Hermite interpolation by rational Gk motions of low degree

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:240

Article

Jaklic, Gasper^1,2,3  Juettler, Bert⁵  Krajnc, Marjeta^1,2  Vitrih, Vito^3,4  Zagar, Emil^1,2 

[1] Univ Ljubljana, FMF, Ljubljana, Slovenia

[2] IMFM, Ljubljana, Slovenia

[3] Univ Primorska, IAM, Koper, Slovenia

[4] Univ Primorska, FAMNIT, Koper, Slovenia

[5] Johannes Kepler Univ Linz, IAG, A-4040 Linz, Austria

关键词: Motion design;    Geometric interpolation;    Rational spline motion;    Geometric continuity;   

DOI  :  10.1016/j.cam.2012.08.021

来源: Elsevier

【 摘 要 】

Interpolation by rational spline motions is an important issue in robotics and related fields. In this paper a new approach to rational spline motion design is described by using techniques of geometric interpolation. This enables us to reduce the discrepancy in the number of degrees of freedom of the trajectory of the origin and of the rotational part of the motion. A general approach to geometric interpolation by rational spline motions is presented and two particularly important cases are analyzed, i.e., geometrically continuous quartic rational motions and second order geometrically continuous rational spline motions of degree six. In both cases sufficient conditions on the given Hermite data are found which guarantee the uniqueness of the solution. If the given data do not fulfill the solvability conditions, a method to perturb them slightly is described. Numerical examples are presented which confirm the theoretical results and provide evidence that the obtained motions have nice shapes. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free