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Geometric Attitude Controls And Estimations On The Special Orthogonal Group Open Access

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This dissertation is concerned with spacecraft attitude control and estimation problems from the point of view of geometric mechanics. The controllers and observers are built on the special orthogonal group without any parameterizations, where the attitude dynamics is treated in a global and unique manner.The dissertation is composed of three parts. A leader-follower attitude formation control scheme is reported such that the leader spacecraft control its absolute attitude with respect to the inertial reference frame and the follower spacecraft control relative attitude with respect to other spacecraft in the formation. The unique feature is that both the absolute attitude and the relative attitude control systems are developed directly in terms of the line-of-sight observations, where attitude determination and estimation processes are not required.Second, an angular velocity observer is developed such that the estimated angular velocity is guaranteed to converge to the true angular velocity asymptotically from almost all initial estimates. Then, the presented observer is integrated with a proportional-derivative attitude tracking controller to show a separation type property for attitude tracking in the absence of angular velocity measurements.A hybrid observer for the attitude dynamics of a rigid body is proposed to guarantee global asymptotic stability. By designing a set of attitude error functions, attitude estimates are expelled from undesired equilibria to achieve global asymptotic stability. To guarantee that the estimated attitudes evolve on the special orthogonal group, a numerical algorithm based on the Lie group method is presented.

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