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- W2153832674 abstract "This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E3, the sphere S3 and hyperboloid H3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO (1,3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) isin SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form" @default.
- W2153832674 created "2016-06-24" @default.
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- W2153832674 date "2006-12-01" @default.
- W2153832674 modified "2023-09-25" @default.
- W2153832674 title "Integrating Control Systems defined on the Frame bundles of the Space Forms" @default.
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- W2153832674 doi "https://doi.org/10.1109/cdc.2006.377804" @default.
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