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IMA Journal of Mathematical Control and Information 1989 6(4):465-473; doi:10.1093/imamci/6.4.465
© 1989 by Institute of Mathematics and its Applications
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Cubic Splines on Curved Spaces

LYLE NOAKES, GREG HEINZINGER and BRAD PADEN

Department of Mathematics, University of Western Australia Nedlands WA 6009, Australia
Department of Electrical Engineering and Computer Science, and The Electronics Research Laboratory, University of California Berkeley, CA 94720, USA
Department of Mechanical Engineering, and THE NSF Center for Robotic Systems in Microelectronics, University of California Santa Barbara, CA 93106, USA

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 R3. For SO(3), the Euler-Lagrange equations reduce to interesting nonlinear systems of ordinary differential equations in R3.


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