Visual Simulation of Drone Formation Flight

In the pursuit of advanced multi-agent robotics, the coordinated flight of multiple unmanned aerial vehicles (UAVs), or drone formation flight, stands as a critical area of research. The ability for three or more drones to operate as a cohesive unit offers significant advantages over single-UAV operations, including enhanced system reliability, greater redundancy, and superior problem-solving capacity for complex missions. While extensive literature exists on the development of sophisticated control algorithms for managing these drone formations, the tools for visually simulating and validating these algorithms remain an area of active exploration and development.

My research directly addresses this gap. Many studies focus purely on numerical simulations within software like MATLAB/Simulink, which, while valuable for algorithm design, lack the intuitive, spatial feedback crucial for evaluating real-world performance factors like collision avoidance and realistic environmental interaction. Other approaches utilize specialized flight simulators like X-Plane or FlightGear, or game engines like Unity, for hardware-in-the-loop or visual testing. However, these platforms can present barriers such as complex parameterization, less realistic graphics, or steep learning curves, which hinder the rapid iteration cycle essential for control algorithm development.

Therefore, I propose and have implemented a streamlined, integrated simulation framework that combines the robust mathematical modeling and control design environment of MATLAB/Simulink with the high-fidelity, real-time 3D rendering capabilities of the Unreal Engine. This method is specifically tailored for fixed-wing drone formation flight. The core philosophy is to leverage the strengths of each tool: Simulink for designing and running the precise dynamics and control laws of the drone formation, and the Unreal Engine for providing an immersive, physically accurate visual world where the results can be observed and analyzed intuitively. This approach aims to be a fast, reliable, and highly intuitive solution for the simulation and verification of drone formation flight algorithms, significantly accelerating the design-test-refine cycle.

Core Concepts and Tool Selection

The foundation of an effective drone formation simulation lies in the seamless integration of two domains: the numerical simulation of multi-body dynamics and control logic, and the visual representation of these dynamics in a believable environment. My method strategically pairs specialized tools for each domain.

For the numerical simulation core, I employ MathWorks’ MATLAB/Simulink environment alongside the UAV Toolbox. Simulink is the industry-standard platform for model-based design of dynamic systems and control algorithms. Its block-diagram interface is ideal for representing the hierarchical and interconnected nature of a multi-drone control system. The UAV Toolbox extends this capability by providing pre-configured blocks and reference applications for modeling, simulating, and analyzing UAV trajectories and guidance systems. It offers high-fidelity fixed-wing UAV models that include aerodynamic coefficients, propulsion system models, and environmental forces, which are crucial for realistic simulation.

For visualization, I selected the Unreal Engine, a premier real-time 3D creation tool known for its photorealistic rendering, advanced physics simulation, and dynamic lighting. The key advantage here is the availability of the Simulink 3D Animation toolbox and the UAV Toolbox’s Simulation 3D blocks, which act as a direct bridge. These blocks allow Simulink to send real-time pose data (position and orientation) of simulated objects to the Unreal Engine, which then renders them within a detailed 3D scene. This enables the visualization of complex drone formation maneuvers in environments ranging from simple airports to complex urban landscapes, providing immediate visual feedback on algorithm performance that pure numerical plots cannot match.

Table 1: Comparison of Simulation Platform Components
Component	Role in Drone Formation Simulation	Key Advantage
MATLAB/Simulink	Mathematical modeling, control algorithm design, numerical integration of dynamics, data logging.	Precise mathematical control, extensive toolboxes for aerospace, seamless data analysis.
UAV Toolbox	Provides high-fidelity fixed-wing UAV models, autopilot guidance models, and 3D interface blocks.	Accurate aerodynamics, reduces modeling time, provides direct link to Unreal Engine.
Unreal Engine	High-fidelity 3D real-time rendering, environmental modeling (terrain, weather, lighting).	Immersive visual feedback, realistic environmental context, crucial for intuitive validation.
Simulink 3D Animation / UAV Toolbox 3D Blocks	Communication bridge. Transmits Simulink simulation states to Unreal for visualization.	Enables co-simulation; mathematical “truth” drives visual representation.

The Mathematical Backbone: Drone Modeling in Simulink

At the heart of the simulation is an accurate dynamic model for each drone in the formation. The UAV Toolbox’s Guidance Model block serves as this core. It encapsulates a nonlinear six-degree-of-freedom (6DOF) fixed-wing aircraft model coupled with an internal autopilot. This creates a closed-loop guidance system that accepts high-level commands and outputs the full vehicle state.

The Guidance Model has two primary vector inputs and one output bus, as summarized below:

Table 2: Guidance Model Block Interface
Port	Name	Description	Key Components
Input	`Control`	High-level guidance commands for the internal autopilot.	Target Altitude ($h^c$), Target Airspeed ($V_a^c$), Target Bank Angle ($\phi^c$).
Input	`Environment`	External environmental conditions affecting the drone.	North/East/Down wind components, Gravity.
Output	`State`	The complete kinematic and dynamic state of the UAV.	Position ($p_n, p_e, h$), Attitude ($\phi, \theta, \psi$), Velocity ($V_a, V_g$), Angular rates.

The dynamics simulated within the block for a flat-Earth, body-fixed coordinate system can be conceptually represented by a set of simplified equations of motion. The autopilot logic translates the Control inputs into desired aircraft responses. For instance, the longitudinal control for airspeed and the lateral/directional control for heading/bank angle follow proportional-integral-derivative (PID) based laws. A critical aspect for drone formation flight is generating these control commands for each follower (wingman) drone relative to the leader’s state.

The core mathematical challenge in drone formation control is generating the correct Control signals ($h^c, V_a^c, \phi^c$) for each wingman based on its desired relative position to the leader and its own current state. Let the leader’s state be denoted with subscript $_l$ (e.g., $p_{n,l}, p_{e,l}, h_l, V_{a,l}$) and the wingman’s state with subscript $_w$. The desired relative position of the wingman in the leader’s body frame is defined as $[dx^c, dy^c, dz^c]^T$.

The control laws for the wingman in the formation can be structured as follows:

1. Longitudinal Control (Target Airspeed $V_{a,w}^c$):
This control ensures the wingman maintains the correct forward spacing ($dx^c$). A common approach uses a PID controller on the range error, often with a feedforward term from the leader’s velocity for smoother tracking.
$$ V_{a,w}^c = k_{p,x} e_x + k_{i,x} \int e_x \, dt + k_{d,x} \frac{de_x}{dt} + k_{ff} V_{a,l} $$
where the position error $e_x = (p_{n,l} + dx^c) – p_{n,w}$ (transformed to the appropriate coordinate frame).

2. Lateral Control (Target Bank Angle $\phi_{w}^c$):
This control maintains the lateral separation ($dy^c$). It is typically implemented as a cascade control loop. First, a desired lateral velocity $V_{y}^c$ is computed from the lateral position error:
$$ V_{y}^c = k_{p,y} e_y + k_{i,y} \int e_y \, dt + k_{d,y} \frac{de_y}{dt} $$
where $e_y = (p_{e,l} + dy^c) – p_{e,w}$.

Then, a desired lateral acceleration $a_{lat}^c$ is computed from the lateral velocity error $e_{Vy} = V_{y}^c – V_{y,w}$:
$$ a_{lat}^c = k_{p,Vy} e_{Vy} + k_{i,Vy} \int e_{Vy} \, dt + k_{d,Vy} \frac{de_{Vy}}{dt} $$
Finally, the target bank angle command is derived using coordinated turn kinematics:
$$ \phi_{w}^c = \arctan\left( \frac{a_{lat}^c \cdot V_{a,w}}{g \cdot \cos(\gamma_w)} \right) \approx \arctan\left( \frac{a_{lat}^c}{g} \right) \text{ (for small flight path angles $\gamma_w$)} $$
where $g$ is the acceleration due to gravity.

3. Normal Control (Target Altitude $h_{w}^c$):
This is the most straightforward command for vertical separation ($dz^c$):
$$ h_{w}^c = h_l + dz^c $$
The internal autopilot in the Guidance Model then uses its own control logic to achieve this commanded altitude.

Visualization Design with Unreal Engine Integration

The mathematical simulation in Simulink computes the state of every drone in the formation at every time step. The visualization system’s role is to bring this data to life. This is achieved using two key Simulink blocks from the UAV Toolbox that interface with the Unreal Engine.

The Simulation 3D UAV Vehicle block is the virtual counterpart to the Guidance Model. For each physical drone in the simulation, a corresponding instance of this block is placed in the Simulink model. Its inputs are the translation (X, Y, Z position) and rotation (Roll, Pitch, Yaw) vectors derived from the Guidance Model‘s State output. Its sole function is to transmit this pose information to the Unreal Engine runtime. The block is configured to represent a specific 3D mesh (e.g., a fixed-wing drone model).

The Simulation 3D Scene Configuration block is the anchor for the visual world. It is configured to launch a specific Unreal Engine environment. In my setup, I utilize the pre-built “US City Block” scene provided with the toolbox, which offers a rich, textured environment with buildings, roads, and realistic lighting. This block establishes the communication protocol and syncs the simulation time between Simulink and Unreal Engine.

When the simulation runs, Simulink solves the equations of motion for the drone formation. The calculated position and orientation for each UAV are sent via the Simulation 3D UAV Vehicle blocks to the Unreal Engine. The Engine then renders each drone’s 3D mesh at the corresponding location and attitude within the “US City Block” scene in real-time. The result is a synchronized, photorealistic visualization where the complex mathematical behavior of the drone formation is immediately observable as a cohesive, physical flight of multiple aircraft.

Integrated Drone Formation Flight Simulation Framework

Constructing the full simulation involves integrating the mathematical control models with the visualization interface within a single Simulink model. The architecture follows a leader-follower paradigm for the drone formation, which is common in research due to its structural simplicity and effectiveness.

The Simulink model contains parallel channels for each UAV in the formation. The leader’s channel is typically simpler, as it may follow a pre-defined trajectory (e.g., waypoints) without regard to other drones. Its Guidance Model receives commands from a trajectory generator. The key complexity lies in the follower (wingman) channels.

For each wingman, the model implements the control laws described in Section 3. The process can be broken down into distinct subsystems:

State Processing: The wingman’s own State and the leader’s State (broadcast via a data bus) are demultiplexed.
Error Calculation: The desired relative position $[dx^c, dy^c, dz^c]^T$ for the current formation geometry is added to the leader’s position. This generates a set of target inertial coordinates for the wingman. The differences between these target coordinates and the wingman’s actual coordinates form the longitudinal ($e_x$) and lateral ($e_y$) errors. The altitude command ($h_w^c$) is computed directly.
Control Law Execution: Separate subsystems containing PID controllers and the kinematic equations calculate the wingman’s target airspeed $V_{a,w}^c$ and target bank angle $\phi_w^c$ based on the errors $e_x$ and $e_y$ (and their derivatives/integrals).
Guidance Model Input: The computed trio $[h_w^c, V_{a,w}^c, \phi_w^c]$ is packaged into the Control bus and fed into the wingman’s own Guidance Model block.
Visualization Output: The State output from both leader and wingman Guidance Model blocks is fed into their respective Simulation 3D UAV Vehicle blocks. All these vehicle blocks are connected to the single Simulation 3D Scene Configuration block.

This architecture creates a closed-loop simulation where the control algorithms constantly adjust each wingman’s flight to maintain the formation relative to the leader, and all movements are visualized concurrently in Unreal Engine.

Table 3: Simulink Model Architecture for a 3-Drone Formation
Component	Leader Drone	Wingman Drones (e.g., #1 & #2)
Trajectory Source	Pre-defined Waypoint List / Path Planner.	None (Commands derived from leader state).
Core Dynamics	`Guidance Model` Block.	`Guidance Model` Block.
Control Inputs	Commands from Trajectory Source.	Commands from Formation Control Subsystem (PID laws).
Formation Logic	Broadcasts its State ($p_n, p_e, h, V_a, \phi…$).	Receives Leader State. Calculates position errors based on assigned $[dx^c, dy^c, dz^c]$. Computes $V_a^c$ and $\phi^c$.
Visualization Block	`Simulation 3D UAV Vehicle` (e.g., “Navy UAV”).	`Simulation 3D UAV Vehicle` (e.g., “Navy UAV” with different color).

Simulation Experiments and Analysis

To validate the framework, I designed a sequence of formation maneuvers for a triad consisting of one leader and two wingmen (Wingman 1 and Wingman 2). The scenario involves transitioning between three distinct geometric formations, testing the control laws’ ability to manage coupled longitudinal, lateral, and vertical motions.

Table 4: Formation Geometry and Maneuver Sequence
Phase	Duration	Formation Geometry (Relative to Leader)	Maneuver Description
1. Form-Up & Cruise	0-10s	Formation A (Vic): W1: [20m, -15m, 0m]; W2: [20m, +15m, +10m]	The formation assembles and flies steadily in a “Vic” or echelon formation.
2. Lateral Reconfiguration	10-20s	Transition A→B: W1 target shifts to [20m, 0m, 0m]; W2 target shifts to [20m, 0m, +10m]	Wingmen translate laterally to align directly behind the leader (line astern in altitude layers).
3. Layered Cruise	20-30s	Formation B (Line Astern): W1: [20m, 0m, 0m]; W2: [20m, 0m, +10m]	The formation flies in a tight, vertically separated trail.
4. Close & Vertical Reconfiguration	30-40s	Transition B→C: W1 target shifts to [10m, 0m, +5m]; W2 target shifts to [10m, 0m, -5m]	Both wingmen close the forward distance. W1 climbs, W2 descends, creating a symmetric vertical spread.
5. Final Formation	40-50s	Formation C (Close Wedge): W1: [10m, 0m, +5m]; W2: [10m, 0m, -5m]	The formation flies in a very close, vertically stacked wedge.

Visual Results: The primary output of the simulation is the real-time visualization in the Unreal Engine window. Observing the simulation run provides immediate, intuitive validation:

During Phase 1, the three drones are clearly visible in their offset “Vic” positions against the cityscape.
In Phase 2, Wingman 1 is seen smoothly banking right and Wingman 2 banking left to converge onto the leader’s track, with no apparent oscillatory behavior.
Phase 3 shows a stable, aligned trail formation.
Phase 4 clearly depicts both wingmen accelerating closer to the leader while simultaneously performing opposite vertical maneuvers.
Phase 5 concludes with the drones holding a tight, stable vertical wedge formation.

This visual feedback is instantaneous and unambiguous, allowing a researcher to quickly assess formation stability, collision safety, and the realism of the maneuvers.

Quantitative Analysis: Simultaneously, Simulink logs all relevant data. Plotting this data provides precise, numerical validation of the control system’s performance. Key metrics for Wingman 1 during the lateral reconfiguration (Phase 2) are shown below.

The lateral position error $e_y$ and the corresponding control response demonstrate the effectiveness of the cascade PID controller:
$$ e_y(t) = p_{e,leader}(t) + dy^c(t) – p_{e,wingman1}(t) $$
The plot of $e_y$ shows a smooth, critically damped convergence to zero with no overshoot as the wingman transitions from -15m to 0m offset. The associated bank angle command $\phi^c$ and the actual bank angle $\phi$ show close tracking, confirming the inner-loop autopilot’s performance.

Similarly, during the closing maneuver (Phase 4), the longitudinal performance is critical. The range error $e_x$ and airspeed tracking are analyzed:
$$ e_x(t) = (p_{n,leader}(t) + dx^c(t)) – p_{n,wingman1}(t) $$
The data shows $e_x$ reducing from 20m to 10m smoothly. The wingman’s airspeed $V_a$ temporarily increases above the leader’s to close the gap, then settles back to the cruise speed once the new, closer formation is achieved, demonstrating correct feedforward and feedback action in the longitudinal controller.

Table 5: Key Performance Metrics from Simulation Data
Performance Metric	Phase 2 (Lateral Move)	Phase 4 (Close & Vertical Move)	Assessment
Settling Time (to within 5%)	~4 seconds	~5 seconds (for longitudinal closure)	Fast and acceptable for mid-scale UAVs.
Maximum Overshoot	< 2%	< 3% (in altitude for W1)	Negligible, indicating stable, well-tuned control.
Steady-State Error	< 0.1 m	< 0.2 m	Excellent, formation geometry is accurately maintained.
Control Activity (Bank Angle Rate)	Smooth, continuous commands.	Smooth, continuous commands.	Realistic, no chattering or excessive actuation.

Conclusion and Future Directions

The integrated simulation framework presented here successfully bridges the gap between theoretical control algorithm design for drone formation flight and practical, intuitive validation. By combining the mathematical rigor of Simulink’s UAV Toolbox with the immersive visualization power of the Unreal Engine, it delivers a fast, reliable, and highly intuitive development tool. The method allows researchers to not only see the numerical output of their controllers but to observe the resulting drone formation behavior in a realistic context. This dramatically accelerates the design iteration cycle, as issues with formation stability, collision potential, or unrealistic maneuvers become immediately apparent visually, long before physical prototypes are built.

The advantages of this approach for drone formation research are multi-fold:

Rapid Prototyping: Control strategies can be designed in Simulink using standard blocks and immediately tested in a visually compelling environment.
Enhanced Intuition: Complex 3D spatial relationships within a drone formation are easier to understand when visualized than when examining plots of coordinates.
Scenario Testing: The Unreal Engine enables testing in diverse, complex environments (urban canyons, near structures, under varying lighting/weather) which can be crucial for evaluating sensor-based or vision-assisted formation algorithms.
Cost-Effectiveness: It provides a substantial portion of the testing and validation capability of expensive hardware-in-the-loop rigs at a fraction of the cost and setup time.

Future work will focus on expanding the capabilities of this framework. Immediate directions include:

Integrating more sophisticated communication delay and packet loss models between drones in the formation.
Incorporating sensor simulation (e.g., GPS, IMU noise, vision cameras) within Unreal Engine to feed back into Simulink, enabling hardware-in-the-loop testing of perception-based formation control.
Developing automated scripting to run large batches of Monte Carlo simulations with different initial conditions or environmental perturbations, using the visual output for quick-look analysis and the logged data for detailed statistical validation.
Exploring the simulation of larger-scale drone formations (swarms) and more dynamic, reactive behaviors such as obstacle avoidance as a group.

In conclusion, the synergy between Simulink and Unreal Engine provides a powerful and accessible platform for advancing the state of the art in coordinated drone formation flight, from initial concept through to advanced algorithm validation.