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This article presents an attitude tracking control scheme with Hölder continuity and finite-time stability. The first part of this article discusses and compares the features of first-order multivariable Hölder-continuous systems with coupled-scalar sliding-mode systems. The advantages of Hölder-continuous systems over sliding-mode systems are presented from the perspectives of control continuity and noise robustness. Thereafter, a Hölder-continuous second-order differentiator is presented with its stability and robustness properties. This is followed by its use in an attitude tracking control scheme, which is covered in the second part of the article. The proposed tracking control scheme is designed directly on the state-space of rigid-body rotational motion, which is the tangent bundle of the Lie group of 3D rotations. The control scheme design, its stability, and its robustness properties are obtained through Lyapunov stability analyses. The proposed Hölder-continuous design is compared with three comparable sliding-mode designs. Numerical simulations on a simulated CubeSat demonstrate the performance of the proposed control scheme and compare it with the sliding-mode control schemes. The numerical simulations also compare the proposed control scheme with other state-of-the-art sliding-mode control approaches in existing research publications. The comparison results demonstrate that the proposed Hölder-continuous attitude control scheme exhibits lower control efforts and tracking control errors over these sliding-mode control schemes in simulations that incorporate actuator dynamics and measurement uncertainties. 

This article presents an estimation scheme for a rotating rigid body in the presence of unknown disturbance torque and unknown bias in angular velocity measurements. The attitude, angular velocity and disturbance torque are estimated from on-board control inputs, landmark vector measurements, and angular velocity measurements. The estimated attitude evolves directly on the special orthogonal group SO(3) of rigid body rotations. A Lyapunov analysis is given to prove that the proposed estimation scheme is almost globally Lyapunov stable in the absence of measurement noise and dynamic disturbance. The estimation scheme is discretized as a geometric integrator for practical implementation. The geometry-preserving properties of this numerical integrator preserve the Lie group structure of the configuration space, and give long time numerical stability. Numerical simulations demonstrate the stability and robustness properties of the proposed scheme. 

This article presents an extended state observer for a vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The extended state observer is applicable to a multi-rotor aerial vehicle with a fixed plane of rotors, modeled as an under-actuated system on the state-space TSE(3), the tangent bundle of the six-dimensional Lie group SE(3). This state-space representation globally represents rigid body motions without singularities. The extended state observer is designed to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It guarantees stable convergence of disturbance estimation errors in finite time when the disturbances are constant, and finite time convergence to a bounded neighborhood of zero errors for time-varying disturbances. This extended state observer design is based on a Hölder-continuous fast finite time stable differentiator that is similar to the super-twisting algorithm, to obtain fast convergence. Numerical simulations are conducted to validate the proposed extended state observer. The proposed extended state observer is compared with other existing research to show its advantages. A set of experimental results implementing disturbance rejection control using feedback of disturbance estimates from this extended state observer is also presented. 

This article presents a framework for model-free control design for mechanical systems without velocity measurements and with an unknown dynamics, considered as a bounded disturbance input. The system states consist of zeroth-order (e.g position) and first-order (e.g velocity) vectors, but only the zeroth-order states are the measured outputs. This model-free control framework is based on a first-order signal differentiator and a finite-time stable extended state observer that simultaneously estimates the states and the bounded disturbance input in real time with guaranteed bounds on accuracy of the estimates. The estimates provided by this observer are used to track a desired output trajectory and compensate the disturbance in real time. Overall nonlinear stability and robustness of the observer is shown theoretically and verified through numerical simulations. The proposed method can be applied to second-order systems and their teams, like mobile robots, unmanned aerial vehicles, unmanned (under)water vehicles and space vehicles. 

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. 

Position tracking control in three spatial dimensions in the presence of unknown or uncertain dynamics, is applicable to unmanned aerial, ground, (under)water and space vehicles. This work gives a new approach to model-free position tracking control by designing an extended state observer to estimate the states and the uncertain dynamics, with guaranteed accuracy of estimates. The estimated states and uncertainties can be used in a control scheme in real-time for position tracking control. The uncertainty (disturbance input) estimate is provided by an extended state observer (ESO) that is finite-time stable (FTS), to provide accuracy and robustness. The ideas of homogeneous vector fields and real-valued functions are utilized for the ESO design and to prove FTS. The estimated disturbance is then utilized for compensation of this uncertainty in real-time, and to enhance the stability and robustness of the feedback tracking control scheme. 

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. 

Relative motion estimation of one rigid body with respect to another is a problem that has immediate applications to formations and maneuvers involving multiple unmanned vehicles or collision avoidance between vehicles. A finite-time stable observer for relative attitude estimation of a rigid object using onboard sensors on an unmanned vehicle, is developed and presented here. This observer assumes sensor inputs from onboard vision and inertial sensors, with the vision sensors measuring at least three points on the object whose relative locations with respect to a body-fixed frame on the object are also assumed to be known. In the absence of any measurement noise, the estimated relative attitude is shown to converge to the actual relative pose in a finite-time stable manner. Numerical simulations indicate that this relative attitude observer is robust to persistent measurement errors and converges to a bounded neighborhood of the true attitude.