Sub-Riemannian geometry and Carnot-Caratheodory spaces find their applications in geometric phases and in nonholonomic motion planning while the calculation of the sub-Riemannian length minimizers is a problem for geometric control theory. The results of smooth sub-Riemannian geodesics are interesting and important but it cannot always measure distance by means of abnormal extremals. It is only smooth in homogeneous systems whose state spaces are compact.
|Number of pages
|Journal of Mathematical Systems, Estimation, and Control
|Published - Jan 1 1997
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