The Geometry of Optimal Control Solutions on some Six Dimensional Lie Groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E
³
, the spheres S
³
and hyperboloids H
³
with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO