The authors regret to inform that an incorrect transfer function was included in Eq. (12). The correct transfer function is: [Formula Presented] The selected gains were [Formula Presented]. This leads to a real pole at 0.964 and two complex poles at 0.965 ± 0.0445i. The difference of the model compared to the measured step response has now reduced, the largest difference being 4.8% of the final step value at 0.14 s. The mistake does not influence any of the conclusions drawn in the paper. The authors would like to apologize for any inconvenience caused.

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Nonlinear dynamic inversion (NDI) is a nonlinear feedback linearization technique that has been widely applied to flight control systems [1,2]. Using state feedback and the inverted nonlinear system dynamics, NDI can significantly reduce controller development costs by avoiding gain scheduling and Jacobian linearization at a multitude of operating points. However, the control performance of NDI is directly dependent on required detailed knowledge of the model. As a simplified and enhanced NDI method [3], incremental nonlinear dynamic inversion (INDI) [4,5] has been proposed to reduce the model dependency and improve the robustness against model uncertainties. Instead of using a global nonlinear model, in INDI the dynamic inversion is implemented on a locally linearized system model that is updated at every sampling period, for which the control input is calculated in an incremental manner. Unlike NDI, for which full knowledge of the complete system dynamics is needed, INDI only requires explicit knowledge of the system’s control effectiveness matrix.@en

This paper presents a sampled-data form of the recently reformulated incremental nonlinear dynamic inversion (INDI) applied for robust spacecraft attitude control. INDI is a combined model- and sensor-based approach mostly applied for attitude control that only requires an accurate control effectiveness model and measurements of the state and some of its derivatives. This results in a reduced dependency on exact knowledge of system dynamics which is known as a major disadvantage of model-based nonlinear dynamic inversion controllers. However, most of the INDI derivations proposed in the literature assume a very high sampling rate of the system and its controller while also not explicitly considering the available sampling time of the digital control computer. Neglecting the sampling time and its effect in the controller derivations can lead to stability and performance issues of the resulting closed-loop nonlinear system. Therefore, our objective is to bridge this gap between continuous-time, highly sampled INDI formulations and their discrete, lowly sampled counterparts in the context of spacecraft attitude control where low sampling rates are common. Our sampled-data reformulation allows explicit consideration of the sampling time via an approximate sampled-data model in normal form widely known in the literature. The resulting sampled-data INDI control is still robust up to a certain sampling time since it remains only sensitive to parametric uncertainties. Simulation experiments for this particular problem demonstrate the bridge considered between INDI formulations which allows for low sampling control rates.@en

Optical flow-based control strategies have always inspired robotic scientists, especially those in the field of Micro Air Vehicles (MAVs), thanks to their computational efficiency and relative simplicity. A major problem is that the success of optical flow control is governed by the availability of distance estimates, while optical flow provides only the ratio of velocity to distance. Therefore, with only monocular visual information, the inherent nonlinearity of optical flow observables has imposed several challenges in the controller design. In this paper, we propose a newly formulated controller, Extended Incremental Nonlinear Dynamic Inversion (EINDI), to deal with nonlinearities in the system output, such as optical flow control problems. The proposed method unlocks the potential of its predecessor (INDI) in output feedback control by removing the common assumption of time-scale separation, allowing internal dynamics to exist, and requiring only the input and output measurements. Furthermore, the EINDI method has been implemented on an MAV and tested successfully for optical flow landing in a simulation and a real-world outdoor environment. Both simulation and flight test results show 1) good tracking performance of the EINDI control compared to the conventional feedback control, 2) smooth landing trajectories without any oscillation, and 3) fast adaptation of the EINDI control even for landings at different heights and desired setpoints.

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Managing air data sensor fault detection and diagnosis (FDD) in the presence of atmospheric turbulence is challenging since the effects of faults and turbulence are coupled. Existing FDD approaches cannot decouple the faults from the turbulence. To address this challenge, this brief first proposes a novel kinematic model that incorporates the effects of the turbulence. This model is valid inside the entire flight envelope, and there is no need to design a linear parameter varying system. Then, the double-model adaptive estimation algorithm is extended to achieve unbiased state estimation even in the presence of unknown disturbances. The proposed approach is validated using generated turbulence data with various scale lengths and intensities. More importantly, the proposed approach is successfully validated using the real flight test data of a business jet when it is experiencing atmospheric turbulence.

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In this paper, an online flight envelope protection system is developed and implemented on impaired aircraft with structural damage. The whole protection system is designed to be a closed loop of several subsystems, including system identification, damage classification, flight-envelope prediction, and fault-tolerant control. Based on the information given by damage classification, the flight envelopes are explicitly retrieved, processed online from the database, and fed into the fault-tolerant controller, which makes the protection system adaptive to a wide range of abnormal conditions. Simulation results show that with envelope protection, loss-of-control accidents are more likely to be prevented, since excessive commands to the controller are restricted based on the updated information of the changed flight envelopes. In this way, the fault tolerance of the impaired aircraft can be effectively enhanced.

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Heuristic dynamic programming is a class of reinforcement learning, which has been introduced to aerospace engineering to solve nonlinear, optimal adaptive control problems. However, it requires an off-line learning stage to train a global system model to represent the system dynamics. This paper uses an incremental model in heuristic dynamic programming to improve the online learning ability, which is incremental model based heuristic dynamic programming. The trait of the online identification of the incremental model makes this method an option for fault-tolerant control and partially observable control problems. This study, therefore, also extends this method to deal with partial observability. The presented method has been validated on two different online tracking problems: missile fault-tolerant control with full-state measurements and also spacecraft attitude control disturbed with liquid sloshing under partially observable conditions. The results reveal that the proposed method outperforms the conventional heuristic dynamic programming method in fault-tolerant control tasks, deals with partial observability, and is robust to internal uncertainties and external disturbances.

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In this paper, an online flight envelope protection system is developed and implemented on impaired aircraft with structural damage. The whole protection system is designed to be a closed-loop of several sub-systems, including system identification, damage classification, flight-envelope prediction and fault-tolerant control. Based on the information given by damage classification, the flight envelopes are explicitly retrieved and processed online from the database and fed into the fault-tolerant controller, which makes the protection system adaptive to a wide range of abnormal conditions. Simulation results show that with envelope protection, loss-of-control accidents are more likely to be prevented, since both the controller and pilots are aware of the shrunken flight envelopes after damage and excessive commands are restricted. In this way, the fault-tolerance of the impaired aircraft can be effectively enhanced. @en

In order to further expand the flight envelope of quadrotors under actuator failures, we design a nonlinear sensor-based fault-tolerant controller to stabilize a quadrotor with failure of two opposing rotors in the high-speed flight condition (>8 m/s). The incremental nonlinear dynamic inversion approach which excels in handling model uncertainties is adopted to compensate for the significant unknown aerodynamic effects. The internal dynamics of such an underactuated system have been analyzed, and subsequently stabilized by redefining the control output. The proposed method can be generalized to control a quadrotor under single-rotor-failure and nominal conditions. For validation, flight tests have been carried out in a large-scale open jet wind tunnel. The position of a damaged quadrotor can be controlled in the presence of significant wind disturbances. A linear quadratic regulator approach from the literature has been compared to demonstrate the advantages of the proposed nonlinear method in the windy and high-speed flight condition.@en

A variable stability in-flight simulator has the capabilities to change the response of an aircraft in-flight, often without changing the physical properties of the aircraft. The ability to adjust the aircraft response characteristics and handling qualities has various purposes, such as pilot training, control system development, and handling quality research. A variable stability control system is designed for a medium-range business jet using incremental nonlinear dynamic inversion. The performance of the in-flight simulator is verified by two experiments, one conducted in a fixed-base flight simulator and one in a Cessna Citation II laboratory aircraft. The fly-by-wire actuation system in the Cessna Citation II is based on its existing autopilot, inheriting the limited performance and safety protections. The simulator experiment shows differences between the experienced handling qualities for a reference model and the designed controller combined with aircraft dynamics. These differences mainly arise due to actuator saturation for specific handling quality settings. The in-flight experiment supports the simulator findings but also reveals how the available control authority around the initial condition is limited due to constraints of the fly-by-wire system.

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This paper presents an agile and robust spacecraft attitude tracking controller using the recently reformulated incremental nonlinear dynamic inversion (INDI). INDI is a combined model- and sensor-based control approach that only requires a control effectiveness model and measurements of the state and some of its derivatives, making a reduced dependency on exact system dynamics knowledge. The reformulated INDI allows a non-cascaded dynamic inversion control in terms of Modified Rodrigues Parameters (MRPs) where scheduling of the time-varying control effectiveness is done analytically. This way, the controller is only sensitive to parametric uncertainty of the augmented spacecraft inertia and its wheelset alignment. Moreover, we draw some parallels to time-delay control (TDC) -more familiar in the robotics community- which have been shown to be equivalent to the incremental formulation of proportional-integral-derivative (PID) control for second order nonlinear systems in controller canonical form. Simulation experiments for this particular problem demonstrate that INDI has similar nominal performance as TDC/PID control, but superior robust performance and stability.

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This paper designs an incremental nonlinear dynamic inversion control law for free-flying flexible aircraft, which can regulate rigid-body motions, alleviate gust loads, reduce the wing root bending moment, and suppress elastic modes. By fully exploring the sensor measurements, the model dependency of the proposed control law can be reduced while maintaining desirable robustness, which simplifies the implementation process and reduces the onboard computational load. The elastic states are observed online from accelerometer measurements, with a Padé approximation to model the pure time delay. Theoretical analyses based on the Lyapunov methods and the nonlinear system perturbation theory show that the proposed control has inherent robustness to model uncertainties, external disturbances, and sudden actuator faults. These merits are demonstrated by time-domain simulations in various spatial turbulence and gust fields, as well as by a Monte Carlo study.@en

High-speed flight in GPS-denied environments is currently an important frontier in the research on autonomous flight of micro air vehicles. Autonomous drone races stimulate the advances in this area by representing a very challenging case with tight turns, texture-less floors, and dynamic spectators around the track. These properties hamper the use of standard visual odometry approaches and imply that the micro air vehicles will have to bridge considerable time intervals without position feedback. To this end, we propose an approach to trajectory estimation for drone racing that is computationally efficient and yet able to accurately estimate a micro air vehicle’s state (including biases) and parameters based on sparse, noisy observations of racing gates. The key concept of the approach is to optimize unknown and difficult-to-observe state variables so that the observations of the racing gates best fit with the known control inputs, estimated attitudes, and the quadrotor dynamics and aerodynamics during a time window. It is shown that a gradient-descent implementation of the proposed approach converges ∼4 times quicker to (approximately) correct bias values than a state-of-the-art 15-state extended Kalman filter. Moreover, it reaches a higher accuracy, as the predicted end-point of an open-loop turn is on average only ∼20 cm away from the actual end-point, while the extended Kalman filter and the gradient descent method with kinematic model only reach an accuracy of ∼50 cm. Although the approach is applied here to drone racing, it generalizes to other settings in which a micro air vehicle may only have sparse access to velocity and/or position measurements.

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This paper proposes a novel and practical framework for safe flight envelope estimation and protection, in order to prevent loss-of-control-related accidents. Conventional analytical envelope estimation methods fail to function efficiently for systems with high dimensionality and complex dynamics, which is often the case for high-fidelity aircraft models. In this way, this paper develops a probabilistic envelope estimation method based on Monte Carlo simulation. This method generates a probabilistic estimation of the flight envelope by simulating flight trajectories with extreme control effectiveness. It is shown that this method can significantly reduce the computational load compared with previous optimization-based methods and guarantee feasible and conservative envelope estimation of no less than seven dimensions. This method was applied to the Innovative Control Effectors aircraft, an overactuated tailless fighter aircraft with complex aerodynamic coupling between control effectors. The estimated probabilistic flight envelope is used for online envelope protection by a database approach. Both conventional state-constraintbased and novel predictive probabilistic flight envelope protection systems were implemented on a multiloop nonlinear dynamic inversion controller. Real-time simulation results demonstrate that the proposed framework can protect the aircraft within the estimated envelope and save the aircraft from maneuvers that otherwise would result in loss of control. @en

A study addresses offline construction of the database. The main focus and contribution of this study are database building and interpolation for the Database-Driven Safe Flight Envelope Prediction System (DEFEND) system. More importantly, through complexity analysis, the database approach is shown to be feasible for onboard real-time implementation within the aircraft control laws. Reachability analysis as the method to compute safe flight envelopes, as the theory provides a set-valued insight into safety and control design of dynamic systems. One advantage of this method is that all possible trajectories can be computed from all available control strategies and initial states, which naturally meets the safety guarantees. The computed results are called reachable sets, which are defined as a set of states that reach a certain target set within a certain time horizon and current control authority. Two sets of envelopes are computed using the level-set method toolbox. One is the pitching envelope, referred to the motion in the longitudinal plane with horizontal tail damage. The other is the rolling envelope, referred to the motion in the lateral plane with wing tip loss.

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To explore the aerodynamic effects on a quadrotor in the high-speed flight regime and establish an accurate nonlinear model, free-flight tests with a quadrotor are carried out in a large-scale wind tunnel. The flight data reveal that complex aerodynamic interactions could appear and significantly influence the forces and moments acting on the quadrotor, which indicate the inaccuracy of state-of-art models established based on helicopter aerodynamic theory. To cope with this problem, gray-box models considering these effects are identified from flight data using a stepwise system identification approach, which combines both prior knowledge of rotorcraft aerodynamic properties as well as data observations. Previous models introduced in the literature are compared with the gray-box models. Validation results show an 80% reduction of moment model residuals and a 20% reduction of force model residuals. @en

This paper proposes an Incremental Sliding Mode Control driven by Sliding Mode Disturbance Observers (INDI-SMC/SMDO), with application to a quadrotor fault tolerant control problem. By designing the SMC/SMDO based on the control structure of the sensor-based Incremental Nonlinear Dynamic Inversion (INDI), instead of the model-based Nonlinear Dynamic Inversion (NDI) in the literature, the model dependency of the controller and the uncertainties in the closed-loop system are simultaneously reduced. This allows INDI-SMC/SMDO to passively resist a wider variety of faults and external disturbances using continuous control inputs with lower control and observer gains. When applied to a quadrotor, both numerical simulations and real-world flight tests demonstrate that INDI based SMC/SMDO has better performance and robustness over NDI based SMC/SMDO, in the presence of model uncertainties, wind disturbances, and sudden actuator faults. Moreover, the implementation process is simplified because of the reduced model dependency and smaller uncertainty variations of INDI-SMC/SMDO. Therefore, the proposed control method can be easily implemented to improve the performance and survivability of quadrotors in real life.

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This paper proposes incremental nonsingular terminal sliding mode control for a class of multi-input and multi-output nonlinear systems considering model uncertainties, external disturbances, and sudden actuator faults. This method is free from singularity because it does not involve any negative fractional power. The convergence time in both reaching and sliding phases are proved to be finite. Moreover, by fully exploiting sensor measurements, the proposed incremental control method simultaneously reduces model dependency and the uncertainty remaining in the closed-loop system. The reduction of model dependency simplifies the implementation process and reduces the computational load, while the reduction of uncertainty decreases the minimum possible sliding mode control gains, which is beneficial to chattering reduction. These merits are verified by a quadrotor trajectory tracking problem. Simulation results demonstrate that the proposed method has better robustness against model uncertainties, gusts, and actuator faults than the model-based nonsingular terminal sliding mode control in the literature.

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For mitigating the chattering effect in the sliding mode control (SMC), many adaption mechanisms have been proposed to reduce the switching gains. However, less attention is paid to the control structure, which influences the resulting uncertainty term and determines the minimum possible gains. This paper compares three control structures for inducing higher-order sliding modes in finite time: nonlinear dynamic inversion (NDI) based SMC, higher-order sliding mode control (HOSMC) with artificially increased relative degree, and the recently proposed incremental nonlinear dynamic inversion (INDI) based SMC. The latter two control structures have reduced model dependency as compared to NDI-SMC. Moreover, their nominal control increments are found to be approximately equivalent if the sampling interval is sufficiently small and if their gains satisfy certain conditions. Under the same circumstances, the norm value of the resulting uncertainty using INDI-SMC is several orders of magnitude smaller than those using other control structures. For maintaining the sliding modes, the minimum possible gains required by HOSMC approximately equal those needed by INDI-SMC divided by the sampling interval. Nevertheless, these two approaches have comparable chattering degrees, which are effectively reduced as compared to NDI-SMC. The analytical results are verified by numerical simulations.

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This paper proposes a novel and practical framework for safe flight envelope estimation and protection, in order to prevent loss-of-control-related accidents. Conventional analytical envelope estimation methods fail to function efficiently for systems with high dimensionality and complex dynamics, which is often the case for high-fidelity aircraft models. In this way, this paper develops a probabilistic envelope estimation method based on Monte Carlo simulation. This method generates a probabilistic estimation of the flight envelope by simulating flight trajectories with extreme control effectiveness. It is shown that this method can significantly reduce the computational load compared with previous optimization-based methods and guarantee feasible and conservative envelope estimation of no less than seven dimensions. This method was applied to the Innovative Control Effectors aircraft, an over-actuated tailless fighter aircraft with complex aerodynamic coupling between control effectors. The estimated probabilistic flight envelope is used for online envelope protection by a database approach. Both conventional state-constraint-based and novel predictive probabilistic flight envelope protection systems were implemented on a multi-loop nonlinear dynamic inversion controller. Real-time simulation results prove that the proposed framework can protect the aircraft within the estimated envelope and save the aircraft from maneuvers that otherwise would result in loss of control. @en