.770	−0.251	0.653	0.715	0.927	−0.094	0.245	0.268
4	0.8	−0.174	0.746	0.208	0.794	−0.219	0.940	0.262	0.922	−0.085	0.363	0.101
5	1	0	0.785	0	0.785	0	1	0	0.924	0	0.383	0