Adaptation, gyro-ree stabilization, and smooth angular velocity observers for attitude tracking control applications
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This dissertation addresses the problem of rigid-body attitude tracking control under three scenarios of high relevance to many aerospace guidance and control applications: adaptive attitude-tracking control law development for a spacecraft with time-varying inertia parameters, velocity-free attitude stabilization using only vector measurements for feedback, and smooth angular velocity observer design for attitude tracking in the absence of angular velocity measurements. Inertia matrix changes in spacecraft applications often occur due to fuel depletion or mass displacement in a flexible or deployable spacecraft. As such, an adaptive attitude control algorithm that delivers consistent performance when faced with uncertain time-varying inertia parameters is of significant interest. This dissertation presents a novel adaptive control algorithm that directly compensates for inertia variations that occur as either pure functions of the control input, or as functions of time and/or the state. Another important problem considered in this dissertation pertains to rigid-body attitude stabilization of a spacecraft when only a set of inertial sensor measurements are available for feedback. A novel gyro-free attitude stabilization solution is presented that directly utilizes unit vector measurements obtained from inertial sensors without relying on observers to reconstruct the spacecraft's attitude or angular velocity. As the third major contribution of this dissertation, the problem of attitude tracking control in the absence of angular velocity measurements is investigated through angular velocity observer (estimator) design. A new angular velocity observer is presented which is smoothed and ensures asymptotic convergence of the estimation errors irrespective of the initial true states of the spacecraft. The combined implementation of a separately designed proportional-derivative type controller using estimates generated by the observer results in global asymptotic stability of the overall closed-loop tracking error dynamics. Accordingly, a separation-type property is established for the rigid-body attitude dynamics, the first such result to the author's best knowledge, using a smooth (switching-free) observer formulation.