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This article presents an estimation scheme for the six degree-of-freedom position and attitude of an aerial vehicle by integrating an inertial measurement unit (IMU) and a low-cost real-time kinematic GPS unit, which delivers a precise relative position measurement corrupted by a time-delay. Assuming that the time-delay is known, the extended Kalman filter is generalized to fuse the time-lagged position measurement from GPS with the synchronous attitude and angular velocity measurements from IMU. More specifically, it is formulated as an optimal prediction where the past state is corrected by the position measurement before being propagated up to the current time with the history of the IMU measurements. This provides a compact formulation to merge multiple sensors with varying time-delays in an optimal fashion. The efficacy of the proposed approach is illustrated by a numerical example, experimental data collected over a Navy research vessel, and an outdoor autonomous flight of a quadrotor unmanned aerial vehicle.

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.

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.