This paper presents an active fault-tolerant flight control system (FCS) design for the dual-system/hybrid VTOL UAV configuration that maximally exploits its inherent over-actuation abilities to provide higher levels of fault-tolerance and reliability compared to that of the other VTOL UAVs configurations up to this point. The significance of this study is to convert the main drawback of having the vertical rotors as dead weights during the cruise to a key advantage where all the UAV's controls are kept active during all the flight phases raising the UAV's fault-tolerance and maneuverability abilities. The FCS proposed elaborates on a new architecture for the hierarchical automatic control loops using the dynamic inversion control to design the trajectory tracking virtual commands and employing optimal dynamic control allocation to optimally resolve the controls redundancy. Regarding fault-tolerance, the presented FCS handles simultaneous failures and jamming of all the control surfaces during flight where the control commands to the healthy controls (vertical rotors) were automatically adapted such that the trimming and trajectory tracking were successfully maintained till the mission end. Additionally, this paper addresses for the first time the employment of the controls redundancy to enhance the VTOL UAV's maneuverability in fault-free cases, where we present a study of reducing the minimum turn radius of the UAV when the vertical rotors are employed with the control surfaces during the maneuver. A reduction of 38% in the coordinated steady-level minimum turn radius turn at 35 m/sec flight speed was achieved.
1 Introduction
Over the last few decades, there has been a growing interest in Unmanned aerial vehicles (UAVs) and their use in civil and military applications, from reconnaissance and surveillance to hobby and recreational uses. Quite recently, considerable attention has been paid to vertical takeoff and landing (VTOL) UAVs as they gather the abilities of the efficient cruise of Fixed-wing UAVs and the hover and VTOL abilities of Rotary-wing UAVs together, enabling VTOL UAVs to perform missions of high flight range with having the ability to takeoff and land from any point without the need to runways [1]. Accordingly, the design of flight control systems for different configurations of VTOL UAVs is currently an active area of research with open challenges [2].
With a growing interest in civil applications of VTOL UAVs like the air taxi projects and the increasing rule of UAVs generally in the military fields, the Fault-tolerance control system design (FCS) of VTOL UAVs is gaining much interest these days with the safety and fail-safe operation requirements raising requiring the proposed FCSs to have higher abilities to handle probable failures of various components and actuators during flight without affecting the safe completion of the missions and narrowing the chances for the accidental-ending flights [3‐5].
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In this study, we introduce a new design of active fault-tolerance flight control system (FCS) for the dual-system VTOL UAV configuration as the one shown in Fig. 1, also called hybrid VTOL UAVs and quadplane UAVs in the literature. The hybrid VTOL UAV configuration is a fixed-wing airframe with the conventional control surfaces and a fixed horizontal thrust element (puller or pusher), plus additional fixed rotors oriented vertically to perform vertical takeoff and landing with no tilting mechanisms needed for the vertical thrust rotors or the wing. This configuration is considered the simplest VTOL UAV configuration compared to other ones, such as tiltwing, tiltrotor, and tailsitter configurations [1]. However, the state of the art of FCSs of hybrid VTOL UAVs wastes the inherent controls' redundancy of such a VTOL UAV configuration by using the vertical rotors only during the VTOL and hover phases and shutting them down during the cruise flight, making them dead weights on board thus reducing the UAVs flight range and endurance [1]. This technique is generally referred to as having different active sets of the vehicle's controls during different flight phases, where the controls surfaces and the horizontal thrust are the active controls during the cruise phase and the vertical rotors are the active set during the VTOL and hover phase, and they are all used in the transition phase during which the airplane accelerates from the hover condition to cruising with at least the minimum stall speed (forward transition) and vice versa (back transition) from the cruise to hover before performing the landing. The main reason behind this technique is to resolve the redundancy of this UAV's controls during the cruise where the vertical rotors and the control surfaces can have similar maneuvering effects, which gets harder to resolve during sophisticated flight phases such as the transition phases at which the airplane's control surfaces are having varying effectiveness with the upstream flow speed. However, if the FCS of hybrid VTOL UAVs is reworked such that it can make use of the UAV's controls' redundancy by employing the vertical rotors with the control surfaces through all the phases of flight, it would acquire a higher level of fault-tolerance against possible faults of the control surfaces during the cruise phase and would have improved dynamic performance with the vertical rotors aiding the control surfaces during the transient phases. Adding these new performance abilities to the inherent merits of the simple design which involves no tilting mechanisms advances the hybrid VTOL UAV configuration ahead of the other VTOL configurations in terms of safety and reliability which is the primary contribution and motivation behind this work.
Fig. 1
Dual-system (hybrid) VTOL UAV
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Fault-tolerance control of various VTOL UAV configurations is currently an active research topic [6‐15] aiming to realize the most reliable VTOL UAV solution that features VTOL and hover abilities, long flight range and endurance, higher payload capacity, sufficient fault-tolerance level against inflight faults/failures. A few recent works have addressed the problem of employing the redundancy or over-actuation of the hybrid VTOL UAVs to improve the fault-tolerance abilities of such airplanes [11‐15] in which fault-tolerance controllers (FTC) were introduced to make use of the vertical rotors in handling the control surfaces faults/failures during the forward flight. The current state of the art of FCSs of the hybrid VTOL UAV configuration, and other VTOL UAVs in general, can be taken as the Px4 flight controller [16], which is widely used in professional and amateur activities providing open source fully autonomous flight controller that is able to perform real flights requiring the user to tune a set of parameters and controller's gains according to the UAV controlled. However, the current efforts in the literature and the current state of the art of hybrid VTOL UAVs FCSs do not make full use of the potential of the hybrid VTOL UAV configuration regarding the fault-tolerance and performance abilities. Therefore, in this work, we present an active fault-tolerance FCS for the hybrid VTOL UAV configuration that offers autonomous trajectory tracking over the entire flight mission while securing active fault-tolerance against simultaneous total failures of the UAV's control surfaces, in addition to employing that redundancy in the fault-free case to enhance the UAV's maneuverability of hybrid VTOL UAV.
In the introduction section, we aim to present a comprehensive review of the current efforts in the literature on the "fault-tolerance FCS design of VTOL UAVs" to provide the researchers with interest in this topic with a panoramic view of the current state in the research and practice fields of the problem. The literature review is divided into three subsections. In Sect. 1.1, we present a bird's-eye overview of the recent works on the fault-tolerance of different configurations of VTOL UAVs, in general, to observe the capabilities of different VTOL UAV configurations up till now. The current level of fault-tolerance abilities of the different VTOL UAVs configurations is compared against the results obtained for the hybrid VTOL UAV configuration with the FCS proposed in this paper to highlight the significance and advancements realized with the hybrid VTOL UAV in the fault-tolerance regards through this work. In Sect. 1.2, we focus on the FCSs of the hybrid VTOL UAV configuration particularly where we compare the FCS proposed here with the recently presented fault-tolerant FCS designs in the literature to emphasize the novelties of the proposed FCS and the gaps we aimed to address. In Sect. 1.3, the designed FCS is compared with the current state of the art of the already used FCS of hybrid VTOL UAV, which is the Px4 flight controller, to observe the contributions of the presented FCS and its newly offered features.
1.1 Current Fault-Tolerance Abilities of Different VTOL UAVs Configurations
In this subsection, the current state of the fault-tolerance of various VTOL UAV configurations is surveyed in turn.
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Multirotor UAVs (quadrotor, hexarotor, octarotor, etc.) have long been subject to the fault-tolerance control (FTC) design problem in the literature. Although multirotors feature VTOL and hover abilities, they are not considered a category of VTOL airplanes, which are the focus of our study, as they rely on vertical thrust to generate lift instead of aerodynamic lift from a fixed-wing resulting in a limited flight speed and endurance as mentioned in the survey work [1]. Nonetheless, to provide a broad overview of VTOL UAVs' fault-tolerance field, we provide a glimpse of the common multirotors' fault-tolerance abilities and refer the interested reader to [6, 17] focusing on multirotors fault-tolerance exclusively. Generally, the fault-tolerance capabilities of multirotors can be summarized as follows; quadrotors are known to be unable to withstand a single rotor total failure without sacrificing yaw stability or having an angular velocity about a vertical axis [18]. For multirotors with more than 4 propellers, handling a single total failure of one of the rotors without sacrificing control over the attitude is achievable, however, withstanding simultaneous total failure of more than one rotor depends on the total number and arrangement of the rotors and the position of the inoperable rotors with respect to each other. [17] presents the different fault cases in terms of the number and relative positions of the fault rotors and the fault-tolerance chances in each case.
Tailsitter VTOL UAV configuration has the least number of controls among all VTOL UAVs configurations with no tilting mechanisms incorporated. Its lack of controls' redundancy makes it less fault-tolerant than the tiltrotor and hybrid VTOL UAVs configurations. In [7], the fault-tolerance of the tailsitter VTOL UAV was addressed, where the authors studied the single elevon failure during cruise and hover phases and the propellers' failures during the cruise. Elevon's failure at hover was handled by sacrificing the yaw control. In cruise, it was handled by differential thrust, which allowed fault-tolerance to a limited range of locking angles of the elevon given the power limits of the thrusters. In case of single/double propellers' failure at cruise, the altitude hold was sacrificed, and elevons were used to glide the UAV near a constant velocity with a continuous descent. However, faults during the transition phases and keeping the trajectory tracking under the fault-existence conditions were not feasible due to the lack of redundancy of this airframe configuration making the tailsitter the least reliable VTOL UAV configuration against total failures of controls during flight by losing the ability to keep the UAV's altitude and rotational degrees of freedom under full control in fault conditions.
Tiltrotor VTOL UAV configuration has a single set of thrusters that provide the vertical thrust required to takeoff vertically and hover and are tilted at the hover point to provide the horizontal thrust required to transition to forward flight. In [8], fault-tolerance of tiltrotor VTOL UAV was addressed for the first time by addressing a single failure of a motor, a tilting servo, or a control surface. The authors employed the flight control loops of the Px4 flight controller and replaced its control allocation module with a new dynamic control allocation algorithm to handle various faults during the cruise and hover phases. The proposed method necessitates knowing the inoperable effector and its setting value at failure occurrence, i.e., the locking angle of a jammed control surface. Motor and control surfaces' failures were handled by varying the motors' speeds and tilt angles. Based on the results in [8], it can be concluded that the tilting servos are very critical and essential to handle various faults. For instance, failure of a single tilting servo was checked only at hover, but having a fault at even a single tilting servo during the cruise was not addressed, which makes the tiltrotor VTOL UAV's fault-tolerance mainly dependent on the tilting servos. Moreover, the study did not address simultaneous failures of more than one effector and also did not address faults during the transition phases. A limitation of the dynamic allocator presented in [8, 14] is that it offers no handling for the unattainable wrench commands of the flight controller module, i.e., the maneuvering commands that are not achievable by the feasible control limits of the UAV. This idea is emphasized clearly later in this text when we explain the framework of the VTOL UAV FCS in Sect. 3 and discuss the handling technique employed in our control allocation algorithm to handle the unattainable desired maneuvering commands.
Tiltwing FTC design was addressed in [9], where sliding mode controller and control allocation were used to design the velocity and altitude tracking controllers during the forward flight phase only. The redundant controls considered in the model were the control surfaces and the propellers' speeds, with the tilt angles of the wings held constant. The FTC handled a fault scenario in which all control surfaces failed, and the motors were used to perform pitching and rolling maneuvers. Apart from the non-inclusion of the wings' tilt angles among the controls, the FTC presented is applicable to a single flight phase of flight and does not offer an integral FCS architecture of tiltwing VTOL UAV that secures fault-tolerance and trajectory tracking over the entire flight mission, which has not been presented in the literature yet for the tiltwing configuration up to our knowledge.
The configurations discussed above are classified as under-actuated vehicles. Another category of VTOL UAVs is the fully actuated UAVs, which are those with enough controls that directly control all the UAV's rotational and translational motions. An example is the Tilted hexacopter presented in [10], in which each of the rotors is tilted by a certain angle so that the rotors can produce thrust along the 3 axes in addition to moments about them, in contrast to conventional rotors that can give vertical thrust only in addition to the 3 moments. As illustrated in [10], such UAVs do not feature controls redundancy despite the number of controls available; therefore, they cannot withstand total failures of even a single effector, and only degradation of an actuator's performance can be discussed, which makes such a configuration less fault-tolerant than all other configurations discussed earlier despite the number of its controls and sophisticated design.
Table 1 summarizes the previous discussion and compares the fault-tolerance aspects of different VTOL UAVs configurations. The goal of the comparison is to highlight the efficacy and advantages of the hybrid VTOL UAV configuration distinguishing it from the other ones regarding fault-tolerance. The hybrid VTOL UAV's properties are based on the results obtained in the work presented in this paper.
Table 1
Comparison of fault-tolerance capabilities of common VTOL UAVs configurations according to the current FCSs available
1.2 Active Fault-Tolerant FCS of Hybrid VTOL UAV Configurations
Focusing on the hybrid VTOL UAV configuration, the work presented in this paper is compared with the former efforts on the same problem. Alwi and Edwards have made a significant contribution to the fault-tolerance topic in general by employing sliding mode control and online control allocation to various fault-tolerance problems [19‐21]. Mizrak, Alwi, and Edwards addressed the FTC of hybrid VTOL UAV configuration in [11, 12]. In [11], FTC for the cruise phase was presented, which controls the UAV's altitude, velocity, and roll angle. The sliding mode stability was checked, and trajectory tracking was kept under simultaneous failures of the control surfaces and rotors. In [12], the VTOL phase was only considered, and simultaneous faults and failures of a subset of the vertical rotors' failures (8 rotors) were achieved. Prochazka et al. [13‐15] addressed the same problem and presented two FTC designs. In [15], an FTC design based on integral sliding modes and pseudo-inverse control allocation was presented. Hardware in the loop test (HIL) was performed to validate the closed-loop performance only under the elevator's failure during forward flight. In [13], a nonlinear dynamic inversion controller was designed with an optimization-based control allocation algorithm that solved the allocation problem in two steps where a quadratic programming problem is solved in each step to find the controls' commands that achieve the desired controller commands with minimum controls' usage. The aerodynamic effect of the spinning of the vertical rotor on the UAV's stability derivatives was estimated using computational fluid dynamics (CFD) analysis performed at one flow speed and fixed rotational speeds of the vertical rotors which limited the analysis to the longitudinal flight only and the flight and vertical rotors rotational speeds that were used in the CFD analysis. Some limitations related to those previous works that were overcome in this work are listed below.
The mentioned works considered only the cruise flight phase and did not present a complete architecture of a FCS that achieves both fault-tolerance and trajectory tracking over the whole flight mission.
In [11, 15], the vertical rotors are used only when faults occur to the primary controls (the control surfaces) and kept inactive during the fault-free conditions.
In [11, 15], the pseudo-inverse control allocation was employed, which has two main drawbacks; firstly, it does not consider the saturation limits on the controls, and secondly, it results in inadmissible controls' commands (beyond the saturation limits) in response to nearly half of the attainable acceleration commands set (acceleration commands that feasible controls can achieve) [22]. In other words, it wastes much of the UAV's control power. The pseudo-inverse control allocation algorithm is tied with the sliding mode control framework for FTC design as it is necessary to perform the stability analysis of the sliding mode [23].
In [13], the control allocator can be more efficient regarding the computational load, where the solution is computed by solving two quadratic programming problems at each time step. In this work, the allocation problem is solved as a single linear programming problem that achieves the same goal with less computation needed.
None of the previous works addressed the employment of vertical rotors with the control surfaces during the fault-free case to enhance the UAV's maneuverability.
Table 2 compares the novelties of the FCS presented in this work compared to the previous contributions in the literature discussed above.
Table 2
Comparison of the current fault-tolerant FCS proposed for the hybrid VTOL UAVs
Design of FTC schemes for trajectory tracking over the entire flight
–
–
–
✓
Handling faults at which flight phases
Cruise (Longitudinal flight only)
Cruise (Longitudinal flight only)
VTOL and Cruise
All phases, including the transition phases
Handling Simultaneous total failures
–
–
✓
✓
Employing vertical rotors during fault-free conditions
–
✓
–
✓
Control allocation technique
Pseudo inverse
Optimization-based (Quadratic Programming)
Pseudo inverse
Optimization-based (Linear Programming)
Maneuverability enhancement
–
–
–
✓
Testing performed
Simulation
Hardware in the loop (HIL)
Simulation
Simulation
1.3 Current Fault-Tolerance Abilities of Different VTOL UAVs Configurations
Considering the Px4 flight controller, taken as the state of the art of VTOL UAV FCSs. The Px4 control architecture of the hybrid VTOL UAV can be found through this link.1 The flight controller for the hybrid VTOL UAV presented by Px4 is based on having two separate controllers; a multicopter controller that only controls the vertical rotors and a fixed-wing controller that only controls the control surfaces. The multicopter controller is solely run during the VTOL phase, the fixed-wing controller is solely run during the cruise phase, and both are run concurrently during the transition phase from hover to forward flight (forward transition) after the vertical takeoff and vice versa (backward transition) before the vertical landing, where the vertical rotors are shut down during the forward flight phase. Recently the static mixer of the Px4 controller was replaced by a dynamic control allocation, which resolves the redundancy between controls of the same group, i.e., redundancy among the control surfaces only when the fixed-wing controller is running and redundancy among the vertical rotors when the multicopter controller is running.2
Although the Px4 is employed successfully with this configuration in real flights, it does not exploit the full capabilities of this VTOL configuration in terms of fault-tolerance and maneuverability. The key to capitalizing on the full capabilities of such configuration is to employ the vertical rotors with the control surfaces during the whole flight envelope. To achieve that, the design of the control loops should be reworked considering the nature of the hybrid VTOL UAV configuration with all the controls being active during all the phases and employing dynamic control allocation to resolve the redundancy between them. However, up till the latest version of the Px4 flight stack, such merit is not realized as the original technique of having parallel mutlicopter and fixed-wing controllers with two separate control allocation modules associated with each of them is followed; hence, the vertical rotors cannot be used to compensate for the control surfaces faults during the fixed-wing mode. However, the Px4 flight controller architecture is very versatile that it is generic for other VTOL UAV configurations such as the tailsitter and the tiltrotor, which is an outstanding feature but at the cost of non-exploiting the full potential of individual configurations such as the hybrid VTOL UAV configuration. Another room for improvement of the Px4 VTOL UAV controller is the transition control logic, where the transition success is highly dependent on the values supplied by the user such as the transition time and the values of thrust and flight speed values specifying the end of the transition phase which would result in the stall of the UAV if not precise enough, also, the altitude is not maintained during the transition where the transition process is implemented in an open-loop fashion by gradually increasing the forward thrust over the transition time hoping the UAV will develop a sufficient speed at the end of that transition time in the forward transition for instance.3
Moreover, the Px4 uses the pseudo-inverse control allocation algorithm, which we stated its downsides earlier. One of the contributions in the work presented here is the replacement of the current technique of having parallel mutlicopter and fixed-wing controllers, the currently prevailing design concept of the hybrid VTOL UAV FCSs [16, 24‐26], with a new design scheme that can deal with the hybrid VTOL UAV as a whole with all its available controls during all the flight phases, and hence, the vertical rotors can be employed with the control surfaces over the whole flight mission. The design of the proposed control scheme is detailed in Sect. 3. We list the downsides of the current state of the art of the Px4 that we try to overcome with the FCS presented in this study.
Having the vertical rotors as dead weights during the forward flight phase reduces the UAV's endurance and range.
Dependence of the success of the transition flight phase on the values of the transition time and transition thrust supplied by the user instead of having an automatic feedback control scheme for such phase.
Inability to employ the vertical rotors to compensate for the control surfaces' failures during the cruise flight phase.
Reliance on the pseudo-inverse control allocation algorithm which fails to find the feasible control commands for much of the attainable moment set of the UAV [22].
The main contribution of this work is to reveal the capabilities of the hybrid VTOL UAVs configuration compared to the other VTOL UAVs configurations regarding fault-tolerance and reliability. This is achieved by presenting a new FCS design for the hybrid VTOL UAV that alleviates its main drawback of having the vertical rotors as dead weights during the forward flight phases by employing them through the whole flight mission to handle severe failure cases of the primary controls and to enhance the maneuverability of the UAV during the fault-free cases. The results achieved show that hybrid VTOL UAVs can handle fault cases that other VTOL UAVs configurations cannot handle. The novelties of the proposed FCS presented can be concluded as follows:
Presenting a new FCS of the hybrid VTOL UAV configuration ensuring active fault-tolerance, enhanced maneuverability, and trajectory tracking over the entire flight mission from takeoff to landing.
Active fault-tolerance against simultaneous total failures of all the primary controls (control surfaces) during cruise and transition phases and completing the required mission without affecting the trajectory tracking.
Optimal dynamic control allocation design for employing the controls' redundancy. The control allocator features the following: achieving required acceleration commands maximally, minimizing controls' effort and induced drag, considering controls' saturation limits, and handling unattainable acceleration commands from the controller.
Employing the controls' redundancy in fault-free cases to enhance the UAV's maneuverability.
Performing forward and backward transitions automatically while maintaining the altitude hold during the transitions and handling total failures of the control surfaces during both transitions
The rest of the paper is organized as follows, Sect. 2 presents the dynamic modeling and the UAV's parameters used in the simulations, Sect. 3 is devoted to the FCS design, Sect. 4 illustrates the simulation results, and finally Sect. 5 concludes with a summary.
2 Dynamic System Modeling
The dual-system VTOL UAV can be modeled as a multirotor airframe mounted on a fixed-wing airframe to add the hover and VTOL capabilities to a typical fixed-wing airplane. Assuming the rigidity of the airplane, the equations of motion for small air vehicles presented in [27] can be used to model the UAV's motion in 3-dimensional space. The motion can be fully described by 12 states, 3 angular velocity components and 3 linear velocity components in the body axis, 3 Euler angles defining the orientation of the body axis w.r.t the earth fixed axis, and 3 components of the position of the airplane w.r.t the earth fixed axis. The rigid body 6 degrees of freedom (6-DOF) set of equations of motion comprises two groups of equations, the Dynamics and Kinematics equations.
The Dynamics equations relating applied forces and moments to the time rate of change of linear and angular velocities in the body axis.
The \(F=[{f}_{x},{f}_{y},{f}_{z}{]}^{T}\&H=[L,M,N{]}^{T}\) are the vectors representing the total forces and moments acting on the airplane due to aerodynamic, thrust, and gravity effects which are calculated from another set of equations then substituting their numerical values in Eq. (1) to solve for the states. \(V=[u,v,w{]}^{T} \& \omega =[p,q,r{]}^{T}\) are the linear and angular velocity vectors in the body axis, \(m\) is the airplane's mass, and \(I\) is the inertia tensor.
The Kinematics equations, Eq. (2), relate the velocity and angular rates vectors \(V \& \omega\) in the body axis to the velocity and Euler angles' rates in the inertial frame of reference, which describes the orientation of the airplane in the 3-dimensional space. Integrating them yields the position and attitude of the airplane w.r.t the inertial axis.
where \(P=[x,y,z{]}^{T}\)& \({\rm A}=[\phi ,\theta ,\psi {]}^{T}\) are the position vector w.r.t the inertial frame of reference and the attitude of the airplane described by the Euler angles, \({R}_{1} \& {R}_{2}\) are the transformation matrices used in Eq. (2) which are functions of the Euler angles as expressed in Eq. (3)
where \({C}_{\theta },{S}_{\phi }\) are short-hand abbreviations of \(\mathit{cos}\theta ,\mathit{sin}\phi\) and so on.
Equation (1) & (2) are the 12 ordinary differential equations describing the change of the 12 states of motion \(x(t)=[V,\omega ,A,P{]}^{T}\) in response to the applied forces and moments on the airplane. The system of equations of motion is solved by numerical integration for the values of the states vector \(x\) at each time step, Runge–Kutta 4th order numerical integration method [28] was used in our simulations with a time step of 0.01 s.
The total force acting on the airplane is the summation of the aerodynamic, gravity, and thrust forces as given in Eq. (4). The total moments are due to aerodynamics and thrust only, assuming the body axis origin is located at the center of gravity CG.
The gravity forces acting on the airplane are a function of the airplane's mass \(m\), gravitational acceleration g, pitch angle \(\theta\), and roll angle \(\phi\) and are given in Eq. (5)
The aerodynamic and thrust forces and moments can be calculated as the summation of the contributions of the fixed-wing and the multirotor airframes. The aerodynamic and thrust forces and moments of the fixed-wing and the quadrotor are calculated separately and are summed together to find the total forces and moments acting on the VTOL UAV; the aerodynamic interaction between the rotors and the fixed-wing airframe is neglected in this study, similar to other earlier studies in the literature [3, 4, 10]. For dual-system VTOL UAVs, there are no data or mathematical models yet available that allow for calculating the aerodynamic forces and moments of the whole airplane accounting for the aerodynamic effect of the spinning of the vertical rotor on the fixed-wing airframe.
2.1 Fixed-Wing Airframe Model
Porchazka et al. [13] performed CFD simulations to estimate the aerodynamic derivatives of the Aerosonde HQ VTOL UAV at a certain flight speed and certain running speed of the vertical rotors; however, the derivatives calculated cannot be used throughout the whole flight envelope with different flight speeds and rotational speeds of the vertical rotors. The mass and inertia parameters of the Aerosonde HQ UAV calculated in [13] were used in our study with the original aerodynamic derivatives of the fixed-wing Aerosonde UAV supplied in [27].
The thrust force \({f}_{{t}_{fw}}\) from the fixed-wing airframe is given in Eq. (6) as follows
The aerodynamic forces and moments from the fixed-wing airframe are given as a function of the airplane's flow conditions, derivatives, and geometric parameters in addition to the control surfaces inputs as in Eq. (7). Where \(\rho\) is the ambient air density, \({\delta }_{t}\in [\mathrm{0,1}]\) is the throttle input signal to the forward thrust propeller. Other parameters describing the motor and the propeller are supplied in [27].
The inputs \({\delta }_{a},{\delta }_{e},{\delta }_{r}\) are the aileron, elevator, and rudder deflections, respectively, and \(S,c,b\) are the wing's area, chord, and span, respectively. All control surfaces deflections are under the limits \(-2{5}^{\circ }\le {\delta }_{i}\le 2{5}^{\circ }\). Reference [27] includes values of all required coefficients and the parameters needed to calculate the lift and drag coefficients at a wide range of angles of attack including pre- and post-stall angles of attack. The aerodynamic lift and drag forces are transformed to the body axis as in Eq. (8)
The fixed-wing airframe contribution to the moments due to thrust is zero assuming the thrust line coincides with the airplane's x-axis; thus, the aerodynamic moments are as in Eq. (9)
Quadcopter airframe contributes to the forces and moments exerted on the airplane by the thrust forces of each vertical rotor and the torques generated by them due to the rotors' position relative to the center of gravity (CG) [29]. The thrust \(T\) and torque \(\tau\) created by the \({i}^{th}\) rotor are given by Eq. (10)
where \({K}_{T}\&{K}_{D}\) are the coefficients relating the thrust and torque of a rotor to its propeller rotational speed \(\omega\), as they vary according to the brushless motor used and the propeller, those coefficients are determined experimentally. Each two opposite rotors have the same spinning directions opposite to the other pair of rotors. The total thrust and moments exerted by the rotors are given as a function of the rotors’ rotational speeds as in Eq. (11) [29]
The parameters \({d}_{x}\&{d}_{y}\) are the relative offset positions of the vertical rotors w.r.t the airplane CG and their numerical values for our model are supplied in [13]. The coefficients \({K}_{T}\&{K}_{D}\) of the quadrotor system of the Aerosonde HQ UAV are not available; however, experimental data of the multirotor system of a VTOL UAV with similar mass and size [30] were used in our simulations. The aerodynamic contribution of the quadcopter system is neglected; the contributions of the quad are given in Eq. (12)
The values of total forces and moments acting on the UAV are obtained by adding the contribution of the fixed-wing airframe, calculated from Eq. (6), (8), and (9), and the quadcopter airframe's contribution, calculated from Eq. (12), in addition to the gravity forces of Eq. (5).
2.3 Dual-System VTOL UAV Model
Adding the fixed-wing and quadcopter airframes contributions to find the total forces and moments acting on the airplane, we obtain a multi–input–multi–output (MIMO) dynamic system describing the UAV's flight motion. The inputs are \(\left[\begin{array}{cc}\begin{array}{ccc}{\delta }_{a}& {\delta }_{e}& {\delta }_{r}\end{array}& \begin{array}{cccc}\begin{array}{cc}{\delta }_{t}& {\Omega }_{1}\end{array}& {\Omega }_{2}& {\Omega }_{3}& {\Omega }_{4}\end{array}\end{array}\right]\) where \({\Omega }_{i}={{\omega }_{i}}^{2}\) , the 12 states are\(\left[\begin{array}{cccc}V& \omega & A& P\end{array}\right]\), and the outputs are selected to be the total velocity, angle of attack, sideslip angle, and the flight path angle \(\left[\begin{array}{cccc}{V}_{t}& \alpha & \beta & \gamma \end{array}\right]\).
The redundancy/over-actuation property of the model appears clearly at this point; for example, a pitching motion can be obtained through the fixed-wing airframe contribution by deflecting the elevator or through the quadcopter airframe contribution by changing the rotational speeds of the forward or backward rotors. The same principle applies to other degrees of freedom, like roll, yaw, and acceleration along the z-axis.
A high fidelity nonlinear simulation model was created in the Simulink/MATLAB environment to simulate the dynamics of the dual-system VTOL UAV. The model was trimmed at different flight speeds using the Linearization toolbox in Simulink to find the equilibrium values for all the inputs and states for a steady-level flight at different flight speeds. Table 3 contains the VTOL UAV's trim points, including the elevator's trim angle and thrust at different flight speeds and angles of attack. Those trim points are used to validate the performance of the closed-loop system after applying the controller and the control allocation module. It was observed that the control allocation module designed commands the exact trim values of the inputs according to the desired flight speed at the steady-state condition, as discussed later in the results section.
Table 3
Trim points of steady-level cruising flight at different flight speeds
\({V}_{t}\)(m/sec)
\(\alpha\)(rad)
\({\delta }_{e}\)(rad)
\({\delta }_{t}\)
18
0.27605
− 0.25656
0.25879
20
0.20948
− 0.20596
0.27225
25
0.10629
− 0.12754
0.33450
30
0.04987
− 0.08466
0.39891
33
0.02757
− 0.06771
0.43800
35
0.01577
− 0.05874
0.46417
40
− 0.00638
− 0.041908
0.5298
3 Flight Control System Architecture
The flight control system is made up of 2 modules; the controller module and the control allocation module, as shown in Fig. 2. The FCS is based on dynamic inversion in which a controller module is to generate the desired closed-loop dynamics of the UAV, which are a subset of the UAV's accelerations and are called the virtual controls. Those desired accelerations are passed to the control allocation module that commands the UAV's controls to generate the desired accelerations. The dynamic inversion method fits perfectly with the control allocation, and both are employed together in the FCSs of modern aircrafts currently [22]. Any control design method can be used to design the controller module to calculate the virtual inputs, and then, control allocation calculates the actual inputs to the UAV's controls corresponding to those virtual inputs. The design's central question is to determine the acceleration commands/virtual inputs that will be passed from the controller to the control allocator and how they should be calculated at various phases of flight. The key aspect of this architecture is to separate the control allocation problem from the trajectory tracking problem, making the FCS flexible and generic enough to handle any overactuated system.
Fig. 2
FCS top-level layout
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As illustrated in Sect. 3.1, our controller module should pass 4 acceleration commands to the control allocator at each time step in the fault-free case, and only 3 acceleration commands in the fault-existence case. The way of calculating each acceleration command is dependent on the flight phase. This approach differs from the common way of giving only the 3 rotational acceleration commands as in [22], due to the different nature of the hybrid VTOL UAV configuration. As the system is overactuated, multiple combinations of control actions exist that achieve a given commanded set of accelerations. The control allocation module designed in this study is based on optimization methods [31, 32] such that it calculates the optimum combination of controls that achieves the desired acceleration while optimizing over a certain cost function, as will be shown in Sect. 3.2.
3.1 Controller Module
The controller module calculates the desired accelerations \({\left(\dot{p},\dot{q},\dot{r},{a}_{z}\right)}_{\mathrm{des}}\), the 3 rotational accelerations plus the z-component of the linear acceleration, for the UAV to follow the desired trajectory during all the flight phases. In this work, the successive loop closure method [27] with classical PID controllers [33] is used to design the controller module. The controller module consists of 2 separate controllers, a VTOL controller for the vertical takeoff and landing and the back transition phases and a cruise controller for the forward transition and cruise phases. Switching between the 2 controllers occurs according to the current phase of flight, such that only one controller is active at a time. The VTOL and cruise controllers calculate \({\left(p,q,r,{a}_{z}\right)}_{des}\), and the regulator block shown in Fig. 2 calculates the desired angular accelerations \({\left(\dot{p},\dot{q},\dot{r}\right)}_{des}\) from the angular rates using additional feedback control loops and PID controls.
Figure 3 represents a flowchart of the controller module logic and how each of desired acceleration commands is calculated by the successive loop closure method during every flight phase during the fault and fault-free cases.
Fig. 3
Successive loop closure schemes for calculating the required accelerations at each phase of flight
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3.1.1 VTOL Controller
The VTOL controller (for vertical takeoff and landing and back transition) is very similar to traditional quadcopter controllers as the airplane is considered a quadcopter during this phase.
The acceleration along the Z-direction command is calculated from the error in the altitude as Eq. (13). The PID gains in (13) are used for the remaining control loops in the VTOL controller.
The pitch and roll accelerations’ commands \({p}_{com},{q}_{com}\) are calculated similarly from the error between the desired pitch and roll angles and their feedback values. The calculation of roll rate command is shown in Eq. (14), and the pitch rate command is calculated similarly.
The desired pitch & roll angles are calculated in an outer loop based on the error between the body axis velocity components \((u, v)\) and their desired values set to zero. In this way, the airplane is kept from moving in X or Y directions during the hovering and VTOL phases. During the back transition phase (from cruise to hover), the airplane decelerates until the velocity components \((u, v)\) become zero, which is needed to reach the hover condition. The pitch angle command is calculated as in Eq. (15), and the roll angle command is calculated in a similar way but with \({e}_{v}=v\) instead of \({e}_{u}\).
The yaw acceleration command is calculated from the error in the yaw angle and the forward thrust set to zero.
3.1.2 Cruise controller
The Cruise controller (for cruise and forward transition) resembles the fixed-wing airplane’s autopilots [35]; it only differs in the addition of the acceleration along the Z-direction to the calculated commands.
The acceleration along the Z-direction command is calculated as the resultant of the weight and aerodynamic force components along the Z-axis as in Eq. (16). Thus, the vertical thrust is used with the aerodynamic forces to balance the weight, performing transition with no altitude loss as in [16, 36] and enabling coordinated turns at higher bank angles which resulted in reduced turn radii.
The pitch rate command is calculated from the error between the desired pitch rate and its feedback value; an outer loop calculates the desired pitch rate from the error in pitch angle, which is set to be the desired climb angle \(\gamma\) calculated from the error in altitude to achieve the altitude hold. The roll acceleration command is calculated from the error between the desired roll rate and its feedback value. An outer loop calculates the desired roll rate as the error between the desired roll angle and its feedback value. The desired roll angle is set to be the needed bank angle to achieve coordination [35], which is a function of the flight speed and the desired yaw rate as in Eq. (17)
$$\phi =\frac{{V}_{t}}{g}\dot{\psi }$$
(17)
The yaw damper loop calculates the yaw acceleration command [35]. A separate velocity control loop calculates the forward thrust.
3.2 Control Allocation Module
The control allocator (CA) module role is to resolve the controls' redundancy and calculate the final commands of all the control surfaces and vertical rotors based on the desired accelerations \({\left(\dot{p},\dot{q},\dot{r},{a}_{z}\right)}_{\mathrm{des}}\) given by the controller module. Given a set of desired rotational accelerations, it can be achieved using the vertical rotors or the control surfaces or using them altogether. Control allocation solves the over-actuation problem by calculating the combination of control actions that achieve the desired accelerations taking into consideration their saturation limits [22]. Surveying of the various control allocation techniques are presented in [22, 31], and the linear programming technique was selected for our CA design. The designed CA can achieve the desired acceleration maximally with admissible control actions while minimizing the energy consumption by minimizing the control actions' magnitudes.
The control allocation problem statement is given as follows. Our UAV dynamics derived in Sect. 2 can be casted as in Eq. (18)
$$\dot{x}=f\left(x\right)+Bu$$
(18)
Control allocation problem statement: Given the effectiveness matrix \(B\) and the current states \(x\) find the control action \(U\) to achieve the desired dynamics \({\dot{x}}_{des}\) such that \({u}_{l}<u<{u}_{u}\) where \({u}_{l} \& {u}_{u}\) are the lower and upper bounds of the control actions vector. The nominal acceleration is defined in Eq. (19)
$${\dot{x}}_{\mathrm{nom}}=f\left(x\right)$$
(19)
where \({\dot{x}}_{nom}\) is considered the nominal accelerations obtained when applying nominal controls \({u}={u}_{nom}=0\) at the current states \(x\). The nominal accelerations and the effectiveness matrix are calculated at each instant as they depend on the current states by the onboard model (OBM) as shown in Sect. 3.3, to perform the dynamic inversion [22]
The commands passed to the CA is the difference between the desired acceleration and the nominal acceleration vectors as in Eq. (20)
As advised by [22], the term \(\lambda\) introduced in the equality constraint \(\mathrm{Bu}={\lambda m}_{\mathrm{des}}\) instead of just \(\mathrm{Bu}={m}_{\mathrm{des}}\) to handle the control commands that are unattainable by feasible control actions satisfying the condition \({u}_{l}\le u\le {u}_{u}\) which would result in a set of incompatible constraints causing the optimization problem to have no solution. Driving the value of \(\lambda\) to 1 means that the desired acceleration vector \({m}_{\mathrm{des}}\) is achieved maximally. The L1 norm is selected for the second term in the cost function to keep the cost function linear. The \(\epsilon\) is a tuning parameter indicating the weighting of minimizing the control actions objective w.r.t achieving the desired accelerations vector objective. The vector \({W}_{u}\) represents the weight given to control actions usage; the higher the weight given to the elevator, the less it is used. \(u\) is a 7 × 1 vector containing the 3 control surfaces deflections and the 4 input signals of the vertical rotors. The limits on \({u}_{l}\&{u}_{u}\) used in our simulations are given in Eq. (22), \({u}_{p}\) is a constant vector supplied to the CA with the remaining parameters that represent the preferred controls setting vector (zeros in our case), which the CA minimizes the deviation of the solution vector \(u\) from it
Casting the CA linear program into the standard linear programming problem form, Eq. (23), is an essential step to apply the solving algorithms to it and write the embedded code that implements the algorithm solving the problem as a part of the flight control system software.
$$\begin{gathered} \mathop {\min }\limits_{x} J\left( x \right) = C^{T} x \hfill \\ {\text{Such that}} \hfill \\ Ax = b \hfill \\ x \ge 0 \hfill \\ \end{gathered}$$
(23)
The final form of the proposed CA program in Eq. (21) in the standard form is introduced here after adding the slack variables and manipulating the constraints equations to arrive at the final standard form. The elements of our CA program in the standard form are given in Eq. (25) with \(n=7\)
where \(u\) which is the final control action is replaced as shown in Eq. (25).
$$u={u}_{p}+{u}^{+}-{u}^{-}$$
(25)
The linear program is solved using the interior point method predictor–corrector algorithm [37], where the interior point method has been proven to be more efficient than the well-known simplex method for this type of problem [38].
In cases of fault existence, the command of the acceleration along the Z-direction is dropped down and only the 3 rotational accelerations are passed to the control allocator. The fault detection and isolation (FDI) design is not in the scope of this study; thus, it is assumed that once faults happen they are detected, which is done in similar studies [11‐15]
3.3 Onboard Model (OBM)
The OBM is essential to perform the dynamic inversion step and supplying the required inputs to the CA, which are: the effectiveness matrix \(B\), the upper and lower limits of the control actions \({u}_{u} \& {u}_{l}\), the term \(\epsilon\), the weighting vector \({W}_{u}\), and the nominal accelerations term \({\dot{x}}_{\mathrm{nom}}\).
The nominal accelerations and the effectiveness matrix are calculated at each time instant during the flight, and their values are passed to the control allocator module. Comparing Eq. (1) & (2) to Eq. (18) \(B\) can be calculated as in Eq. (26) & (27)
The nominal accelerations are calculated from Eq. (18) by setting all controls to zero. In cases of fault existence, the corresponding vector to the faulty controls in the effectiveness matrix \(B\) is set to zeros so that the control allocator uses the healthy controls only, as shown in the results section.
4 Results
Animations of the following results can be found through this link.4
4.1 Fault-Tolerance Test
The fault-free test case represents a complete mission from takeoff to landing with no faults encountered throughout the flight. This mission represents the baseline for comparison with the fault cases. The mission goes as follows.
Vertical takeoff to altitude (50 m)
Forward transition at constant altitude ending to a cruise condition of flight speed (Vt = 25m/sec)
Cruise at altitude (70 m) and flight speed (Vt = 33 m/sec)
Loiter forming 2 circles, steady level coordinated turning at a constant speed
Cruise at altitude (70 m) & flight speed (Vt = 33 m/sec)
Back transition to hover condition
Vertical landing
The fault scenario tested represents performing the same mission but with total failure of all the control surfaces occurring during the flight, having them locked at their positions where the elevator is jammed at an arbitrary nonzero angle. A comparison of the fault-existence and fault-free scenarios is shown in Figs. 4 to 9.
Fig. 4
Flight trajectory of VTOL UAV in fault and fault-free cases
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Figure 4 shows the 3-dimensional flight trajectory of the dual-system VTOL UAV performing the required mission, including the following phases (vertical takeoff – hover – forward transition – cruise – loiter – backward transition – vertical landing) and compares the 3-dimensional flight trajectory in fault and fault-free cases. The FCS performed the intended mission successfully during fault-free and fault-existence cases. The total failure of all the control surfaces during the forward transition phase was handled. The vertical rotors were employed to compensate for that severe failure throughout the flight mission. The back transition phase was the most affected by the elevator jamming; however, the FCS employed the rotors to overcome that influence and decelerate the airplane to hover while keeping the altitude hold, as shown in Fig. 5. The main drawback of the dual-system VTOL UAV of having the vertical rotors as dead weights during the cruise flight phase can now be overcome and converted to a significant fault-tolerance ability by employing the redundancy of the controls during the whole flight envelope, as proposed in this study. Completing such a mission under this severe fault scenario is a unique ability that the dual-system VTOL UAV inherently possesses compared to the other VTOL configurations as earlier discussed which is revealed by the FCS design presented here.
Fig. 5
Altitude and velocity responses in fault and fault-free cases
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Figure 5 shows the altitude and velocity responses in fault and fault-free cases compared to their desired trajectories. The time instant of fault occurrence (t = 40 s) is indicated in the figure. It can be seen that altitude and velocity hold were performed during all the phases, including the loiter and the forward and backward transitions despite the fault-existence.
Figure 6 shows the Euler angles' responses, and the pitch angle is compared against the trim values, listed earlier in Table 3, at the different flight speeds. It is seen that the control allocator did not command any undesired control actions that could cause rolling or yawing of the airplane during the symmetric flight conditions, and only banking occurred during the loiter phase. At the time instant of fault occurrence, the pitch angle dropped suddenly due to the locking of the elevator at the zero-deflection position; however, the pitch angle was driven to its trim value by the action of the rotors which were employed by the control system to trim the airplane instead of the elevator and also performed the loiter maneuver exactly like the fault-free case instead of the ailerons and the rudder.
Fig. 6
Euler angles responses, pitch angle compared to its trim value according to flight speed
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Figures 7 and 8 show the control surfaces and the forward thrust commands. The merits of the control allocation appear here clearly; all the control actions commanded are within their allowable limits. Due to its optimizing behavior, the CA uses the healthy controls wisely to respond to the controller's commands. As a validation, the trim values of each flight condition's thrust and elevator commands were plotted along with the values commanded by the allocator where the control allocator commands the very same values of the trim commands at the steady-state in the fault-free case. In the fault-existence case, all the control surfaces were locked after the fault happened. The rudder and ailerons were not used during the loitering, and the elevator was not locked at the trim conditions; however, the control system relied on the rotors to automatically compensate for the control surfaces failures to trim the airplane and perform the loitering.
Fig. 7
Aileron & rudder deflections in fault and fault-free cases
Fig. 8
Elevator & thrust commands, elevator compared to its trim values at each flight speed
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Figure 9 shows the control actions of the vertical rotors whose limits are (0,1). In the fault-free case, the rotors aid the control surfaces during the transient periods to perform the desired maneuver, which distinguishes the work presented here. As in [11, 15] the vertical rotors are used only in the fault-existence case, and in the Px4 FCS, the vertical rotors are not used during the forward flight mode, wasting a great ability of the hybrid VTOL UAV configuration. Moreover, the rotors' commands go to zero at the steady-state period of the cruise phases, i.e., the control system does not use the rotors to trim the airplane as the aerodynamic lift is sufficient to carry the weight, and the elevator only can trim the airplane with no rotors usage as long as the elevator is working, thus preventing excess power usage and extending the airplane's endurance. In the fault-existence scenario, the rotors were used after the fault occurrence to trim the airplane longitudinally and track the desired altitude instead of the elevator. During the loiter, the rotors were used to perform the rule of the rudder and ailerons to turn the airplane and to increase the total lift to keep the altitude instead of the elevator, in addition to performing all other maneuvers according to the intended flight mission profile.
Fig. 9
Vertical rotors commands
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4.2 Maneuverability Enhancement
To our best knowledge, this study is the first to investigate the effect of employing controls redundancy of VTOL UAVs to enhance the UAV's maneuverability. The following results show the effect of the proposed flight control system in enhancing the maneuverability of the dual-system VTOL UAVs by reducing the steady-level turn radius, as the proposed design employs the vertical rotors with the control surfaces during the cruise phase.
To emphasize the maneuverability enhancement, the designed control system was replaced by a flight control system employing the control surfaces only, and both were used to perform steady-level turning at the same flight speed. The bank angle to perform a coordinated turn is given by Eq. (17). The turn radius of a turn can be calculated by Eq. (28) [35].
$$R = \frac{{V^{2} }}{{g\tan \phi }}$$
(28)
As the turn rate \(\dot{\psi }\) increases, the turn radius \(R\) reduces until a minimum turn radius is achieved. For an airplane to turn at a constant altitude, the lift force should be increased such that the vertical component of the lift equalizes the weight, where the lift is increased by deflecting the elevator and thus increasing the angle of attack and pitch angle which may cause advanced stall at the same flight speed. However, the dual-system VTOL UAV can turn at higher bank angles, reducing the minimum turn radius by adding the vertical thrust from the vertical rotors to the aerodynamic lift to balance the weight.
The proposed FCS that employs the rotors with the control surfaces proved to minimize the turn radius of the VTOL UAV compared to the minimum turn radius that can be achieved using the control surfaces only. Reducing the turn radius of steady-level turns is an excellent ability of the dual-system VTOL UAV, which was revealed by the flight control system design proposed in this study which highlights the importance of employing the vertical rotors with the control surfaces during the fault-free cases.
Figure 10 shows the flight trajectory of the same airplane loitering at the same flight speed at the minimum turn radius possible. The blue trajectory is obtained by employing the control surfaces only with the vertical rotors shut off, which is the case of the traditional control systems found in the literature, and the red trajectory is for the same airplane but with the FCS proposed in this study.
Fig. 10
Loitering flight trajectory using control surfaces only compared to using vertical rotors with the control surfaces
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Figure 11 shows the top view of the flight trajectory; the flight speed was 25m/sec; approximately 38% reduction in the turn radius was achieved.
Fig. 11
Top view of the loitering maneuvers
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Table 4 shows a comparison between all the turn parameters in both cases. Case 1 control surfaces are only used, and case 2 control surfaces and rotors are used together.
Table 4
Turn maneuver parameters achieved
Symbol
Quantity
Case 1
Control Surfaces
Case 2
Control Surfaces + Rotors
\(R\)
Minimum Turn Radius (m)
55.46
34.25
\(\dot{\psi }\)
Turn Rate (deg/sec)
25.83
41.82
\(\phi\)
Bank angle (deg)
50.92
63.65
\(\alpha\)
Angle of attack (deg)
11.52
10
\(\theta\)
Pitch angle (deg)
8.381
6.195
Figure 12 shows the Euler angles for both cases; the same change in heading angle \(\psi\) was achieved but achieved faster in case 2 due to the higher turn rate achieved; hence, the loiter in case 2 finished earlier than case 1 with a higher bank angle \(\phi\) in case 2. It is also seen that in case 2, the pitch angle \(\theta\) was the same as its trim value, i.e., the aerodynamic lift was not increased, and the thrust of the vertical rotor was used to increase the total lifting force of the vehicle to balance the weight and maintain the altitude hold. In case 1, the controller increased the pitch angle to increase the aerodynamic lift to balance the weight and achieve the altitude hold, which resulted in banking with a lower bank angle and turn rate and greater turn radius.
Fig. 12
Euler angles responses in the loitering maneuvers
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Another maneuver shown below to exhibit the smoothness of performing forward and back transitions autonomously besides the enhanced maneuverability of the UAV achieved is illustrated below and named the escape maneuver. In this maneuver, the aircraft is required to perform a sudden steady-level sharp turn. The maneuver is performed by 3 techniques as follows:
Using the control surfaces only
Using the vertical rotors with the control surfaces
Making a back transition, then changing heading while hovering, then making a forward transition and recovering the original flight speed
Figure 13 shows the top view of the maneuver. In case 2, a sharper turn was achieved than in case 1, and in case 3, the tightest turn was achieved.
Fig. 13
Top view of the escape maneuver performed by 3 techniques
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Figure 14 shows the altitude and velocity responses in the 3 cases. Altitude hold was achieved in the 3 cases; however, the disturbance in the attitude in case 2 was the most significant. The deceleration and acceleration action in case 3 can be observed with the least disturbance in the altitude. The idea is to highlight the ability of the presented FCS to perform such maneuver in various ways with no need from the user to supply any inputs, giving the user the freedom to choose the mode of the steady-level turn, either by performing transitions or making the turn at the same flight speed, without requiring any further inputs or interference from the operator.
Fig. 14
Altitude and velocity response of the escape maneuver
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5 Discussion and Conclusion
This paper proposes a new architecture for active fault-tolerant FCS design of dual-system/hybrid VTOL UAVs. The paper's primary purpose is to draw the attention to the reliability of this configuration of VTOL UAVs. The advantages gained when the flight control system technique of such configuration is reworked, such that the controls’ redundancy of this vehicle is employed through all phases of flight, turns the drawback of such configuration into tangible and unique points of strength. We have addressed not only the fault-tolerance ability of the proposed FCS but also the maneuverability enhancement achieved and presented an FCS that provides trajectory tracking, active fault-tolerance, and enhanced UAV maneuverability altogether, which was not achieved by current and formerly proposed FCS available in the literature.
Employing the FCS presented here to the hybrid VTOL UAV showed that it can handle the severest fault scenarios out of all VTOL UAVs configurations according to the current state of the art of peer FCS designs. To our best knowledge, this work is the first to study the effect of employing controls redundancy to enhance the maneuverability of VTOL UAV configuration, which was emphasized by reducing the minimum turn radius of the airplane by 38%, which would increase the use of this configuration in a variety of applications such as surveillance and aerial photography. Reducing the minimum turn radius of the hybrid VTOL UAV is a vital outcome of this study. Apart from its novelty, it provides an excellent advantage for that UAV configuration to perform a variety of missions such as navigating through cluttered environments, obstacle avoidance, and in pursuit-evasion games problems encompassing a wide range of UAV's problems of great interest like air-combat problems and active-target-defense problems [39].
Another crucial conclusion made out of this work is that under-actuated vehicles that feature over-actuation w.r.t a subset of its degrees of freedom, specifically the rotational degrees of freedom, are highly more efficient than fully actuated vehicles regarding fault-tolerance, after comparing the fault-tolerance results obtained here and in other similar works compared to the conclusions made about the fully actuated vehicles as advised in [10].
In conclusion, this study has shown the necessity of employing the vertical rotors with the control surfaces of dual-system VTOL UAVs during all flight phases. However, we list here some of the limitations existing. Implementing the dynamic inversion control technique requires accurate feedback measurement, modeling, and identifying the system's parameters. Current commercial flight controllers like Px4 offer sufficient feedback rate and state estimation of the UAV, which encourages to implement the proposed FCS algorithm to the Px4 flight stack and to test its performance in real flights as the following steps to this work. Another research direction is to employ control techniques such as the model reference adaptive control (MRAC) technique to replace the dynamic inversion technique, which does not require having the exact model and parameters of the system. However, parameter identification of the UAV is still necessary for the control allocation which mainly relies on the values of the effectiveness matrix elements, including the control derivatives of all the redundant controls. A question that needs to be targeted is how to model the aerodynamic interaction between the vertical spinning rotors and the airframe. Little research has targeted this problem so far [13, 40], but no complete model for this interaction at all flight speeds and rotational speeds for the vertical rotors has yet been presented. The next stage of our research will be experimental validation of the proposed control system design by performing several flight tests to test the fault and fault-free scenarios, the proposed flight control system modeled in Simulink will be implemented on the Px4 flight controller unit, and a series of wind tunnel tests will be conducted to estimate the stability and control derivatives to study the effect of the spinning rotors experimentally.
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