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The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states. 

This article proposes a novel integral geometric control attitude tracking scheme, utilizing a coordinate-free representation of attitude on the Lie group of rigid body rotations, SO(3). This scheme exhibits almost global asymptotic stability in tracking a reference attitude profile. The stability and robustness properties of this integral tracking control scheme are shown using Lyapunov stability analysis. A numerical simulation study, utilizing a Lie Group Variational Integrator (LGVI), verifies the stability of this tracking control scheme, as well as its robustness to a disturbance torque. In addition, a numerical comparison study shows the effectiveness of the proposed geometric integral term, when compared to other state-of-the-art attitude controllers. In addition, software-in-the-loop (SITL) simulations show the advantages of utilizing the proposed attitude controller in PX4 autopilot compared to using PX4’s original attitude controller. 

Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discretetime, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the Hölder-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the input-dependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controllers. 

Weather, winds, thermals, and turbulence pose an ever-present challenge to small UAS. These challenges become magnified in rough terrain and especially within urban canyons. As the industry moves towards Beyond Visual Line of Sight (BVLOS) and fully autonomous operations, resilience to weather perturbations will be key. As the human decision-maker is removed from the in-situ environment, producing control systems that are robust will be paramount to the preservation of any Airspace System. Safety requirements and regulations require quantifiable performance metrics to guarantee a safe aerial environment with ever- increasing traffic. In this regards, the effect of wind and weather disturbances on a UAS and its ability to reject these disturbances present some unique concerns. Currently, drone manufacturers and operators rely on outdoor testing during windy days (or in windy locations) and onboard logging to evaluate and improve the flight worthiness, reliability and perturbation rejection capability of their vehicles. Waiting for the desired weather or travelling to a windier location is cost- and time-inefficient. Moreover, the conditions found on outdoor test sites are difficult to quantify and repeatability is non-existent. To address this situation, a novel testing methodology is proposed, combining artificial wind generation thanks to a multi-fan array wind generator (windshaper), coherent GNSS signal generation and accurate tracking of the test subject thanks to motion capture cameras. In this environment, the drone being tested can fly freely, follow missions and experience wind perturbations whilst staying in a modest indoor volume. By coordinating the windshaper, the motion tracking feedback and the position emulated by the GNSS signal generator with the drone’s mission profile, it was demonstrated that outdoor flight conditions can be reliably recreated in a controlled and repeatable environment. Specifically, thanks to real-time update of the position simulated by the GNSS signal generator, it was possible to demonstrate that the drone’s perception of the situation is similar to a corresponding mission being executed outdoor. In this work, the drone was subjected to three distinct flight cases: (1) hover in 2 m s−1 wind, (2) forward flight at 2 m s−1 without wind and (3) forward flight at 2 m s−1 with 2 m s−1 headwind. In each case, it could be demonstrated that by using indoor GNSS signal simulation and wind generation, the drone displays the characteristics of a 20 m move forward, while actually staying stationary in the test volume, within ±1 m. Further development of this methodology opens the door for fully integrated hardware-in- the-loop simulation of drone flight operations.