ISSN:
1435-568X
Keywords:
Key words. Riemannian manifolds, Sub-Riemannian structure, Lie groups, Tangent bundle, Sasaki metric, Elastic curves, Normal extremals, Sub-Riemannian optimal control.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
,
Mathematics
,
Technology
Notes:
Abstract. We consider the nonlinear dynamic interpolation problem on Riemannian manifolds and, in particular, on connected and compact Lie groups. Basically we force the dynamic variables of a control system to pass through specific points in the configuration space, while minimizing a certain energy function, by a suitable choice of the controls. The energy function we consider depends on the velocity and acceleration along trajectories. The solution curves can be seen as generalizations of the classical splines in tension for the Euclidean space. The relations with sub-Riemannian optimal control problems are explained.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00009863
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