Robustness properties of quaternion-based attitude control systems



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Both stabilizing and tracking solutions of the rigid-body attitude control problem, using various attitude representations, are now well understood. Based on the sensor availability, numerous full-state feedback or gyro-free output feedback controllers have been proposed and studied. In the dissertation, we revisit classical proportional-derivative (PD) type attitude controllers when the system is subject to uncertainties like time-delay in the feedback loop, measurement errors, external disturbance torques and modeling uncertainties. We not only analyze existing PD-type controllers while considering various types of uncertainties, but also design tracking controllers robust to the system parameter uncertainties. We adopt the quaternion representation for the attitude kinematics so that we can avoid the geometric singularities coming with minimal 3-dimensional parameter representations. For stability and robustness analysis of the PD-type controllers, we do not rely on the linear system framework in which the original dynamics are considered as the sum of the nominal linear part and the nonlinear perturbation part. Instead, another approach is suggested as suitable for the quaternion kinematic representation so that results are not restricted to a neighborhood of the origin. We first deal with one of the common Lyapunov functions used for quaternion-based attitude control problem. Then, through the strictification process, a new Lyapunov function is constructed which can be analyzed based on the standard Lyapunov stability analysis method. As a result, we establish sufficient conditions for locally stability or boundedness of the system subject to aforementioned uncertainties for both PD full-state feedback and PD-like gyro-free output feedback controllers. When our scope is narrowed to the system parameter uncertainties, we propose adaptive controllers that track predefined reference trajectories and estimate the unknown inertial parameters. Specifically, we apply a dynamic scaling-based Immersion and Invariance method for the first time to the attitude tracking problem. We also provide a way to control and estimate the upper bound of a dynamic scaling factor which has not yet been seen in the literature.