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This paper presents a geometric adaptive position tracking control system for a quadrotor unmanned aerial vehicle. In particular, the attitude control system is designed on the product of the two-dimensional unit sphere and the one-dimensional circle such that the direction of the thrust that is critical for position tracking is controlled independently from the yawing direction that is irrelevant to the position dynamics. Compared against the prior work with coupled attitude controls on the special orthogonal group, the proposed controller prevents large yaw errors from causing an undesirable performance degradation in tracking a position command. Further, the control input is augmented with adaptive control terms to mitigate the effects of disturbances, and it is formulated globally on the spheres to avoid singularities and complexities of local coordinates. The efficacy of the proposed control system is illustrated by both numerical examples and indoor/outdoor flight experiments.

This paper presents a control system for a quadrotor unmanned aerial vehicle transporting a payload connected by a link. This system is considered as a multibody system evolving a nonlinear configuration manifold to construct an intrinsic global formulation of the dynamics. Based on this, a geometric control system is proposed such that the payload follows an arbitrary desired trajectory. In particular, the effects of the mass distribution of the link connecting the quadrotor and the payload are explicitly considered in the dynamic model and the stability analysis. Furthermore, the control system is designed to eliminate the adverse effects of disturbances. The efficacy of the proposed geometric tracking control system is illustrated by both a numerical example and an indoor flight experiment.

The attitude of a rigid body evolves on the three-dimensional special orthogonal group, and it is often estimated by measuring reference directions, such as gravity or magnetic field, using an onboard sensor. As a single direction measurement provides a two-dimensional constraint, it has been widely accepted that at least two non-parallel reference directions should be measured, or the reference direction should change over time, to determine the attitude completely. This paper uncovers an intriguing fact that the attitude can actually be estimated by using multiple measurements of a single, fixed reference direction, provided that the angular velocity and the direction measurements are resolved in appropriate frames, respectively. More specifically, after recognizing that the attitude uncertainties propagated over the left-trivialized stochastic kinematics are distinct from those over the right-trivialized one, stochastic attitude observability with single direction measurements is formulated by an information theoretic analysis. These are further illustrated by numerical simulations and experiments.

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 introduces an advanced Lyapunov stability analysis for an attitude observer that has been developed on the special orthogonal group. In particular, when the attitude observer is constructed based on multiple direction measurements toward known reference points, a local exponential stability has been established by linearization, under the assumption that those reference points are fixed in the inertial frame. Several modifications have been proposed to deal with reference directions changing over time. Here, we present an alternative Lyapunov analysis to show that the attitude observer still exhibits exponential stability for time-varying reference directions, under the assumption that the observer gain is sufficiently large relative to the rate of change of the reference directions. These are illustrated by a numerical example, followed by experimental results with visual marker detection in an indoor space.

This paper presents flight test results that demonstrate the effectiveness of a locally exponential and almost-globally stable geometric PID controller for attitude stabilization. The controller is implemented on a low cost off the shelf Arduino based quadrotor platform. The controller requires only a rough estimate of the inertia tensor of the device. It is implemented entirely using the onboard processor and does not require any off board sensing or processing. The results presented show that the implemented nonlinear PID is capable of quickly stabilizing any desired vertically upright configuration for large deviations from the desired equilibrium.