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1989•IMA Journal of Mathematical Control and InformationRequires access

Cubic Splines on Curved Spaces

Lyle Noakes, G. Heinzinger, Brad E. Paden

Open publisher page 268 citations

Abstract

We consider a second-order problem in the calculus of variations, with an application to robotics in mind. The analysis is carried out on a general Riemannian manifold M and then specialized to the case where M is the Lie group SO(3) of rotations in R 3 . For SO(3), the Euler-Lagrange equations reduce to interesting nonlinear systems of ordinary differential equations in R 3 .

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What this paper is about

We consider a second-order problem in the calculus of variations, with an application to robotics in mind. The analysis is carried out on a general Riemannian manifold M and then specialized to the case where M is the Lie group SO(3) of rotations in R 3 . For SO(3), the Euler-Lagrange equations reduce to interesting nonlinear systems of ordinary differential equations in R 3 .

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OpenAlex reports 268 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We consider a second-order problem in the calculus of variations, with an application to robotics in mind. The analysis is carried out on a general Riemannian manifold M and then specialized to the case where M is the Lie group SO(3) of rotations in R 3 . For SO(3), the Euler-Lagrange equations reduce to interesting nonlinear systems of ordinary differential equations in R 3 .

Key concepts: Computer science, Pure mathematics, Mathematics, Geometry

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