Design and experimental testing of safe flight control system for novel vertical take-off and landing aircraft

2.1. Structural design

As shown in Fig. 1, the research object of this paper is a multirotor aircraft with remarkable characteristics that can realize the control of its flight attitude by adjusting the rotational speeds of its rotors. The rotor aircraft structure is more compact without the need for a tail, the thrusting force of the rotor is more balanced than that of a single-rotor aircraft, and the flight attitude is more stable. In addition, it has lower hover and take-off requirements than many other rotor aircrafts [18].

Fig. 1Novel octocopter configuration

Most traditional eight-rotor aircrafts use eight rotors arranged on a single-layer fuselage structure or in pairs on four arms in a coaxial configuration. Compared to single-layer multirotor aircrafts, this work’s two-layer structure has more space by staggering the adjacent rotor, so that it can accommodate larger rotors. As shown in Fig. 2 (a)-(b), when the fuselage arm length $l=L$, the maximum rotor radius of the new octocopter configuration $R=\frac{1}{\sqrt{1-1/\sqrt{2}}}r\approx 3.414r$.

Fig. 2a) Model of flow fields in coaxial double-rotor helicopter; b) model of new octocopter configuration in upper layer; c) model of standard octocopter configuration

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According to the rotor thrust formula, assuming that the thrust coefficient $C_T$ and rotor angular velocity $\mathrm{\Omega }$ are the same, when the rotor diameter increases by more than a factor of 3, the thrust force of the multirotor aircraft can be more than 81 times than that of a single-rotor aircraft with the same fuselage size.

The thrust is $T=\frac{1}{2}\rho \pi R^2{\left(\mathrm{\Omega }R\right)}^2{C}_T$, where $\rho$ is the density, $R$ is the rotor radius, $\mathrm{\Omega }$ is the rotor angular velocity, and $C_T$ is the thrust coefficient. Parameter $C_T$ is constant when the airfoil is fixed. As a preliminary work focused on the feasibility of the novel octocopter, its performance evaluation in this paper is simply based on the advantages of the maximum performance of thrust $T$ from larger rotor radius $R$, ignoring the parameter design related to the airfoil.

Due to the lack of prior studies on the aerodynamic characteristics of coaxial multicopters, the aerodynamic characteristics of a single-rotor helicopter and a coaxial double-rotor helicopter were used to illustrate the possible thrust and aerodynamic efficiency loss of rotor aircrafts with coaxial configuration. Compared to a coaxial double-rotor aircraft, such a rotor structure effectively avoids the aerodynamic interference between the upper and lower rotors. For comparison, the following calculated upper and lower rotor thrusts were distributed, and their tensile strengths were compared to those of the rotor blades of a coaxial rotor. The setting angle of the upper rotor was 9°, and that of the lower rotor was 10°. The qualitative sketch results are shown in Fig. 2 below, which reveals that the thrusts of the upper and lower rotors were reduced compared to those of a single rotor with the same setting angle of a coaxial rotor.

For coaxial rotors, as shown in Fig. 2(c), if they are regarded as two separate rotors in the analysis, considering the influence of the flow fields of the two rotors, the trend of the induced vector gradually increases along the axial direction near the boundary in the downstream direction. For the upper rotor, due to the downward induction of the lower rotor, the practical working angle of attack decreases, so the thrust is smaller than that produced by the single upper rotor for the same collective pitch in the same working state. For the lower rotor, a large part of the airfoil cross-section is in the downwash of the upper rotor, the actual working angle of attack is much smaller, and the thrust loss is much bigger [19].

Therefore, this paper used an octocopter configuration, which was divided into two layers different from coaxial double-rotor configurations. This design both improved the efficiency of the thrust of the single rotor, and effectively avoided the aerodynamic interference between the upper and lower rotors of the coaxial double rotor. Second, octocopter aircrafts do not require a variable pitch system when flying under different conditions. The thrust forces of several rotors must be controlled to complete a flight. An octocopter aircraft is not only easier to manipulate than one with a coaxial double-rotor system, but also requires a less complicated variable pitch and transmission structure. A multirotor aircraft reduces the complexity of the structural design but complicates the installation at the same time.

2.2. Mathematical model

In this paper, a six-degrees-of-freedom simulation model of an octocopter aircraft was established, and Newton-Euler’s six-degrees-of-freedom inertia equation was adopted. The body posture and flight position were described using two coordinate systems: A geodetic coordinate system and a body coordinate system [20]. The Euler-Lagrange and Newton–Euler formulations are the two broadly adopted approaches for the dynamic analysis of robot manipulators [21].

The related coordinate system was firstly defined to establish a mathematical model of the system.

Fig. 3Mathematical system description. O-XYZ– global coordinate frame; o-xyz – moving coordinate frame; θx, θy, and θz– attitude angles; ωi (i= 1~8) – angular rotor velocity; Fi (i= 1~8) – rotor thrust

As shown in Fig. 3, $O$-$x_g{y}_g{z}_g$ is the ground inertial coordinate system, which is a fixed coordinate system with respect to the ground; $O$-$x_b{y}_b{z}_b$ is the body axis coordinate system – the origin $o$ is fixed at the fuselage’s center of gravity, and the axes $x$ and $y$ are fixed in the fuselage. $\theta$ is the angle between $x_b$ and the plane $O$-$x_g{y}_g$, which represents the pitch angle; $\psi$ is the angle between the projection of the axis of the body axis coordinate system $x_b$ in the horizontal plane and the axis of the ground coordinate system $x_g$, which represents the yaw angle; $\varphi$ is the angle between the axis of the body axis coordinate system $z_b$ and the vertical plane through the body's axis $x_b$, which represents the roll angle.

Without considering the linear motion between the two coordinate systems, that is, if it is assumed that $O$ and $o$ coincide with one another, it is possible to rotate the two coordinate systems so that they overlap. Therefore, it is possible to obtain the coordinate transformation matrix of the two coordinate systems:

where $S\theta$ represents $\mathrm{s}\mathrm{i}\mathrm{n}\theta$, $C\theta$ represents $\mathrm{c}\mathrm{o}\mathrm{s}\theta$, and the other signs have similar meanings. $\psi$, $\theta$, and $\varphi$ represent the angles of the yaw, pitch, and roll, respectively. The thrust force of the eight rotors is $F_i$ ($i=$ 1, 2, 3, 4, 5, 6, 7, 8) in the body axis coordinate system, and the thrust of the aircraft $F_B$ can be expressed as:

The thrust $F_E$ in the ground inertial coordinate system is obtained using the coordinate transformation matrix $R$, that is:

Ignoring the air resistance of the aircraft, it is possible to obtain as follows:

where $m$ is the mass of the octocopter aircraft and $g$ represents the gravitational acceleration. As shown in Fig. 3, the forward direction is defined as the positive direction of the $x$-axis in the body axis coordinate system. When the receiver receives a left turn signal, the flight control program increases the speed of rotors 2, 3, and 4 and reduces the speed of rotors 6, 7, and 8, which can increase thrusts $F_2$, $F_3$, and $F_4$ and can reduce thrusts $F_6$, $F_7$, and $F_8$. A rolling moment toward the left of the mass center of the aircraft is then exerted on the blades, making the aircraft perform a rolling to perform the left maneuver. In contrast, when the receiver receives a right turn signal, the flight control program reduces the speed of rotors 2, 3, and 4 and increases the speed of rotors 6, 7, and 8, which can reduce thrusts $F_2$, $F_3$, and $F_4$ and can increase thrusts $F_6$, $F_7$, and $F_8$. A rolling moment toward the right of the mass center of the aircraft is then exerted on the blades, making the aircraft perform rolling to perform the right maneuver. Therefore, the rolling movement can be carried out by controlling the difference in speed between rotors 2, 3, and 4 and rotors 6, 7, and 8.

The principles of the pitching and rolling movements of the multirotor aircraft are similar. When the receiver receives the order of flying forward, the flight control program increases the speed of rotors 4, 5, and 6 and reduces the speed of rotors 1, 2, and 8, which can increase thrusts $F_4$, $F_5$, and $F_6$ and reduces thrusts $F_1$, $F_2$, and $F_8$. A forward pitching moment toward the mass center of the aircraft is then exerted on the blades, making the aircraft perform a flying forward maneuver. In contrast, when the receiver receives the order of pitching backward, the flight control program reduces the speed of rotors 4, 5, and 6 and increases the speed of rotors 1, 2, and 8, which can reduce thrusts $F_4$, $F_5$, and $F_6$ and increases thrusts $F_1$, $F_2$, and $F_8$. A backward pitching moment toward the mass center of the aircraft is then exerted on the blades, making the aircraft perform a flying backward maneuver. Therefore, a pitching movement can be carried out by controlling the difference in speed between rotors 1, 2, and 8 and rotors 4, 5, and 6.

The yawing movement of the multirotor aircraft is mainly realized by the difference in torque between the positive and negative rotors. In the design of a multirotor system, in a view looking down, a rotor with a counterclockwise rotation is generally defined as a positive rotor, while a rotor with a clockwise rotation is defined as a negative rotor. Applying this condition to the aircraft designed in this paper, rotors 2, 4, 6, and 8 are positive rotors, and rotors 1, 3, 5, and 7 are negative rotors. The aircraft can fly in the positive direction by increasing the speeds of rotors 1, 3, 5, and 7 and by reducing the speeds of rotors 2, 4, 6, and 8, while it can fly in the negative direction by reducing the speeds of rotors 1, 3, 5, and 7 and by increasing the speeds of rotors 2, 4, 6, and 8. Therefore, a yawing movement can be carried out by controlling the difference in speed between rotors 1, 3, 5, and 7 and rotors 2, 4, 6, and 8.

$I_X$, $I_Y$ and $I_Z$ define the moments of inertia regarding the three axes of the octocopter aircraft, and $U_2$, $U_3$ and $U_4$ are actual torques generated by eight rotors, which refer to the rolling, pitching, and yawing movements. Assuming that the structure of the octocopter aircraft is completely symmetrical and ignoring air resistance and gyroscopic effects, the equations of small-angle motion for this system are as follows:

where $k_i$, $i=1,...,5$ are constants; $b_1$ and $b_2$ refer to the length of the upper and lower fuselage arms, respectively; ${\omega }_i$, $i=1,...,\mathrm{}8$ represents the angular velocity of the eight rotors.

The total thrust $U_1$ is:

where $a$ is a constant. Finally, it is possible to obtain a simplified mathematical model of the octocopter aircraft as follows:

The verification of model in Eq. (7) can rely on the flight experiment shown in Section 5, which can verify the model of octocopter UAV accurately, rather than relying on computer simulation only.

3.1. Attitude calculation module

The attitude calculation module obtains data from sensor modules, including GPS (Global Positioning System), IMU (Inertial Measurement Unit), barometer, and magnetometer, using the Uorb method. Then, the data, including the speed, position, angle, and angular velocity, can be calculated using the extended Kalman filtering (EKF) algorithm. This module never stops throughout the flight and always provides real-time data for other modules. Fig. 4 presents the attitude algorithm schematic.

Fig. 4Attitude algorithm schematic

3.2. Attitude and position control modules

Position and attitude control are two of the most important modules of a multirotor aircraft. The normal operation of these two modules is related to the flight safety of the aircraft. Attitude control has a high operation speed, which can significantly affect the flight safety, so the attitude control module was designed as the inner loop. The operating speed of the position control is low, which causes a relatively smaller impact on the flight safety, because the position control module was designed as the outer loop. The feedback data of these two modules come from the attitude calculation module, which is also regulated by the flight mode and its related parameters. The PID controller is proposed for attitude and position control, which parameters are pre-set based on the UAV model, and will not be tuned adaptively. The PID controller generates tracking control based on error feedback, and makes the position and attitude of UAV track the desired state in real time.

3.2.1. Attitude control

The attitude control also consists of two parts. The outer loop is controlled by the proportional control of the angle, and the inner loop is controlled by the PID control of the angular velocity. Because the ultimate objective of controlling the rotor’s rotation is the angular velocity, a more complete inner-ring PID control scheme was designed for the angular velocity.

For a given attitude angle ${\left[{\theta }_{xc}{\theta }_{yc}{\theta }_{zc}\right]}^T$, the feedback attitude angle ${\left[{\theta }_x{\theta }_y{\theta }_z\right]}^T$ is:

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$\left\{\begin{array}{l}{U}_{{\theta }_x}=K_{p{\theta }_x}{e}_{{\theta }_x}+K_{i{\theta }_x}{\int }^{}{e}_{{\theta }_x}dt+K_{d{\theta }_x}{\dot{e}}_{{\theta }_x}+{\ddot{\theta }}_{xc},\\ U_{{\theta }_y}=K_{p{\theta }_y}{e}_{{\theta }_y}+K_{i{\theta }_y}{\int }^{}{e}_{{\theta }_y}dt+K_{d{\theta }_y}{\dot{e}}_{{\theta }_y}+{\ddot{\theta }}_{yc},\\ U_{{\theta }_z}=K_{p{\theta }_z}{e}_{{\theta }_z}+K_{i{\theta }_z}{\int }^{}{e}_{{\theta }_z}dt+K_{d{\theta }_z}{\dot{e}}_{{\theta }_z}+{\ddot{\theta }}_{zc},\end{array}\right.$

where $K_p$, $K_i$, $K_d$ are control parameters of the PID controller, $e_{{\theta }_x}={{\theta }_x}_c-{\theta }_x$, $e_{{\theta }_y}={{\theta }_y}_c-{\theta }_y$ and $e_{{\theta }_z}={{\theta }_z}_c-{\theta }_z$ are the rotational errors, and $U_{{\theta }_x}$, $U_{{\theta }_y}$, and $U_{{\theta }_z}$ are the outputs of the attitude control.

Then, the model of rotation can be obtained as:

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$\left\{\begin{array}{l}\begin{array}{l}{\ddot{\theta }}_x=\frac{{\tau }_a^1}{I_X},\\ {\ddot{\theta }}_y=\frac{{\tau }_a^2}{I_Y},\\ {\ddot{\theta }}_z=\frac{{\tau }_a^3}{I_Z},\end{array}\end{array}\right.$

where, the designed control torque is:

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$\left\{\begin{array}{l}\begin{array}{l}{\tau }_a^1=I_X{U}_{{\theta }_x},\\ {\tau }_a^2=I_Y{U}_{{\theta }_y},\\ {\tau }_a^3=I_Z{U}_{{\theta }_z}.\end{array}\end{array}\right.$

Thus, the control torques ${\tau }_a^1$, ${\tau }_a^2$ and ${\tau }_a^3$ are the theoretical PID-designed controllers for actual torques $U_2$, $U_3$ and $U_4$.

Then, it is possible to obtain the attitude control loop. A block diagram of the control scheme is shown in Fig. 5. The attitude and speed of rotation can be obtained by integrating the UAV model mentioned in Eq. (9).

Fig. 5Attitude control loop. UAV, unmanned aerial vehicle

3.2.2. Position control

The aforementioned incremental digital PID control principle is important for achieving precise position control. When the sampling time is very small, the algorithm is accurate, and it is simpler and more flexible than the traditional analog PID control method.

The position controller consists of two parts: The inner loop is the PID speed control, while the outer loop is the displacement control. The main purpose of this structure is to facilitate the control of different flight modes and to enable modular design.

Since speed control is an indispensable part for most of models, with a more complete inner-loop PID control of the speed, the speed can be controlled in specific modes to control the corresponding displacements, as a proportional controller can meet the control requirements.

Similar to the attitude control system design, ${\left[x_c{y}_c{z}_c\right]}^T$ is a desired translational state, and ${\left[xyz\right]}^T$ is the translational state for feedback:

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$\left\{\begin{array}{l}{U}_x=K_{px}{e}_x+K_{ix}{\int }^{}{e}_{x}dt+K_{dx}{e}_u+{\ddot{x}}_c,\\ U_y=K_{py}{e}_y+K_{iy}{\int }^{}{e}_{y}dt+K_{dv}{e}_v+{\ddot{y}}_c,\\ U_z=K_{pz}{e}_z+K_{iz}{\int }^{}{e}_{z}dt+K_{dw}{e}_w+{\ddot{z}}_c,\end{array}\right.$

where $K_p$, $K_i$, $K_d$ are control parameters of the PID controller; $e_x=x_c-x$, $e_y=y_c-y$ and $e_z=z_c-z$ are the translational errors; $e_u={\dot{e}}_x={\dot{x}}_c-u$, $e_v={\dot{e}}_y={\dot{y}}_c-v$ and $e_w={\dot{e}}_z={\dot{z}}_c-w$ are the velocity errors; $u$, $v$ and $w$ are the velocity states for feedback; $U_x$, $U_y$, and $U_z$ are the outputs of the controller:

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$\left\{\begin{array}{l}\ddot{x}=\frac{U_1\left(S\varphi S\psi +C\psi S\theta C\varphi \right)}{m},\\ \ddot{y}=\frac{U_1\left(S\psi S\theta C\varphi -C\psi S\varphi \right)}{m},\\ \ddot{z}=\frac{U_{1}C\varphi C\theta }{m}-g,\end{array}\right.$

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$\left\{\begin{array}{l}{U}_1=\sqrt{m\left(U_x^2+U_y^2+{\left(U_z+g\right)}^2\right)},\\ {\varphi }_c=\frac{\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}\left(\mathrm{s}\mathrm{i}\mathrm{n}{\psi }_c{U}_x-\mathrm{c}\mathrm{o}\mathrm{s}{\psi }_c{U}_y\right)m}{U_1},\\ {\theta }_c=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}\left(\frac{\left(U_{x}m-U_1\mathrm{s}\mathrm{i}\mathrm{n}{\psi }_{c}sin{\varphi }_c\right)}{\left(U_1\mathrm{c}\mathrm{o}\mathrm{s}{\psi }_c\mathrm{c}\mathrm{o}\mathrm{s}{\varphi }_c\right)}\right).\end{array}\right.$

Then, it is possible to obtain the position control, as shown in Fig. 6.

Fig. 6Position control loop, where ϕc, θc, and ψc are the specified attitude angles, and T is the control torque

3.3. Safe flight control system: under actuation

In this paper, it is proved that an octocopter aircraft can continue to fly safely even when one rotor stops functioning. Fig. 7 shows a block diagram of a safe flight control system. Safe flight control is performed by using the attitude angles and angular velocities of the aircraft. The altitude and velocity in the $Z$-direction of the craft are also controlled so that the aircraft does not fall down. Feedback control is used to achieve control using the difference between the expected value and the current value. In this paper, when one of the eight rotors stopped functioning, the other seven rotors were controlled to fly. For example, when rotor 1 stops, the seven rotors of thrust ${F_i}^{\text{'}}$ ($i=$ 2, 3, 4, 5, 6, 7) have the following parameters:

where $K_{px}$, $K_{py}$, and $K_{pz}$ are the proportional gains for the attitude angles ${\theta }_x$, ${\theta }_y$and ${\theta }_z$, respectively; $K_{ph}$ is the proportional gain of the aircraft altitude in the $Z$-direction; $K_{dx}$, $K_{dy}$, and $K_{dz}$ indicate the differential gains for the angular velocities around the $x$, $y$, and $z$ axes; $K_{dh}$ is the differential gain for the velocity in the altitude direction of the aircraft.

In case a rotor stops, the work of the other seven rotors can still complete the attitude control of the pitch, roll, and yaw angles to ensure the safe flight of the aircraft. The aircraft can still be rapidly adjusted to the predetermined flight height and horizontal position and the control system can maintain a fixed-point hover in a stable condition.

Fig. 7Block diagram of safe flight control system

3.4. Stability analysis of the controller

A PID-based controller is proposed for the novel UAV control in this paper, which is one of the earliest control strategies developed. Due to its simple algorithm, good robustness, and high reliability, it is widely used in UAVs’ position and attitude control. As shown in Figs. 5 6, PID is divided into three links, namely proportional ($K_{p{\theta }_x}{e}_{{\theta }_x}$, $K_{px}{e}_x$), integral ($K_{i{\theta }_x}\int e_{{\theta }_x}dt$, $K_{ix}\int e_{x}dt$), and derivative link ($K_{d{\theta }_x}{\dot{e}}_{{\theta }_x}$, $K_{dx}{e}_u$). The functions of each link are as follows:

(1) Proportional link: This link reflects the deviation signal of the UAV position and attitude control system. Once the deviation occurs, the controller immediately takes control to reduce the deviation.

(2) Integral link: This link is used to eliminate the steady-state error after entering the steady-state

(3) Differential link: This link reflects the changing trend of the deviation signal. By introducing an effective early correction signal to the system, the speed of the system is accelerated, and the adjustment time is reduced.

In summary, PID starts from the above three links to achieve the stability of the UAV's position and attitude.

4.1. Power system design

The designed unloaded weight of the octocopter aircraft was 8.85 kg with a fully loaded weight of 20 kg, and the following power system was designed. Considering the service life and flight safety of the motor and that a conventional multirotor aircraft usually takes off at approximately 50 % of the throttle, when the fully loaded weight of the octocopter aircraft was 20 kg, the thrust of the single rotor was approximately 2.5 kg, the hurricane U4114 motor was used, and the KV value was 320. The related parameters of the motor are shown in Table 1. It can be seen that when the U4114 motor was equipped with an 18-inch rotor, the current of the 50 % throttle was 14 A, the thrust was 2375 g, and the eight motors were able to meet the thrust requirement.

It can be seen from the selection of the motor and rotor that the maximum current of the octocopter system was over 100 A, and the maximum power was over 3000 W. Both the current and power were relatively large. Therefore, the power supply of the power system was independent from the power supply of the control system. The power supply system was divided into two parts: A high-power supply system, where a 6c battery of 16,000 mAh was used to power the eight brushless ESCs (Electronic Speed Control) and the eight motors, and a low-power supply system with 3300 mAh 3c batteries to power the flight controller, which is more compact in design but also avoids the interference of the two parts. The power supply system is shown in Fig. 8.

Fig. 8Electrical power generation system

4.2. Hardware design

As shown in Fig. 9, the length of upper fuselage arm was 950 mm and the length of lower fuselage arm was 1500 mm. The vertical distance between the rotor planes was 270 mm. The two layers were fixed and connected by eight long aluminum rods, and a partition was designed between the two layers to hold the necessary hardware of the control system. The partition was secured to the lower layer by a battery rack placed below it. The electrical control and its related wiring were set in the seam, and the fuselage was made of carbon fiber with a thickness of 3 mm.

Fig. 9Structural dimension of octocopter fuselage parameters

The flight control system consisted of two microprocessors. The main controller was based on STM32F427, and the co-controller was based on STM32F100, in order to be able to switch to the co-processor to continue the flight when the master control failed. The GPS in Fig. 10(b) received data from multiple satellites, which was integrated to estimate the position and other relevant information. The GPS was inserted into the flight control system through the flight control external interface, and data interaction with the flight control system was conducted. Fig. 10(c) shows a wireless digital transmitter; its function is data communication with the ground station. It is convenient for the flight control system to tune the parameters and to monitor changes in the flight data in the process of a real-time flight, thus maintaining a safe flight. A wireless digital transmitter, which could cover the range of 1000-1500 m in an ideal environment, was able to meet the requirements of the mission. The transmitter consisted of two identical parts, one plugged into the flight control system’s external interface and another connected to the ground station. The main function of the remote control shown in Fig. 10(a) was the real-time operation of the flight process and the switching of the flight mode. The remote-control receiver was attached to the flight controller.

Fig. 10Hardware system: a) remote control; b) M8N GPS; c) wireless data transmission

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