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This paper presents a geometric control system for a quadrotor unmanned aerial vehicle with decoupled attitude controls. In particular, the attitude control system on the special orthogonal group is decomposed into the reduced attitude controls for the total thrust direction evolving on the two-dimensional unit sphere, and for the remaining one-dimensional rotations about the thrust vector corresponding to the yawing motion. Consequently, the yaw dynamics are controlled separately from the roll and pitch dynamics that are critical for the stability of the translational dynamics of the quadrotor. As such, the proposed controller exhibits improved position tracking capabilities especially for large-angle yawing motions. These are constructed directly on the two-sphere and the one-sphere to avoid complexities and singularities associated with local coordinates. Furthermore, the control systems are augmented with integral terms to deal with fixed disturbances. The efficacy of the proposed method is illustrated by numerical simulation.

This paper presents nonlinear observability criteria for the relative orbital dynamics represented by the solutions of the two-body problem. It is assumed that a chief is on a circular orbit with a prescribed orbital radius, and it measures lines-of-sight toward a deputy only. A differential geometric method, based on the Lie derivatives, is used to derive sufficient conditions for observability of the orbital properties of the deputy. It is shown that under certain geometric conditions on the relative configuration between the chief and the deputy, the nonlinear relative motion is observable from angles-only measurements. The second part of this paper presents a quantitative measure of observability for the relative orbits, and it is formulated by generalizing the observability Gramian of linear dynamic systems. An extended Kalman filter is also developed to numerically illustrate the observability of nonlinear relative orbits with angles-only measurements and to show correspondence between the proposed observability measure and filtered solution accuracy.

This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is impossible to achieve global attractivity. It is illustrated that such attitude observers may yield very slow initial convergence rates, and motivated by this, we propose a hybrid attitude observer that guarantees global asymptotic stability on the special orthogonal group. This is shown to exhibit substantially improved convergence rate uniformly via numerical examples.

This paper presents design and development of an experimental testbed for nonlinear geometric controls of a rigid body. We develop a fully actuated hexrotor UAV that uses six variable pitch propellers to control six degrees of freedom maneuvers, namely three position and three attitude variables, independently. In contrast to the popular quadrotor UAVs that can hover at a single attitude, the hexrotor presented in this paper is capable of hovering at any attitude provided that thrust is sufficiently large. A geometric controller is also developed on the special Euclidean group to track given desired position and attitude trajectories under the effects of unknown disturbances. These are particularly useful for ground tests for large angle rotational dynamics of spacecraft that are combined with arbitrary translational motions. A numerical example that involves a nontrivial maneuver and preliminary experimental tests are also presented.