Rapid Integrated Design Verification of Vertical Take-Off and Landing UAVs Based on Modified Model-Based Systems Engineering

Abstract

Unmanned Aerial Vehicle (UAV) development has garnered significant attention, yet one of the major challenges in the field is how to rapidly iterate the overall design scheme of UAVs to meet actual needs, thereby shortening development cycles and reducing costs. This study integrates a “Decision Support System” and “Live Virtual Construct (LVC) environment” into the existing Model-Based Systems Engineering framework, proposing a Modified Model-Based Systems Engineering methodology for the full-process development of UAVs. By constructing a decision support system and a hybrid reality space—which includes pure digital modeling and simulation analysis software, semi-physical simulation platforms, real flight environments, and virtual UAVs—we demonstrate this method through the development of the electric vertical take-off and landing fixed-wing UAV DB1. This method allows for rapid, on-demand iteration in a fully digital environment, with feasibility validated by comparing actual flight test results with mission indicators. The study results show that this approach significantly accelerates UAV development while reducing costs, achieving rapid development from “demand side to design side” under the “0 loss” background. The DB1 platform can carry a 2.5 kg payload, achieve over 40 min of flight time, and cover a range of more than 70 km. This work provides valuable references for UAV enterprises aiming to reduce costs and increase efficiency in the rapid commercialization of UAV applications.

1. Introduction

In the context of rapid developments in modern aviation technology, Unmanned Air Vehicles (UAVs) have become a significant area of research and application. Especially after the Russo–Ukrainian and Israeli–Palestinian conflicts, small UAVs (with a maximum take-off weight not exceeding 25 kg [1]) have attracted significant attention within the industry due to their low cost and high portability, occupying a large market share.

As the complexity of mission demands continues to increase, there are corresponding demands on the comprehensive performance of UAVs. Vertical Take-Off and Landing (VTOL) UAVs, with their superior adaptability, can well make up for the deficiencies of fixed-wing (FW) UAVs and multi-rotor (MR) UAVs [2]. In addition, due to their flexible take-off and landing capabilities, they have gained widespread attention in a variety of fields such as forest rescue and intercity transport [3].

According to the research of Ducard et al. [3], VTOL UAVs can be categorized into four types: dual-system (DS), tilting rotor (TR), tilting wing (TW), and tail-sitter (TS). Tail-sitter drones, due to their simple mechanical structure, have gained widespread attention [4]. Depending on the power system, tail-sitter drones can be further subdivided into mono thrust transitioning (MTT), collective thrust transitioning (CTT), and differential thrust transitioning types (DTT) [5]. As an example, the flight modes of tail-sitter UAVs are diverse, include vertical take-off and landing, transition mode and horizontal flight, as shown in Figure 1. Different types of VTOL UAVs have similar situations during flight, which poses a great challenge for stable flight under the “0 loss” background.

Ozdemir et al. [2] proposed an iterative design and trade-off approach in UAV design, which was validated through flight tests. However, they noted significant risks associated with complex flight testing. Panigrahi et al. [6] designed a Hybrid VTOL Tilt-Rotor UAV, but during the final experimental phase, they observed pitch instability during flight transitions. Rehan et al. [5] pointed out that only three CTT-type UAVs have been successfully designed in their study of VTOL UAVs. Additionally, they highlighted that DTT-type UAVs face significant challenges in stable flight due to uncertainties during actual flight. Qiao et al. [4] proposed a development process to accelerate UAV commercialization, but their use of wind tunnel testing contradicts the principles of low-cost and rapid development. Chen et al. [7] presented a UAV control system design process, but it was only validated through hovering experiments and did not include fixed-wing flight tests. Ducard et al. [3] indicated that only a few projects involving VTOL UAVs have completed the initial development and testing phases, with even fewer achieving full-scale development. These studies highlight the significant challenges in reducing UAV development and testing costs while shortening the development cycle.

Table 1. Summary of recent studies on VTOL UAVs [6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32].

Refs.	Aerodynamics	Structure	Control	Test	Type
Panigrahi, S. (2021) [6]	√	√	-	√	TR
Rohr, D. (2021) [8]	-	-	√	√	TW
Lv, Z.Y. (2021) [9]	-	-	√	√	TR
Cakir, H. (2022) [10]	√	-	-	-	TW
Li, B. (2020) [11]	-	-	√	√	DTT
Lu, G. (2024) [12]	-	-	√	√	DTT
Zou, X. (2024) [13]	-	-	√	√	CTT
Qi, H. (2024) [14]	√	√	√	√	CTT
Ge, J. (2024) [15]	√	√	√	√	TR
Liang, Z. (2024) [16]	√	√	√	-	TR
Hu, J. (2024) [17]	-	-	√	√	DS
Liu, M. (2024) [18]	-	-	√	√	TR
McIntosh, K. (2024) [19]	-	-	√	-	DTT
Durán-Delfín, J.E. (2024) [20]	-	-	√	-	TR
Athayde, A. (2024) [21]	-	-	√	√	DTT
Kai, J.M. (2024) [22]	-	-	√	√	DS
Wang, Y. (2024) [23]	√	-	-	-	TR
Aláez, D. (2023) [24]	√	-	√	√	TR
Zhao, H. (2023) [25]	-	-	√	√	TR
Xu, S. (2024) [26]	-	√	-	-	TR
Snyder, S. (2024) [27]	-	-	√	-	DS
Suiçmez, E.C. (2024) [28]	-	-	√	√	TW
Yu, Z. (2023) [29]	-	-	√	√	TW
Sun, Z. (2024) [30]	-	-	√	√	DS
Mimouni, M.Z. (2024) [31]	-	-	√	-	TR
Musoles, J.L. (2024) [32]	-	-	√	-	TR

provides an overview of the latest research on VTOL UAVs.

The rise of digital-twin technology in recent years has provided new solutions to these challenges. NASA has applied digital-twin technology in the development of future aircraft for the American Air Force [33]. The Live Virtual Construct (LVC) environment, as an analytical framework for the application of digital twin, includes a live simulation system, which has human–machine interaction capabilities; a virtual simulation system, which consists of a simulation system based on empirical formulas; and constructive simulations where the model is entirely implemented within a digital computer and even has a high level of abstraction [34]. The LVC environment provides new opportunities for operational analysis in the early design stages of a product, allowing for analysis before the product is put into use [35].

Model-Based Systems Engineering (MBSE) is extensively applied in the design of complex systems, particularly in the aircraft design sector [36]. As illustrated in Figure 2a, a notable characteristic of MBSE is the utilization of the “V” model diagram to represent the entire aircraft design process [37]. However, traditional MBSE methodologies involve unidirectional information flow, making it challenging to achieve successful designs at the first attempt. Moreover, MBSE and simulation-based engineering are two distinct activities, even though simulation includes modeling activities [38].

To address this issue, we propose an innovative approach to complex system design by incorporating a fully digital concept into the existing MBSE framework. This new method integrates the decision support system and LVC environment, forming a “W” model diagram, as shown in Figure 2b. Leveraging the powerful computational capabilities of modern computers, this approach facilitates digital modeling and simulation, enabling bidirectional information flow in a complex system design. Additionally, it shifts the focus of the design process from physical model testing (right side) to digital model simulation (left side).

In the LVC environment, the design of complex systems can significantly accelerate update cycles and reduce development costs. This is particularly crucial for the development of VTOL UAVs, as performance-related parameters can be assessed and optimized through testing in the LVC environment. This method expedites the development process, reduces costs, and enhances product reliability. Furthermore, the LVC environment allows for the introduction of various environmental disturbances to validate the robustness of UAV controllers, ensuring stable flight in real-world conditions. This is essential for addressing the non-linearities encountered during the flight of VTOL UAVs.

This paper proposes an efficient development method for highly maneuverable VTOL UAVs, based on the LVC environment. We present a comprehensive and efficient development process and methodology. Section 2 details the complete rapid design process, computational fluid dynamics (CFD) analysis, and prototype design. Section 3 and Section 4 focus on rapid and streamlined modeling and controller design of the UAV. Section 5 conducts full-envelope validation of the UAV in an LVC environment and demonstrates actual flight outcomes.

2. Digital Rapid-Design Architecture Development

In this chapter, we will delve into the specific details of the LVC-environment architecture.

The digital development architecture for UAVs based on the LVC environment consists of five main components: demand analysis and decision-making, overall design, subsystem design, digital simulation, and hardware-in-the-loop testing, as illustrated in Figure 3. Prior to the final flight tests, each stage involves purely digital development. This approach ensures bidirectional flow of information across all components, enabling iterative improvement and optimization of design parameters. Consequently, this significantly reduces development costs and enhances the reliability verification before flight testing.

2.1. LVC Environment Description

LVC environment, as an analytical framework for the application of digital twins, includes a live simulation system, which has human–machine interaction capabilities; a virtual simulation system, which consists of a simulation system based on empirical formulas; and constructive simulations where the model is entirely implemented in a digital computer and even has a high level of abstraction [34,38,39].

2.2. An End-to-End Demand Design-System Architecture

In UAV development, demand analysis and design analysis are two closely related components. Demand analysis serves as the input for UAV design, providing direction through specific demands and performance indicators. Conversely, UAV design acts as a validation of the demand analysis, creating a closed-loop information flow in the development process. Consequently, we propose an end-to-end design concept. In this innovative framework, decision support systems and LVC environment are integrated into every stage of UAV system development, enabling rapid digital development, as shown in Figure 4. This approach shortens the development cycle and enhances the robustness and reliability of product design.

2.2.1. Demand-Analysis Side

In the UAV development process, demand analysis serves as an input, guiding the UAV design through specific demands and performance metrics. This process includes demand analysis, capability analysis, capability model mapping, expert systems, and decision systems. Initially, demands are clarified through market research and war-gaming simulations to support the demand analysis. Subsequently, using the Department of Defense Architecture Framework (DoDAF), the capability demands are decomposed into various metrics, which are then matched with the model library to construct the capability model mapping. The expert system uses fuzzy linguistic variables to handle uncertainties and prioritize capabilities. Finally, the decision system evaluates and selects the most suitable design indicators, providing guidance to the design phase, as illustrated in Figure 5.

2.2.2. Design-Analysis Side

In the design-analysis side, the overall aerodynamic shape of the drone is designed and analyzed by comparing design indicators with the model library. Based on this, subsystem designs such as structural design, control system design, and mission-based load distribution are carried out. Upon completing these designs, the aircraft undergoes preliminary optimization iterations using simulation software. Subsequently, a digital information exchange network is established, integrating digital modeling, model optimization, hardware-in-the-loop simulation, and flight simulation environments, achieving a system with real-time simulation capabilities, as illustrated in Figure 6. This approach allows for the maximum simulation of all flight conditions, ensuring the reliability and performance of the design. Utilizing the AFsim 2.9 flight simulation software, the actual flight environment is replicated. Furthermore, AFsim enables additional verification to ensure the designed drone meets mission requirements, thus achieving an end-to-end development loop. This purely digital information exchange method significantly shortens the drone development cycle and avoids the risks associated with flight failures, ensuring a comprehensive end-to-end development process.

3. The Case of Digital Development of UAVs

3.1. Demand Analysis and Design Indicator Decision

In the early stages of product conceptual design, it is crucial to define the application scenarios and the range of relevant technical parameters (such as take-off weight, dimensions, flight speed, flight duration, and mission payload). Through literature analysis [40] and war-gaming simulations, two key demands were identified: Demand 1 involves deployment on unmanned surface vehicle decks for anti-submarine patrols and Demand 2 involves deployment on patrol vehicles for reconnaissance and early warning missions. Based on the demand derivation using DoDAF and expert systems, the relevant technical parameters for UAVs are presented in

Table 2. Technical parameters for UAVs from demand analysis.

Relevant Parameter	Value
Take-Off and Landing Space Dimensions	≯1.5 m × 1.5 m
Cruise Speed	≮25 m/s
Flight Endurance	≮30 min
Payload	≮1.5 kg
Maximum Overload	≮3 g

. Under the parameters outlined in Table 2, we will proceed with the preliminary design of a tail-sitting UAV, utilizing the mission effectiveness evaluation results from the literature [41].

3.2. Aircraft General Design

Aerodynamic shape design and optimization play a critical role in achieving the performance requirements of the DB1 UAV. To conduct this process, we employed ANSYS Fluent for CFD simulations and design iterations. The RANS model with the k-omega SST turbulence model was adopted, as it provides a good balance between computational efficiency and accuracy in predicting boundary layer behavior. Propeller effects were modeled using the Actuator Disk Model [42], where distributed momentum sources represent the thrust and torque generated by the propellers. This method allowed us to efficiently analyze aerodynamic parameters such as lift-to-drag ratios, load factors, and flow field characteristics across various flight conditions. The insights gained from these simulations informed the iterative optimization of the DB1 UAV’s aerodynamic shape.

3.2.1. Aerodynamic Shape Design and Optimization

Based on the relevant parameter demands put forward in Section 3.1, we have conducted an in-depth analysis of two primary configurations: a winglet-equipped horizontal wing with an H-type propulsion layout and an X-wing tail-mount layout. These analyses focused on the platform’s vertical take-off and landing capabilities, high maneuverability, speed, and airtime demands, taking into account powerplant selection, lift-to-drag ratios, and available g-load factors. We carried out four rounds of iterative revisions in the aerodynamic layout scheme, resulting in changes to the external configuration, as shown in Figure 7.

Plan 1 introduces a cutting-edge UAV design, featuring a circular fuselage with a high aspect-ratio straight wing. Central to this design is a vertical spiral propeller mounted mid-wing, complemented by four sets of vertically oriented motors and propellers. Winglets at each wing end enhance structural support and mitigate wingtip vortices. Computational simulations have revealed that Plan 1 is constrained by its maximum angle of attack and dynamic pressure. While capable of sustaining low g-loads (about 2) during low-speed flight, efficiency diminishes as propeller speed increases. Notably, the maximum achievable g-load declines sharply beyond speeds of 45 m/s, ceasing at approximately 52 m/s as the propeller transitions to a gliding state.

Advancing from Plan 1, Plan 2 incorporates several improvements: a shift to the NACA6412 airfoil for better lift, increased wing-root chord length, expanded wing area, and optimized propeller wing span and lateral positioning. Simulations show a slight increase in pitch maneuvering g-loads over Plan 1. However, lateral load capacity is still limited, and maximum flight speeds fall short of our objectives.

Plan 3 evolves into an X-wing configuration, maintaining the fuselage parameters of previous iterations but replacing the traditional wing layout with an “X” arrangement of four wings. This setup includes four forward-facing propellers and motors at the wingtips, ensuring torque balance during transitional flight phases. Simulation results indicate a minor dip in the lift-to-drag ratio but a substantial boost in overall maneuverability, particularly in pitch. This version aligns closely with our technical specifications, meeting speed, endurance, and other fundamental performance benchmarks.

To further optimize flight performance, we have enhanced the aspect ratio, increased both wing area and taper ratio, and carefully analyzed motor installation angles in tandem with motor selection. Subsequent CFD simulations confirm these modifications, with Plan 4 achieving a maximum lift-to-drag ratio of around 10 and top speeds exceeding 60 m/s. Notably, both pitch and lateral maneuverability at 45 m/s surpass a value of 5. Thus, Plan 4 has been identified as the optimal foundational design, meeting our technical and performance standards. The vehicle’s profile parameters are detailed in

Table 3. Profile parameters of the vehicle.

Type	Parameter	Value
Fuselage	Fuselage diameter	0.15 m
	Length	0.85 m
Wing	Span	1.5 m
	Root chord	0.45 m
	Tip chord	0.3 m
	Trailing-edge sweep angle	${15}^{°}$
	Airfoil	NACA0012
	Wing insertion point (X, Y, Z)	(0.337 m, 0 m, 0 m)
	Wing area (per wing)	0.562 m2
	Number of wings	4
	Wing installation angle	${45}^{°}$$, {135}^{°}$$, {225}^{°}$$, {315}^{°}$

.

3.2.2. Aerodynamic Analysis Results

In the actual design of UAVs, we utilize advanced Computational Fluid Dynamics analysis to elucidate the UAV’s aerodynamic properties. This analytical approach provides invaluable insights for control system designers, enhancing the precision of both controller design and simulation efforts.

• Longitudinal Aerodynamic Performance Analysis

Derived from comprehensive longitudinal aerodynamic calculations, the aircraft’s aerodynamic efficiency is quantitatively illustrated in Figure 8. This figure delineates the variations in the lift coefficient, drag coefficient, lift-to-drag ratio, and pitch-moment coefficient as functions of the angle of attack. Notably, as depicted in Figure 8, the lift-to-drag ratio of the UAV achieves an optimum value of 11 when the angle of attack is meticulously maintained at a specific degree.

Based on the comprehensive CFD wind-tunnel experimental data trends studied by Lyu et al. [43], we fitted the aerodynamic coefficients of the DB1 for angles of attack ranging from −20° to 90° using CFD aerodynamic coefficients obtained at small angles of attack, as shown in Figure 9.

2.

Lateral and Directional Aerodynamic-Performance Analysis

Based on the preliminary calculated aerodynamic coefficients, the maximum available load factor at an angle of attack of $8^{°}$ is calculated within the speed range of 30 m/s to 60 m/s and the height range of 0 m to 5000 m, as shown in Figure 10 and Figure 11. As seen in Figure 10c, the lift-to-drag ratio of DB1 reaches its maximum at an angle of attack of 8°, with a value of approximately 11. Figure 10d demonstrates the DB1’s ability to maintain stable flight under varying sideslip angles and angles of attack, highlighting its effective lateral control and resistance to crosswind disturbances. Figure 11a shows the variation in the DB1 roll moment with respect to different angles of attack and sideslip angles. When the sideslip angle is 0, the roll moment of DB1 changes approximately linearly with the angle of attack, compared to other states. Figure 11b,c illustrate the DB1’s excellent stability and recovery capability when subjected to pitching and yawing disturbances, respectively, further confirming its robustness in maintaining a stable attitude after disturbance.

3.

Available overload Analysis

The assessment of the available load factor for UAVs is critical in determining their maneuverability. As illustrated in Figure 12, the DB1 achieves a normal load factor of 3 g at low heights when the speed exceeds 37 m/s. Notably, when the speed surpasses 45 m/s, the load factor exceeds 4 g, indicating that the UAV exhibits strong maneuverability under these conditions.

4.

Pitch-Maneuver Thrust Analysis

The required thrust comprises two distinct components: first, counteracting the drag generated at a specific angle of attack, and second, neutralizing the pitching moment induced by the corresponding load factor. This balance is crucial for maintaining a stable normal load factor. The calculated thrust-demand curve is shown in Figure 13.

3.3. System Configuration

The DB1 is comprised of several key systems: propulsion system, the control navigation system, and energy system.

3.3.1. Propulsion System

The propulsion system of the DB1 serves a dual role. It not only provides thrust throughout the flight but also generates the necessary control torque for roll, pitch, and yaw maneuvers.

Typically, multi-rotor UAVs are equipped with high-speed motors and large-diameter propellers with a low pitch. In contrast, fixed-wing UAVs generally favor smaller-diameter, high-pitch propellers. Considering the predominant duration of fixed-wing flight in practical scenarios and based on Equations (1)–(4) [44,45], we have opted for the T-MOTOR AT4120 KV250 motor, paired with APC 15 × 10 propellers. Due to the project’s focus on low-cost and rapid development, the selection of the motor and propellers may not be the optimal configuration. For a detailed explanation of the symbols used in this study, refer to Appendix A.

$$T_i\ge mg/n\ast 60\%$$

(1)

$$T_{i_{min}}\ge mg/max \left\{CL/CD\right\}$$

(2)

$$T_i=C_T\rho (N/60{)}^2{D}_p^4$$

(3)

$$M_i=C_m\rho ({N/60)}^2{D}_p^5$$

(4)

3.3.2. Control System

The control navigation system is tasked with maintaining stable control of the unmanned aerial vehicle (UAV) during flight, correcting its trajectory as needed.

Our control system hardware employs a flight control computer developed on the open-source Pixhawk FMUv5 architecture. The primary processor, STM32F765, is complemented by an IO processor, STM32F100, and is equipped with multiple redundant inertial measurement units (IMUs) including ICM-20602, ICM-20689, and BMI1055. Additionally, it features an IST8310 magnetometer and an MS5611 barometer.

The firmware is based on the open-source PX4 architecture. We have modified the source code to map the original tail-sitter model’s servo control for roll, pitch, and yaw channels in PX4 to four distributed motor channels. This allows for differential control of the four motors to execute roll, pitch, and yaw maneuvers in fixed-wing mode.

Ground observation is conducted using QGC V3.5.6 software, which utilizes the mavlink communication protocol for flight status monitoring and mission planning.

3.3.3. Energy System

The energy system supplies primary power to onboard equipment and offers interfaces for electrical power and information transmission.

In accordance with the configuration of the power system, we have selected a 12 S lithium battery to power the entire aircraft. Owing to the unique configuration of the tail-sitter unmanned aerial vehicle, distinct discharge states are observed in the multi-rotor and fixed-wing states. Consequently, we employ a flight-time proportion-based method to estimate and model the battery discharge for each mode.

In the multi-rotor state, we hypothesize that the battery discharge process maintains a constant voltage, while the remaining battery capacity decreases linearly [46,47]. The model is structured as follows:

$$C_b=16.67\left(T_b{I}_b\right)+C_{min}$$

(5)

$$I_b\le {0.001C}_b{K}_b$$

(6)

To ensure the reusability of the battery, the parameter $C_{min}$ is typically set between 0.15$C_b$ and 0.2$C_b$ [46]. For the fixed-wing mode, the discharge model is adopted as follows:

$$C_b=1.5625\left(FV{T}_b\right)$$

(7)

Based on the aerodynamic analysis in Section 3.2, at an angle of attack of 8°, the lift-to-drag ratio is approximately 11, which indicates that the thrust required for steady level flight in a fixed-wing state should exceed 9 N when DB1 weighs 10 kg. According to mission demands, at a flight speed $V$ of 30 m/s and a total endurance of no less than 40 min, the minimum battery capacity needed is 17,607 mAH. Taking into account the assumptions in the modeling process and power losses, the chosen battery capacity $C_b$ should be no less than 20,000 mAH, with a discharge rate exceeding ${\mathrm{K}}_{\mathrm{b}}$ > 10 C.

3.3.4. Detailed Description

In conventional multi-rotor UAVs, the motor mounting angle is typically near 0°, with yaw torque generated solely through differential motor torque, leading to significant response latency in the yaw channel. To enhance the response of the yaw in a multi-rotor state and roll in a fixed-wing state, we have designed a specific motor mount angle, as shown in Figure 14.

While the motor mount angle reduces the effective thrust output along the body axis, the resultant force in the yOz plane enhances the UAV’s agility. Upon obtaining test data from the official APC propeller website and conducting interpolation, as shown in

Table 4. Correlation of thrust and torque with rotational speed for APC propellers.

Type	RPM	Thrust	Motor_Torque	Tiyz_Torque
No Mount Angle	5836.21	24.5 N	0.5927 N·m	0 N·m
Mount Angle	5880.58	24.9 N	0.6027 N·m	4.32 N·m

, we observed notable differences. For instance, during hovering, the actual thrust output of motors with a mount angle is increased by 1.54% compared to those without an angle. However, the torque generated within the yOz plane is 11.9 times greater than that of motors without a mount angle.

$$T_{ix}=T_i\ast cos(10°)$$

(8)

$$T_{iyz}=T_i\ast sin(10°)$$

(9)

$$T_{iy}=T_{iz}=T_{iyz}\ast \mathit{sin}(45°)$$

(10)

3.3.5. Cost Considerations

Cost control is a crucial aspect in the development of unmanned systems. To further reduce the development costs of the DB1, its casing is fabricated using wooden molds, with the airframe constructed from wooden laminates and composite materials. Except for the flight control computer, all other hardware components are commercially sourced, and software for ground observation and communication is obtained from open-source communities.

3.3.6. Prototype

The design parameters and specifications of the DB1 prototype are illustrated in Figure 15 and

Table 5. DB1 weight parameters.

Parameter	Value
Diagonal Size	1.3 m
Body mass	2.5 kg
Propulsion system	2 kg
Energy system (22,000 mAh)	4 kg

, succinctly summarizing the distinctive design features of the DB1.

• The DB1 employs an “X” configuration to achieve high maneuverability during high-speed flight;
• Distinct from VTOL UAVs, the DB1 is capable of executing STT (Short Take-Off and Transition) with a minimal turning radius under special conditions;
• The differential drive method of the motors enables the DB1 to have a more rapid control response during flight;
• Despite the limited design space, the DB1 achieves a maximum lift-to-drag ratio of 11.

4. Dynamic Modeling and Controller Design

In this section, we present the kinematic and dynamic modeling of the DB1. When modeling the UAV, the effects of aerodynamic forces, thrust and gravity in different coordinate systems must be considered. Therefore, coordinate transformations must be performed. The transformations between the different coordinate systems are shown in Figure 16a. The DB1 body-axis coordinate system is shown in Figure 16b. The ground coordinate system adopts North–East–Down (NED).

4.1. Dynamic Model

In the process of modeling the DB1, the following assumptions are made:

Assumption 1. 

The UAV is considered as a rigid body;

Assumption 2. 

In the multi-rotor state, air resistance and drag torque are neglected;

Assumption 3. 

The nonlinear model is simplified by ignoring higher-order terms.

Based on the principles of low-cost and rapid design and development, our model construction relies entirely on mathematical formulas and publicly available data, without conducting individual tests on components, such as wind tunnel testing.

4.1.1. DB1 Model

Building on Assumptions 1 and 2, the following dynamical model is established:

$$\left\{\begin{array}{c}{}_{ }{}^g\dot{\mathit{P}}={\mathit{R}}_b^g\ast {}_{ }{}^b\mathit{V}\\ {}_{ }{}^b\dot{\mathit{V}}=-{\left[{}_{ }{}^b\mathit{\omega }\right]}_{\times }\ast {}_{ }{}^b\mathit{V}+{\displaystyle \frac{{}_{ }{}^b\mathit{F}}{m}}\\ \begin{array}{c}\dot{\mathsf{\Omega }}=\mathit{W}\ast {}_{ }{}^b\mathit{\omega }\\ \mathbf{J}\ast {}_{ }{}^b\dot{\mathit{\omega }}=-{}_{ }{}^b\mathit{\omega }\ast \left(\mathit{J}\mathit{*}{}_{ }{}^b\mathit{\omega }\right)+{}_{ }{}^b\mathit{M}\end{array}\end{array}\right.$$

(11)

Following Assumption 3, a horizontal position channel model is developed:

$$\left[\begin{array}{c}\varphi \\ \theta \end{array}\right]=\left[\begin{array}{c}{\displaystyle \frac{-sin\left(\psi \right)\ast {}^g\dot{u}+sin\left(\psi \right)\ast {}^g\dot{v}}{g}}\\ {\displaystyle \frac{-cos\left(\psi \right)\ast {}^g\dot{u}-sin\left(\psi \right)\ast {}^g\dot{v}}{g}}\end{array}\right]$$

(12)

4.1.2. Control Efficiency Model

Based on Equation (11), a detailed analysis of force and torque has been conducted:

$${}_{ }{}^b\mathit{F}={\mathit{R}}_g^b\ast m{}_{ }{}^g\mathit{G}+{}_{ }{}^b\mathit{T}+{({\mathit{R}}_b^v )}^{\mathrm{T}}{}_{ }{}^v{\mathit{F}}_a$$

(13)

$${}_{ }{}^b\mathit{M}={\mathit{G}}_{\mathit{a}}+{}_{}{}^b\mathit{\tau }+{\left({\mathit{R}}_b^v\right)}^{\mathrm{T}}\mathbf{*}{}_{ }{}^v{\mathit{M}}_a$$

(14)

During flight, the rotational directions of the propellers on the DB1 are illustrated in Figure 16b.

• Motor Thrust and Torque Model

The distributed differential mechanism is employed for flight maneuvering in the DB1 design, which includes motor installation angles along the body coordinate system. The motor thrust is decomposed as follows:

A rightward roll is defined as positive, an upward pitch as positive, and a rightward yaw as positive.

$${}_{ }{}^b\mathit{T}=\left[\begin{array}{c}{T}_{\mathit{x}}\\ T_{\mathit{y}}\\ T_{\mathit{z}}\end{array}\right]=\left[\begin{array}{c}{T}_{1x}+T_{2x}+T_{3x}+T_{4x}\\ T_{1y}-T_{2y}-T_{3y}+T_{4y}\\ {-T}_{1z}+T_{2z}-T_{3z}+T_{4z}\end{array}\right]$$

(15)

$${}_{}{}^b\mathit{\tau }=\left[\begin{array}{c}{\tau }_x\\ {\tau }_y\\ {\tau }_z\end{array}\right]=\left[\begin{array}{c}{M}_1+(T_{1xy}\ast {\displaystyle \frac{d}{2}})+M_2+(T_{2xy}\ast {\displaystyle \frac{d}{2}})-M_3-(T_{3xy}\ast {\displaystyle \frac{d}{2}})-M_4-(T_{4xy}\ast {\displaystyle \frac{d}{2}})\\ +{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{1x}-{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{2x}+{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{3x}-{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{4x}\\ -{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{1x}+{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{2x}+{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{3x}-{\displaystyle \frac{\sqrt{2}}{2}}\ast {\displaystyle \frac{d}{2}}\ast T_{4x}\end{array}\right]$$

(16)

2.

Gyroscopic Torque Model

In multirotor drones, gyroscopic torque refers to the torque generated by the high-speed rotation of the rotors, which significantly impacts the drone’s stability and attitude control.

$${\mathit{G}}_{\mathit{a}}=\left[\begin{array}{c}{Ga}_x\\ {Ga}_y\\ {Ga}_z\end{array}\right]=\left[\begin{array}{c}0\\ J_{RP}(p\ast (-{\omega }_1-{\omega }_2+{\omega }_3+{\omega }_4\left)\right)\\ J_{RP}(q\ast ({\omega }_1+{\omega }_2-{\omega }_3-{\omega }_4\left)\right)\end{array}\right]$$

(17)

3.

Aerodynamic Forces and Torque Model

The aerodynamic and torque model of the DB1 is crucial for fixed-wing flight conditions. To enhance the accuracy and robustness of the model against disturbances, the impact of external wind disturbances on the flight state is included. The model can be expressed as follows:

$${}_{ }{}^v{\mathit{F}}_a=\left[\begin{array}{c}-D\\ Y\\ -L\end{array}\right]=\left[\begin{array}{c}-{\displaystyle \frac{1}{2}}\rho {‖{}_{ }{}^v{\mathit{V}}_a‖}^2{C}_D{S}_w\\ {\displaystyle \frac{1}{2}}\rho {‖{}_{ }{}^v{\mathit{V}}_a‖}^2{C}_Y{S}_w\\ -{\displaystyle \frac{1}{2}}\rho {‖{}_{ }{}^v{\mathit{V}}_a‖}^2{C}_L{S}_w\end{array}\right]$$

(18)

$${}_{ }{}^v{M}_a=\left[\begin{array}{c}\overline{L}\\ M\\ N\end{array}\right]=\left[\begin{array}{c}-{\displaystyle \frac{1}{2}}\rho {‖{}_{ }{}^v{\mathit{V}}_a‖}^2{C}_{\overline{L}}{S}_{w}b\\ {\displaystyle \frac{1}{2}}\rho {‖{}_{ }{}^v{\mathit{V}}_a‖}^2{C}_M{S}_w{c}_A\\ -{\displaystyle \frac{1}{2}}\rho {‖{}_{ }{}^v{\mathit{V}}_a‖}^2{C}_{N}b\end{array}\right]$$

(19)

$${}_{ }{}^v{\mathit{V}}_a={}_{ }{}^v\mathit{V}+{\mathit{R}}_g^v\ast {}_{ }{}^g{\mathit{v}}_w$$

(20)

$${}_{ }{}^g{\mathit{v}}_w={}_{ }{}^g{\mathit{w}}_{tur}+{}_{ }{}^g{\mathit{w}}_{gust}+{}_{ }{}^g{\mathit{w}}_{const}+...$$

(21)

4.2. Controller Design

In this chapter, the controller design process for the DB1 is divided into three parts: multi-rotor state controller design, transition control law design, and fixed-wing state controller design. Owing to its ease of development and lack of need for a precise mathematical model of the controlled object, a cascaded Proportional (P) plus Proportional–Integral–Derivative (PID) control structure is employed in our controller design.

4.2.1. Multi-Rotor State

The design of the vertical take-off controller comprises an inner loop and an outer loop, as shown in Figure 17. The outer loop is dedicated to position control, and the inner loop manages attitude control. The outer loop employs a cascaded P + PID control strategy, and the design of the inner loop is consistent with that of the outer loop.

4.2.2. Fixed-Wing State

Unlike the design of multi-rotor controllers, the fixed-wing controller design is divided into lateral and longitudinal channels. In the longitudinal channel’s outer loop control, the Total Energy Control System (TECS) utilizes a multi-input multi-output control strategy, as shown in Figure 18a. This approach simplifies achievement of the desired flight performance compared to traditional flight control methods. Importantly, the core of TECS does not require specific information about the aircraft [48], which greatly facilitates rapid aircraft development. The efficiency, simplicity, and success of TECS have been demonstrated in multiple studies. As shown in Figure 18b, the outer loop of the fixed-wing state employs a combination of TECS and the L1 navigation system. The inner loop consists of cascaded P + PID controllers, with feedforward control added to the angular velocity loop to compensate for air damping in the fixed-wing state, as shown in Figure 18c.

4.2.3. Transition-State Control-Law Design

Learning from the lessons of flight accidents during the aircraft development process, the robustness of control is crucial for achieving a smooth transition from multi-rotor to fixed-wing states. It is essential to ensure sufficient forward velocity for generating the necessary lift during such a transition maneuver. Therefore, before designing the control law for the transition phase, we must consider the following parameter constraints: (1) a design based on CFD analysis of various wing types and airframes, usually the angle of attack $\left|\mathrm{a}\right|<15°$; (2) to prevent stall phenomena, as per the CFD analysis in Section 3.2, the minimum safe flying speed of the DB1 in fixed-wing mode should be identified $V_{min}^{FW}\ge 24\mathrm{m}/\mathrm{s}$. Additionally, different propellers produce varying thrust at different flying speeds, as documented in

Table 6. Thrust corresponding to APC 15 × 10 propeller RPM and flight speed.

${}^{\mathit{b}}\mathit{V}^{\mathit{*}}$		6000	7000	8000	9000
	N
29 m/s		2.494 N	10.583 N	20.955 N	32.422 N
34 m/s		0	3.407 N	11.606 N	23.886 N
40 m/s		0	0	2.229 N	11.797 N
45 m/s		0	0	0	2.833 N

, according to APC’s official data. To ensure adequate thrust during flight, the transition speed should be $V_{min}^{FW}\le V^{Trans}\le V_{max}^{FW}$. Simultaneously, to maintain stable flight, the speed typically should not exceed $V_{cmd}^{Trans}=V_{min}^{FW}+0.15V_{max}^{FW}$.

Inspired by the studies in References [47,48], to avoid stall phenomena and unpredictable disturbances, we have established a relationship between transition time ${\mathrm{T}}_{\mathrm{c}\mathrm{m}\mathrm{d}}^{\mathrm{T}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}}$, horizontal velocity, and attitude channel constraints in the inner loop during the forward transition process. This approach is designed to ensure stability of the aircraft during the transition phase, while effectively managing potential dynamic changes.

$$V^{Trans}=V_{cmd}^{Trans}(1-e^{-K_V^{Trans}\ast T^{Trans})}$$

(22)

$$\theta =90°\ast e^{-K_{\theta }^{Trans}\ast V^{Trans}}+C$$

(23)

5. Simulation and Test Validation

To validate the effectiveness of the designed DB1, we first assumed perfect state information and developed a dynamic model in the MATLAB/Simulink R2022b environment, where we conducted controller parameter tuning and simulations. Subsequently, the controller code was embedded into the actual DB1 control system, and its effectiveness was verified through tests in the LVC environment. Finally, the overall reliability of DB1’s design was confirmed through outdoor flight tests, thereby completing the development of the initial version of DB1.

5.1. Simulation Results

5.1.1. Multi-Rotor State Simulation

To ensure the reliability of the multi-rotor state controller design, we conducted tests on both the roll and pitch channels, as illustrated in Figure 19. For the roll channel, we performed step-response tests with step amplitudes ranging from $\pm 10°$ to $\pm 40°$, as shown in Figure 19a. For the pitch channel, step-response tests were conducted with amplitudes from $\pm 10°$ to $\pm 80°$, as depicted in Figure 19b. The focus on the pitch channel is particularly crucial, as its signal tracking is a key indicator of attitude transitions, which are essential for achieving smooth transitions between flight modes. Additionally, the signal tracking responses of the roll and pitch channels in the multi-rotor state are instrumental in ensuring the safety of flight during fixed-wing state tests, such as stall protection [49]. These tests are fundamental in verifying that the controller can handle the dynamic requirements of both rotor and fixed-wing flight conditions, thereby contributing to the overall robustness of the DB1 design.

5.1.2. Transition-State Simulation

The transition-state control law of DB1 is crucial for stabilizing transitions across multiple states. To verify the control law designed in Section 4.2.3, feasibility simulations were conducted on DB1’s transition speed $V^{Trans}$ and pitch angle $\theta$. The transition time was set to 10 s with an expected transition speed $V_{cmd}^{Trans}$ of 30 m/s. The fixed-wing equilibrium angle of attack constant $C$ was 8°. Simulation results are illustrated in Figure 20.

5.1.3. Multi-State Hybrid Flight Simulation

To further validate the reliability of the controller design, we conducted a multi-state hybrid simulation to assess its feasibility. As illustrated in Figure 21a, DB1 takes off in the multi-rotor state, with its position and attitude controlled by the multi-rotor controller. Once the UAV reaches an height of 50 m, DB1 transitions into the fixed-height mode. During the transition from the multi-rotor state to the fixed-wing mode, the pitch angle, constrained by forward velocity, gradually decreases from 90° to 8°, successfully completing the transition. The simulated flight trajectories of DB1 during the multi-rotor stage, transition stage, and fixed-wing stage are depicted in Figure 21b. The comprehensive flight simulation results presented in Figure 21 demonstrate that the state controllers of DB1 meet all the design requirements.

5.2. LVC-Environment Simulation Results

In typical workflows, after completing control law simulations in Matlab/Simulink, the next step toward actual flight testing involves converting the simulation code into software code. Various methods exist for validating the software code, such as hardware-in-the-loop simulation [50]. In our approach, we apply a similar principle by constructing an LVC environment to validate the full aircraft software code and hardware system design, ensuring their reliability and suitability for real-world application.

To simplify the design, the DB1 eliminates the use of traditional servos for controlling flight attitudes in fixed-wing mode, opting instead for differential motor speeds to achieve pitch, roll, and other flight attitude controls. This approach presents challenges in the mapping between motors and control channels. To validate the reliability of DB1’s power mapping and control system, we conducted tests in an LVC environment, focusing on the mapping between motor speeds, transition-state control laws, fixed-wing roll, and climb performance, as illustrated in Figure 22.

As illustrated in Figure 22a–c, the motor signals of DB1 increase gradually with decreasing pitch angle during the transition phase (red area), achieving attitude changes in height-hold mode. During the fixed-wing phase (yellow area) from 50 s to 150 s, the motor output signals exhibit distinct patterns: the signal output from Motor 2 is significantly lower than that of the other motors, while Motors 1 and 3 remain at high levels, and Motor 4 increases moderately during left roll. This behavior aligns with the trajectory shown in Figure 22d, indicating that DB1 is performing a left roll and climb. Furthermore, between 260 s and 400 s, the minimum motor output signal shifts from Motor 2 to Motor 4, reflecting DB1’s completion of left and right rolls in sequence, consistent with Figure 22a. Throughout the fixed-wing phase, DB1 maintains a small pitch angle, which correlates with the higher signals of Motors 1 and 3 compared to the other motors in Figure 22c. Therefore, by analyzing the motor responses mapped to different flight maneuvers shown in Figure 22a–d, we can confirm the reliability of the software code execution and the accuracy of the mapping between motors and control channels.

5.3. Flight Test Results

While LVC-environment flight simulations effectively validate the reliability of DB1’s foundational design, thereby averting potential UAV development failures due to design flaws, actual flight testing remains indispensable. To validate the feasibility of DB1 and study the similarity between its performance and design simulations, extensive flight tests were initially conducted on DB1 in various multi-rotor states, as depicted in Figure 23. These preliminary flight tests significantly refined the control parameters relevant to multi-rotor states, contributing to the assurance of DB1’s performance in unforeseen states during subsequent performance tests, such as stall protection [51].

Due to the lack of a reliable environmental model, such as a wind disturbance model, in our LVC environment simulation, we conducted a 30 min manual flight test of DB1 under ground wind speeds of 8–11 m/s to better assess its environmental adaptability [52]. The flight test was divided into two parts: multi-rotor-state stability testing and fixed-wing-state flight testing.

In the first part, the stability of DB1 in the multi-rotor state was evaluated. Due to the wing surface design and layout, DB1 is susceptible to wind disturbances while in the multi-rotor state. The experimental results, shown in Figure 24 (blue section), indicate that the roll and pitch controllers in the multi-rotor state achieve satisfactory response tracking characteristics, even with a 30° command input. However, the figure also reveals minor overshoot during the hovering phase, caused by random wind disturbances. To improve wind resistance in future optimizations, we plan to enhance the controller design by implementing strategies such as active disturbance rejection control or adding feedforward control.

In the fixed-wing state, the experimental data (yellow section) shows that due to higher wind speeds at height, DB1’s pitch control can only meet basic response tracking requirements. This may be attributed to significant wind disturbances and the reduced effective thrust generated by the propellers at high speeds. In contrast, the roll control demonstrated excellent response tracking, consistent with the design principle discussed in Section 3.3.4, where the installation angle was increased to enhance roll torque in fixed-wing mode.

It is noteworthy that the response tracking characteristics of all control channels remained stable and reliable during the transition between multi-rotor and fixed-wing states. Additionally, unlike traditional fixed-wing UAVs, DB1 possesses the capability of STT (Skid-to-Turn) maneuvers. However, due to the lack of prior analysis in this area, a slight stall occurred during the actual flight [53].

During testing in a high-wind environment, there was a significant discrepancy between the actual flight speed of DB1 and the preset values, as shown in Figure 24c. This deviation is primarily due to the impact of tailwind and headwind conditions on DB1’s actual flight speed, although the aircraft was still able to maintain normal flight. Figure 24d illustrates that in a multi-rotor state, the voltage drops rapidly during DB1 high-climb rates. In contrast, in the fixed-wing state, the voltage decreases slowly with changes in flight speed. However, it is important to note that when transitioning from a fixed-wing to multi-rotor state, there is a significant voltage drop, which poses a risk to stable flight. Therefore, during flight planning, it is essential to preset a voltage warning threshold. For example, during the fixed-wing flight phase, if the voltage drops below 30%, an immediate transition to multi-rotor state should be initiated to prevent a potential crash due to insufficient voltage.

Furthermore, the inclusion of the multi-rotor state in this test led to significant energy consumption. To extend the overall flight time, future tests should consider shortening the duration of the multi-rotor state, thereby increasing the time spent in fixed-wing mode. In this experiment, we conducted a 31 min flight test. With optimized flight time allocation across different modes, it is theoretically possible to achieve over 40 min of flight duration.

6. Conclusions

As a hybrid of fixed-wing and multi-rotor technologies, VTOL UAVs hold significant potential for both military and civilian applications. Instead of pursuing unguided UAV development, this study introduces an innovative rapid UAV development method by integrating market demands into the design process. By embedding decision support systems and LVC environment into MBSE, we address the traditional challenges of long development cycles and high costs. To validate the proposed method, we designed a unique tail-sitter UAV, DB1, based on specific mission requirements. Simulations, LVC environment simulations, and real-world flight tests demonstrate that DB1 meets mission requirements while achieving rapid UAV development.

In the design of DB1, we adopted a fully digital development approach. By leveraging both traditional simulations and LVC environment simulations, we thoroughly identified and corrected DB1’s design flaws within a purely digital environment, ultimately achieving rapid development from “customer to designer” with “0-loss”. The term “0-loss” refers to our methodology’s ability to reduce unnecessary damage to aircraft prototypes during testing caused by design flaws. By identifying and correcting potential issues in the digital development phase, we minimize the risk of costly and destructive errors in physical testing, thus ensuring a more efficient and cost-effective development process.

Additionally, given that such VTOL UAVs employ a single power system to control multiple flight modes, the reliability of channel mapping is critical. Through LVC environment simulations, we validated the stability of transitions between different flight modes and the reliability of control-channel mapping for DB1.

Simulation results and flight tests confirm the success of the DB1 UAV design. This study provides a viable pathway for UAV companies with limited funding to achieve rapid commercialization.

In future work, we will focus on optimizing and exploring the performance of DB1’s controllers, applying the latest control methods such as model-free control and neural network control. Additionally, we aim to enhance the fidelity of the LVC environment models using extensive high-confidence flight test data, thereby further improving the credibility of the digital UAV development process.