Cubic spline algorithms for orientation interpolation

✍ Scribed by I. G. Kang; F. C. Park

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 217 KB
• Volume: 46
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19990910)46:1<45::aid-nme662>3.0.co;2-k

✦ Synopsis

This article presents a class of spline algorithms for generating orientation trajectories that approximately minimize angular acceleration. Each algorithm constructs a twice-di erentiable curve on the rotation group SO(3) that interpolates a given ordered set of rotation matrices at speciÿed knot times. Rotation matrices are parametrized, respectively, by the unit quaternion, canonical co-ordinate, and Cayley-Rodrigues representations. All the algorithms share the common feature of (i) being invariant with respect to choice of ÿxed and moving frames (bi-invariant), and (ii) being cubic in the parametrized co-ordinates. We assess the performance of these algorithms by comparing the resulting trajectories with the minimum angular acceleration curve.