| Abstract: |
| In the first part of the talk, a rigid body controller designed on the tangent bundle $\mathsf{TSE}(3)$ of the Lie group $\mathsf{SE}(3)$ is introduced. The use of $\mathsf{SE}(3)$ simplifies the controller design by allowing one control law to be obtained for translational and rotational motions, despite the presence of rotational/translational coupling terms. The system states considered in the control design are rotational and translational displacements and velocities of the body. Control design on $\mathsf{TSE}(3)$ results in almost global asymptotic stability of the resulting motion which is proved via a Morse-Lyapunov-based approach. In the second part of the talk, a decentralized consensus control of a formation of rigid body spacecraft is presented in the framework of geometric mechanics while accounting for a constant communication time delay between spacecraft. The consensus problem is converted into a local stabilization problem of the error dynamics associated with the Lie algebra $\mathfrak{se}(3)$ in the form of linear time-periodic delay differential equations (DDEs) with a single discrete delay in the case of an elliptic orbit. |
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