Research Article
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 |
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