Simultaneous actuator and inertial measurement unit faults pose a significant challenge for flight safety. This study analytically demonstrates the impact of such faults on incremental nonlinear dynamic inversion (INDI)-based controllers and proposes an active fault-tolerant control method that concurrently mitigates these faults and accounts for in-flight turbulence. The method employs an optimal two-stage extended Kalman filter with a higher-order sliding mode differentiator (OTSEKF-HOSM) for inertial measurement unit fault identification, together with a variable forgetting factor recursive least squares (VFF-RLS) algorithm for online on-board model estimation, collectively forming the Active-Adaptive (AA) INDI framework. Numerical simulation results show that AA-INDI outperforms conventional and Adaptive INDI in terms of tracking performance under time-varying inertial measurement faults and sudden actuator failures.

Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual determined for a set of collocation points. Previous work has shown that the number and distribution of these collocation points have a significant influence on the accuracy of the PINN solution. Therefore, the effective placement of these collocation points is an active area of research. Specifically, available adaptive collocation point sampling methods have been reported to scale poorly in terms of computational cost when applied to high-dimensional problems. In this work, we address this issue and present the Point Adaptive Collocation Method for Artificial Neural Networks (PACMANN). PACMANN incrementally moves collocation points toward regions of higher residuals using gradient-based optimization algorithms guided by the gradient of the PINN loss function, that is, the squared PDE residual. We apply PACMANN to several forward and inverse problems, including one with a low-regularity solution and 3D Navier Stokes, and demonstrate that this method matches the performance of state-of-the-art methods in terms of the accuracy/efficiency tradeoff for the low-dimensional problems, while outperforming available approaches for high-dimensional problems. Key features of the method include its low computational cost and simplicity of integration into existing physics-informed neural network pipelines. The code is available at https://github.com/CoenVisser/PACMANN.

Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods, as they overcome the curse of dimensionality. However, as with level-set methods, considerable care needs to be taken in limiting approximation errors, particularly since no guarantees are provided during training on the accuracy of the learned reachable set. To address this limitation, we introduce an ϵ-approximate Hamilton-Jacobi partial differential equation (HJ-PDE), which establishes a relationship between training loss and accuracy of the true reachable set. To formally certify this approximation, we leverage Satisfiability Modulo Theories (SMT) solvers to bound the residual error of the HJ-based loss function across the domain of interest. Leveraging Counter Example Guided Inductive Synthesis (CEGIS), we close the loop around learning and verification, by fine-tuning the neural network on counterexamples found by the SMT solver, thus improving the accuracy of the learned reachable set. To the best of our knowledge, Certified Approximate Reachability (CARe) is the first approach to provide soundness guarantees on learned reachable sets of continuous dynamical systems.

As quadrotors continue to become more popular for personal and commercial use, improving their safety is essential, especially in impaired operating states. With (asymmetric) blade damage(ABD) being a potentially dangerous type of impairment, it is beneficial to understand how it affects the dynamic behavior of a quadrotor. This research examines the effects of blade damage on the dynamic model of a quadrotor through system identification techniques. Time scaleseparation is used to split the low-frequency aerodynamic behavior and high-frequency (HF) dynamics. Aerodynamic models are identified using stepwise regression, and a novel approach for modeling HF dynamics –relying purely on on board sensors– using spectral analysis and simplex B-splines has been developed. A majority of the aerodynamic models surpass R ² values of 0.95, and the HF models exceed R ² values of 0.90. The findings provide new insights and implications for diagnosing ABD in quadrotors.

To improve the safety of commercial air transport, pilots are required to train on simulators to recognize the characteristics of an impending stall and subsequently correctly recover from it. To prevent negative training, it is important that the accuracy of the used simulation models is sufficiently high. A key approach for modeling the nonlinear, unsteady aerodynamic effects during the stall is by using Kirchhoff's theory of flow separation. However, widespread difficulties exist in correctly estimating the stall-related parameters of nonlinear flow separation models from flight test data. Therefore, the research in this paper aims to increase the obtained model accuracy by making optimal use of already existing flight data via introduction of a slice-based modeling method. This is done by analyzing the change in the parameter estimate values when applying the system identification procedure to sliced partitions of simulated flight data, for both the pre-stall and post-stall phases. These partitions incrementally increase in size with time from the stall initiation. The simulation data is generated to be representative of the available flight test data, but with known ‘truth’ values for all estimated model parameters. The estimated value for each partition was compared to the true parameter setting in the simulation model used to create the data. It was also investigated whether this coincided with points of increased Fisher information in the data. Manually, an optimal window was found for each parameter for which the estimated value and truth value were equal and sufficient Fisher information was present. For the stall-related parameters the optimal window is often not more than 10 s wider than the stall. For the linear stability and control derivatives it is found that using more data generally results in a better estimate. Finally, the optimal window sizes were used for parameter estimation on the real flight test data. Even though this method represents a prototype, in more than half of the validation cases a decrease in MSE of 10% to 35% was achieved. This shows that the new slice-based modeling method is able to improve the accuracy of nonlinear stall models without the need to gather more flight data and may have applications that reach beyond the realm of stall modeling.

Neglecting actuator dynamics in nonlinear control and control allocation can lead to performance degradation, especially when considering fast dynamic systems. This paper provides a novel method to account for actuator dynamics in the nonlinear control allocation solution: dynamic incremental nonlinear control allocation, or D-INCA. The incremental approach allows for the implementation of a first order discrete-time actuator dynamics model in the quadratic programming solver. This model is used to find the optimal command inputs in addition to the desired physical actuator deflections, hereby compensating for actuator dynamics delays. D-INCA does not require feedback of higher order output derivatives than the baseline INCA and can be used with nonlinear non-control affine systems. Furthermore, with adaptive DINCA, or AD-INCA, an actuator dynamics parameter estimator is introduced to adapt the actuator model online, minimizing actuator tracking errors after actuator failures.

Incorporating sensors such as microelectromechanical system (MEMS)-based inertial measurement units (IMUs) and strain gauges into aircraft structures has the potential to complement ground vibration testing results and improve the tracking of structural modes and wing shape in flight, as well as structural health monitoring. This study evaluates the feasibility and accuracy of employing MEMS accelerometers and gyroscopes together with strain gauges to estimate the structural modes of an aircraft. For this purpose, a ground vibration test was carried out on a 1:3 scaled Diana 2 glider model from which the displacement, rotation, and strain modes were estimated. The estimated modal parameters were compared with traditional piezoelectric accelerometer results and Finite Element Method model predictions. The results showed that the modal frequencies, damping ratios, and mode shapes estimated using MEMS IMUs and strain gauges closely matched the reference accelerometer estimates. Furthermore, the combination of displacement, rotation, and strain mode shapes allowed for greater insight into the structural dynamics. The exploratory use of gyroscopes for aircraft GVT allowed the structural torsion to be captured directly, thereby potentially simplifying future GVT setups by eliminating the need for placing accelerometers in pairs across the structure.

One of the most widely applied identification methods for stall modeling using flight test data is based on Kirchhoff’s method of flow separation. However, this approach has not lead to a satisfactory aerodynamic pitching moment model. The introduction of the so-called X-variable, representing the point of flow separation on the wing, interferes with identification of a pitch damping term, that is required for dynamic stability. In general, Kirchhoff methods lead to models that are incompatible with nominal flight envelope models. This paper presents a nonlinear unsteady model of the pitching moment using lag states of the angle of attack measurements, identified from flight test data collected with a Cessna Citation II laboratory aircraft. The model is formulated in terms of well-known stability derivatives and is a one-on-one extension of the nominal envelope model. Model regressors are selected from a large pool of candidates using Multivariate Orthogonal Function Modeling. The candidate pool is based on a newly formulated mathematical model, such that each model contribution has a clear physical interpretation. The model has good predictive abilities and results in a reduction of 55.9% in validation MSE compared to Kirchhoff based pitching moment models.

Identifying individual control effectiveness parameters for aircraft with several distributed control surfaces can be efficiently performed using multisine inputs. While commonly used in flight testing, these inputs were used to identify control effectiveness models for the half version of the subscale Flying V aircraft through wind tunnel experiments, and these were compared with control effectiveness parameters obtained from static deflections. The control effectiveness parameters estimated through multisine inputs were consistently higher than those obtained from static deflections. This occurs due to inertial forces induced by structural vibrations of the wing in the airstream as the multisine excitation frequency approaches the first natural frequency of the wing. The effects of inertial forces when using multisine inputs are not highlighted in the literature, and bring important consequences for using these inputs on flexible aircraft and wings.

Aerodynamic stall has been a critical factor in recent aircraft crashes, leading to revised regulations for simulator-based stall prevention and recovery training. However, the updated regulations still lack an objectively defined level of accuracy for simulators' stall models that ensures effective pilot training. To help determine this required accuracy, this paper investigates how the Just Noticeable Difference (JND) thresholds for deviations in a stall model's ‘stall abruptness’ parameter translate from a passive observer setting (typical JND experiments) to an active flying scenario (realistic training task). An experiment was performed in the SIMONA Research Simulator with 16 active pilots, whose sensitivity to stall abruptness variations was measured in both these scenarios. In the passive scenario, pilots' JND thresholds were measured using a staircase procedure in a symmetric stall maneuver flown by a stall autopilot. In the active scenario, the method of constant stimuli was used to determine the JND thresholds when the pilots themselves actively flew the same stall maneuver. The average JND thresholds for the passive and active scenarios were estimated by fitting a psychometric curve to the combined responses of all participants. Overall, the passive JND thresholds for the stall abruptness parameter, with an average Weber fraction of 0.11±0.094, were lower than those measured in an earlier experiment (0.16±0.14), indicating a higher sensitivity. Furthermore, the psychometric curve of the active experiment was found to lie entirely to the right of the passive psychometric function: the active JND threshold was found to be five times higher than the passive JND threshold. Overall, this indicates a decreased sensitivity to changes in stall abruptness -- and hence a reduced demand on its modeling accuracy -- when pilots are flying a stall themselves.

Online fault detection and diagnosis (FDD) enables Unmanned Aerial Vehicles (UAVs) to take informed decisions upon actuator failure during flight, adapting their control strategy or deploying emergency systems. Despite the camera being a ubiquitous sensor on-board of most commercial UAVs, it has not been used within FDD systems before, mainly due to the nonexistence of UAV multi-sensor datasets that include actuator failure scenarios. This paper presents a knowledge-based FDD framework based on a lightweight LSTM network and a single layer neural network classifier that fuses camera and Inertial Measurement Unit (IMU) information. Camera data are pre-processed by first computing its optical flow with RAFT-S, a state-of-the-art deep learning model, and then extracting features with the backbone of MobileNetV3-S. Short-Time Fourier Transform is applied on the IMU data for obtaining their time-frequency information. For training and assessing the proposed framework, UUFOSim was developed: an Unreal Engine-based simulator built on AirSim that allows the collection of high-fidelity photo-realistic camera and sensor information, and the injection of actuator failures during flight. Data were collected in simulation for the Bebop 2 UAV with 16 failure cases. Results demonstrate the added value of the camera and the complementary nature of both sensors with failure detection and diagnosis accuracies of 99.98% and 98.86%, respectively.

From fault-tolerant control to failure detection, blade damage simulation is integral for developing and testing failure-resilient modern unmanned aerial vehicles. Existing approaches assume partial loss of rotor effectiveness or reduce the problem to centrifugal forces resulting from the shift in the propeller centre of gravity. In this study, a white-box blade damage model based on Blade Element Theory is proposed, integrating both mass and aerodynamic effects of blade damage. The model serves as plug-in to the nominal system model, enables the simulation of any degree of blade damage and does not require costly experimental data from failure cases. A complementary methodology for the identification of the airfoil lift and drag coefficients is also presented. Both contributions were demonstrated with the Bebop 2 drone platform and validated with static test stand wrench measurements obtained at 3 levels of blade damage (0%, 10%, 25%) in a dedicated wind tunnel experimental campaign with velocities up to 12 m/s. Results indicate high accuracy in simulating a healthy propeller. In the presence of blade damage, the model exhibits a relative error between 5% and 24% at high propeller rotational speeds and between 15% and 75% at low propeller rotational speeds.

Unmanned aerial vehicles (UAVs) are becoming an integral part of both industry and society. In particular, the quadrotor is now invaluable across a plethora of fields and recent developments, such as the inclusion of aerial manipulators, only extends their versatility. As UAVs become more widespread, preventing loss-of-control (LOC) is an ever growing concern. Unfortunately, LOC is not clearly defined for quadrotors, or indeed, many other autonomous systems. Moreover, any existing definitions are often incomplete and restrictive. A novel metric, based on actuator capabilities, is introduced to detect LOC in quadrotors. The potential of this metric for LOC detection is demonstrated through both simulated and real quadrotor flight data. It is able to detect LOC induced by actuator faults without explicit knowledge of the occurrence and nature of the failure. The proposed metric is also sensitive enough to detect LOC in more nuanced cases, where the quadrotor remains undamaged but nevertheless losses control through an aggressive yawing manoeuvre. As the metric depends only on system and actuator models, it is sufficiently general to be applied to other systems.

This paper presents a method for identifying flight dynamics models for aircraft that includes effects from the flexible structure and the effects from unsteady aerodynamics. In the time domain, the unsteady aerodynamic effects are often modelled using aerodynamic lag states. The proposed method involves first determining the poles that govern the dynamics for these lag states from flight data. This is followed by reconstructing the time signal histories for these lag states so that they can then be used as part of the model fitting procedure. Flight tests were conducted using a scaled Diana2 glider unmanned aerial vehicle (UAV) in order to collect experimental data for modelling. To be able to measure the response of the aircraft and its structure, the glider was instrumented with a wide range of sensors including accelerometers, gyroscopes and strain gauges placed across the aircraft structure. During the flight, various excitation manoeuvres were conducted by the pilot while the aircraft responses were collected. From these measurements, a full flight dynamics model consisting of both lateral and longitudinal dynamics was then identified. Additionally, a model predicting the tail and wing root loads was also identified. First, a rigid aircraft model was fitted that was then extended with states corresponding to the flexible modes and aerodynamic lags. Comparison between the rigid and extended model showed that the addition of structural modes and aerodynamic lag states to the identified models can lead up to 30% improvement in predicting aircraft responses. In conclusion, the method developed and presented in this paper is able to identify flight dynamics models from flight data that more accurately capture the dynamics of flexible aircraft by including effects from the flexible structure and unsteady aerodynamics.

Ensuring safety in autonomous systems is essential as they become more integrated with modern society. One way to accomplish this is to identify and maintain a safe operating space. To this end, much effort has been devoted in the field of reachability analysis to obtaining control-invariant sets which ensure that a system inside of these sets can remain in these sets, and are thus essential for guaranteeing a system's safety. However, control invariance does not imply that a system can move from any state in the control-invariant set to any other state in the control-invariant set, within a given time horizon. In this paper, we develop an algorithm to obtain a control-invariant set that allows a given system to move from any state in the set to any other state in the set within a given time horizon without having to leave the set. We call this the 'maneuver set', M. We substantiate the algorithm's efficacy through mathematical proof, affirming that the maneuver set obtained through the algorithm is indeed control-invariant. Furthermore, we prove that the system is indeed able to move from any state within this set to any other state in the set. To illustrate the use of our algorithm, we provide the numerical example of a Dubins car, utilising Hamilton-Jacobi-Bellman reachability analysis along with the proposed algorithm in order to obtain M.

This paper addresses the key question that when faults occur either the aircraft system dynamics changes due to the fault or these dynamics are unknown (precisely). This question is addressed for the important case of Air Data Sensor failures, due to e.g. icing, for fixed wing aircraft operating in a nominal fight condition. The solution to this question uses basic ideas from subspace Identification to cast this problem in linear least squares problem with convex constraints (nuclear norm and 1-norm constraints). The latter are relaxations of a rank and cardinality constraint. The presented solution is validated using real-life fight test data.

Accurate modeling of the unsteady aerodynamics during flow separation is critical for effective pilot stall training in Flight Simulation Training Devices and the development of automatic stall recovery controllers. Kirchhoff’s theory of flow separation has gained popularity due to its relative simplicity and suitability for parameter identification from flight data. The goal of this work is to improve an existing Cessna Citation II dynamic stall model’s fidelity by applying Kirchhoff’s method for each wing surface, separately. The main contribution is the identification of asymmetric flow separation development using the flight-derived roll moment and a roll moment model based on the differential flow separation between the wing surfaces. The longitudinal model structures are adopted from the existing, validated baseline stall model. The lateral-directional model outputs are in good agreement with the validation flight data, showing an average reduction of 48% in Mean Squared Error (MSE) compared to the baseline stall model. In contrast, the longitudinal model output results in an average MSE increase of 88%, suggesting that the estimated asymmetric flow separation parameters are unsuitable for longitudinal stall modeling. Hence, a hybrid approach is proposed that combines separate sets of flow separation parameters for the longitudinal and lateral-directional models.

Though control algorithms for multirotor Unmanned Air Vehicle (UAV) are well understood, the configuration, parameter estimation, and tuning of flight control algorithms takes quite some time and resources. In previous work, we have shown that it is possible to identify the control effectiveness and motor dynamics of a multirotor fast enough for it to recover to a stable hover after being thrown 4 meters in the air. In this paper, we extend this to include estimation of the position of the Inertial Measurement Unit (IMU) relative to the Center of Gravity (CoG), estimation of the IMU rotation, the thrust direction of all motors and the optimal combined thrust direction. In order to guarantee a correct IMU position estimation, two prior throw-and-catches of the vehicle with spin around different axes are required. For these throws, a height as low as 1 meter is sufficient. Quadrotor flight experimentation confirms the efficacy of the approach, and a simulation shows its applicability to fullyactuated crafts with multiple possible hover orientations.

Ensuring the reliability and validity of data-driven quadrotor model predictions is essential for their accepted and practical use. This is especially true for grey- and black-box models wherein the mapping of inputs to predictions is not transparent and subsequent reliability notoriously difficult to ascertain. Nonetheless, such techniques are frequently and successfully used to identify quadrotor models. Prediction intervals (PIs) may be employed to provide insight into the consistency and accuracy of model predictions. This paper estimates such PIs for polynomial and Artificial Neural Network (ANN) quadrotor aerodynamic models. Two existing ANN PI estimation techniques - the bootstrap method and the quality driven method – are validated numerically for quadrotor aerodynamic models using an existing high-fidelity quadrotor simulation. Quadrotor aerodynamic models are then identified on real quadrotor flight data to demonstrate their utility and explore their sensitivity to model interpolation and extrapolation. It is found that the ANN-based PIs widen considerably when extrapolating and remain constant, or shrink, when interpolating. While this behaviour also occurs for the polynomial PIs, it is of lower magnitude. The estimated PIs establish probabilistic bounds within which the quadrotor model outputs will likely lie, subject to modelling and measurement uncertainties that are reflected through the PI widths.