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Title:Hermite interpolation by rational G [sup] k motions of low degree
Authors:Jüttler, Bert (Author)
Krajnc, Marjetka (Author)
Jaklič, Gašper (Author)
Žagar, Emil (Author)
Vitrih, Vito (Author)
Files:URL http://dx.doi.org/10.1016/j.cam.2012.08.021
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract: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., geometric 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 an evidence that the obtained motions have nice shapes.
Keywords:mathematics, numerical analysis, motion design, geometric interpolation, rational spline motion, geometric continuity
Year of publishing:2013
Number of pages:str. 20-30
Numbering:Vol. 240
ISSN:0377-0427
UDC:519.65
COBISS_ID:16378713 Link is opened in a new window
Views:750
Downloads:7
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Secondary language

Language:Slovenian
Title:Hermiteova intepolacija z racionalnimi G [na] k zveznimi gibanji nizkih stopenj
Abstract:Interpolacija z racionalnimi gibanji je pomemben izziv v robotiki in sorodnih področjih. V članku opišemo nov pristop h konstrukciji racionalnih gibanj s pomočjo geometrijske interpolacije. S tem zmanjšamo razmik med številom prostostnih stopenj, ki jih ima trajektorija središča togega telesa ter rotacijski del gibanja. Predstavimo splošni pristop h geometrijski interpolaciji z racionalnimi gibanji in podrobno analiziramo dva praktično pomembna primera, ▫$G^1$▫ zvezna gibanja stopnje štiri in ▫$G^2$▫ zvezna gibanja stopnje šest. V obeh primerih podamo zadostne pogoje na Hermiteove podatke, ki zagotavljajo enoličnost rešitve. Če dani podatki ne zadoščajo pogojem za obstoj rešitve, opišemo metodo, kako jih rahlo perturbirati. Članek zaključimo z numeričnimi primeri, ki potrjujejo teoretične rezultate in kažejo na to, da imajo dobljena gibanja lepo obliko.
Keywords:matematika, numerična analiza, načrtovanje gibanja, geometrijska interpolacija, racionalno gibanje, geometrijska zveznost

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