A Drift-Free Left Invariant Control System on the Lie Group SO(3)×R3×R3

An Underactuated Drift-Free Left Invariant Control System on a Specific Lie Group

Motion Control of Drift - Free , Left - Invariant Systems on Lie Groups

In this paper we address the constructive controllability problem for drift-free, leftinvariant systems on nite-dimensional Lie groups with fewer controls than state dimension. We consider small ( ) amplitude, low-frequency, periodically time-varying controls and derive average solutions for system behavior. We show how the pth-order average formula can be used to construct open-loop controls f...

Motion Control of Drift - Free , Left - Invariant Systems on Lie Groups , Part II : A General Constructive Control Algorithm

In this paper we address the constructive controllability problem for drift-free, leftinvariant systems on nite-dimensional Lie groups with fewer controls than state dimension. We consider small ( ) amplitude, low-frequency, periodically time-varying controls and derive average solutions for system behavior. We show how the pth-order average formula can be used to construct open-loop controls f...

Drift-free Left Invariant Control System on G4 with Fewer Controls than State Variables

An optimal control problem on a special nilpotent4-dimensional Lie group is discussed and some of its dynamical and geometrical properties are pointed out.

Left Invariant Contact Structures on Lie Groups

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations. The problem of finding which Lie groups admit a left invariant contact structure (contact Lie groups), is then still wide open. We perform a ‘contactization’ method to construct, in every odd dimension...