The coordinated flight of multiple unmanned aerial vehicles, or drone formation flight, represents a significant advancement in autonomous systems, offering capabilities far beyond those of a single vehicle. My research focuses on the development and validation of control laws for maintaining and maneuvering formations of small, fixed-wing UAVs. The core challenge is to ensure that each follower aircraft maintains a precise relative position to a designated leader, despite atmospheric disturbances and the dynamic maneuvers required by mission profiles. This work details a comprehensive approach, from deriving a simplified aircraft model to designing a decentralized, three-channel control architecture and validating it through extensive nonlinear simulations.
The foundation of any effective control design is a reliable dynamic model. For control law synthesis, a linearized representation of the aircraft’s short-period and Dutch-roll dynamics is often sufficient. The longitudinal motion, governing pitch and airspeed, and the lateral-directional motion, governing roll and yaw, can be decoupled for analysis. Starting from the standard 6-DOF nonlinear equations of motion and applying small-disturbance theory around a steady, level flight condition yields the following state-space models.
For the longitudinal channel, the short-period approximation focuses on angle-of-attack (\(\alpha\)) and pitch rate (\(q\)) dynamics, crucial for altitude and flight path control. The model is given by:
$$
\begin{align*}
\dot{\alpha} &= Z_\alpha \alpha + q + Z_{\delta_E} \delta_E \\
\dot{q} &= M_\alpha \alpha + M_q q + M_{\delta_E} \delta_E
\end{align*}
$$
where \( \delta_E \) is the elevator deflection. The dimensional derivatives \(Z_\alpha, M_\alpha,\) etc., are calculated from non-dimensional stability derivatives, air density (\(\rho\)), velocity (\(V_0\)), wing area (\(S\)), and mean aerodynamic chord (\(\bar{c}\)). For instance, \(M_\alpha = \frac{\bar{q}S\bar{c}}{I_y} C_{m_\alpha}\), where \(\bar{q}=\frac{1}{2}\rho V_0^2\) is the dynamic pressure and \(I_y\) is the moment of inertia.
The lateral-directional model, essential for bank angle and side-slip control, is described by the state vector \([\beta, p, r]^T\), representing sideslip angle, roll rate, and yaw rate. The governing linear equations are:
$$
\begin{align*}
\dot{\beta} &= Y_\beta \beta + \frac{Y_p}{V_0} p + \left(\frac{Y_r}{V_0} – 1\right) r + Y_{\delta_A} \delta_A + Y_{\delta_R} \delta_R \\
\dot{p} &= L_\beta \beta + L_p p + L_r r + L_{\delta_A} \delta_A + L_{\delta_R} \delta_R \\
\dot{r} &= N_\beta \beta + N_p p + N_r r + N_{\delta_A} \delta_A + N_{\delta_R} \delta_R
\end{align*}
$$
Here, \( \delta_A \) and \( \delta_R \) are aileron and rudder deflections, respectively. The control design process for the drone formation hinges on these foundational models.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Mass | \(m\) | 10 | kg |
| Wing Area | \(S\) | 1.14 | m² |
| Wingspan | \(b\) | 3.0 | m |
| Mean Aerodynamic Chord | \(\bar{c}\) | 0.38 | m |
| Roll Moment of Inertia | \(I_x\) | 1.6 | kg·m² |
| Pitch Moment of Inertia | \(I_y\) | 2.5 | kg·m² |
| Yaw Moment of Inertia | \(I_z\) | 3.2 | kg·m² |
| Trim Velocity | \(V_0\) | 20 | m/s |
The geometry of the drone formation is defined in a path-following frame attached to the leader aircraft. The control objective is to drive three separation errors to zero: the forward (\(f_e\)), lateral (\(l_e\)), and vertical (\(h_e\)) distance errors. These errors are derived from the relative positions of the wingman (subscript \(W\)) and the leader (subscript \(L\)) in the leader’s velocity frame. Let \(\mathbf{p}_{L/W} = [x_L-x_W, y_L-y_W, z_L-z_W]^T\) be the relative position in an inertial North-East-Down frame, and \(\mathbf{V}_L = [V_{Lx}, V_{Ly}, V_{Lz}]^T\) be the leader’s velocity vector. The horizontal speed is \(V_{Lxy} = \sqrt{V_{Lx}^2+V_{Ly}^2}\). The desired separations are \(f_c\), \(l_c\), and \(h_c\). The errors are computed as:
$$
\begin{aligned}
f_e &= \frac{V_{Ly}(y_L-y_W) + V_{Lx}(x_L-x_W)}{V_{Lxy}} – f_c \\
l_e &= \frac{V_{Ly}(x_L-x_W) – V_{Lx}(y_L-y_W)}{V_{Lxy}} – l_c \\
h_e &= (z_L – z_W) – h_c
\end{aligned}
$$
Their derivatives, which feed into the controller, are:
$$
\begin{aligned}
\dot{f}_e &= V_{Lxy} – \frac{V_{Lx}V_{Wx}+V_{Ly}V_{Wy}}{V_{Lxy}} – l_e \dot{\chi}_L \\
\dot{l}_e &= \frac{V_{Lx}V_{Wy} – V_{Ly}V_{Wx}}{V_{Lxy}} + f_e \dot{\chi}_L \\
\dot{h}_e &= V_{Lz} – V_{Wz}
\end{aligned}
$$
where \(\dot{\chi}_L\) is the leader’s turn rate. This formulation effectively decomposes the 3D drone formation problem into three separate channel controls.
The control architecture employs a cascaded inner-outer loop structure, leveraging the natural timescale separation between fast attitude dynamics and slower translational kinematics. The outer loop generates attitude or throttle commands to reduce position errors, and the inner loop acts as a high-bandwidth attitude-hold autopilot to track these commands.
Forward Separation Control
The forward channel controls the throttle (\(\delta_T\)) to match the leader’s speed profile and maintain the desired longitudinal spacing. The dynamics from throttle command to forward velocity can be approximated by two first-order lags in series: one for the engine/thrust response and one for the aircraft’s speed response. A simplified model is:
$$
G_{\delta_T}^{V}(s) = \frac{K_T}{1+\tau_T s} \cdot \frac{K_V}{1+\tau_V s}
$$
The forward control law uses feedback on the forward error and its derivative, blended with the leader’s throttle command (\(\delta_{T_L}\)) received via communication:
$$
\delta_{T_W} = \delta_{T_L} – K_{\dot{f}_e} \dot{f}_e – K_{f_e} f_e
$$
Gains \(K_{\dot{f}_e}\) and \(K_{f_e}\) are tuned using root-locus methods on the linearized forward model to ensure stable and responsive speed tracking for the drone formation.
Lateral Separation Control
Lateral separation is managed by controlling the bank angle (\(\phi\)) to induce a coordinated turn, which creates a lateral acceleration. The outer-loop kinematics relate lateral error to the heading difference (\(\Delta \chi = \chi_W – \chi_L\)) and bank angle:
$$
\begin{aligned}
\dot{l}_e &\approx V_0 \Delta \chi \\
\Delta \dot{\chi} &= \frac{g}{V_0} \phi_W \quad \text{(for coordinated turn)}
\end{aligned}
$$
The outer-loop control law commands a bank angle to nullify lateral error:
$$
\phi_{cmd} = -K_{\dot{l}_e} \dot{l}_e – K_{l_e} l_e
$$
This commanded bank angle is added to the leader’s bank angle (\(\phi_L\)) to form a total bank angle command for the wingman. The inner-loop lateral autopilot must track this \(\phi_{cmd}\). It uses the linear lateral dynamics model. A typical inner-loop control law for roll attitude and damping is:
$$
\begin{aligned}
\delta’_{A_W} &= -K_p p_W – K_\phi (\phi_W – \phi_{cmd}) \\
\delta_{R_W} &= \delta_{R_L} – K_r r_W
\end{aligned}
$$
The total aileron command is \(\delta_{A_W} = \delta_{A_L} + \delta’_{A_W}\). This hierarchical design ensures stable and accurate lateral station-keeping within the drone formation.
Vertical Separation Control
Vertical separation is controlled via the pitch attitude (\(\theta\)), which governs the flight path angle. The outer-loop kinematics simplify to:
$$
\dot{h}_e = V_0 (\theta_W – \theta_L) \quad \text{(for small angles)}
$$
The outer-loop law commands a pitch angle offset:
$$
\theta_{cmd} = -K_{\dot{h}_e} \dot{h}_e – K_{h_e} h_e
$$
The total pitch command for the wingman is \(\theta_{ref} = \theta_L + \theta_{cmd}\). The inner-loop longitudinal autopilot, based on the short-period model, tracks this command:
$$
\delta’_{E_W} = -K_q q_W – K_\theta (\theta_W – \theta_{ref})
$$
The total elevator command is \(\delta_{E_W} = \delta_{E_L} + \delta’_{E_W}\). This structure effectively manages vertical spacing in the drone formation.
| Control Channel | Gain | Symbol | Typical Value |
|---|---|---|---|
| Forward | Error Derivative | \(K_{\dot{f}_e}\) | 5.23 |
| Error | \(K_{f_e}\) | 0.65 | |
| Lateral | Outer Loop: Error Derivative | \(K_{\dot{l}_e}\) | 0.20 |
| Outer Loop: Error | \(K_{l_e}\) | 0.13 | |
| Inner Loop: Roll Rate | \(K_p\) | 0.15 | |
| Inner Loop: Roll Angle | \(K_\phi\) | 1.20 | |
| Inner Loop: Yaw Rate | \(K_r\) | 0.40 | |
| Vertical | Outer Loop: Error Derivative | \(K_{\dot{h}_e}\) | 0.01 |
| Outer Loop: Error | \(K_{h_e}\) | 0.005 | |
| Inner Loop: Pitch Rate | \(K_q\) | 0.20 | |
| Inner Loop: Pitch Angle | \(K_\theta\) | 0.20 |
The performance of the proposed drone formation control laws was evaluated through high-fidelity nonlinear simulation in a 6-DOF environment. The first scenario tests basic two-aircraft formation keeping. The leader follows a trajectory involving straight flight and coordinated turns. The wingman starts with significant initial position errors (\(f_e(0)=-25m, l_e(0)=50m\)). The desired formation is defined by \(f_c=-25m, l_c=25m, h_c=0m\). The results demonstrate that the controller rapidly drives the separation errors to near zero, typically within 20-30 seconds, establishing a tight formation. During subsequent leader turns and a climb maneuver, errors transiently increase due to kinematic coupling but are quickly rejected once the maneuver stabilizes, proving the robustness of the control design.
For multi-vehicle drone formations, a critical architectural decision is the communication and reference topology. Two primary strategies were investigated:
- Leader-Follower Mode: All wingmen track the state of a single leader aircraft.
- Predecessor-Follower Mode: Each vehicle in the string tracks the state of the vehicle immediately ahead of it.
A comparative simulation of a three-vehicle string formation reveals a fundamental difference. In the predecessor-follower mode, any tracking error in the first wingman propagates and is amplified down the chain. This leads to larger transient errors and less precise overall formation geometry during maneuvers. The leader-follower mode eliminates this error propagation, as all wingmen react to the same reference command. Consequently, the leader-follower strategy was selected for its superior performance in maintaining precise formation geometry, a key requirement for effective drone formation operations.
The capability to hold and change formations under dynamic conditions is paramount. A simulation with three UAVs was conducted. The initial formation is a “Vic” or echelon shape. During flight, the leader executes waypoint-based maneuvers. Upon crossing specific spatial triggers, the desired formation parameters for each wingman are switched. The simulation successfully demonstrates sequential formation changes: from the initial “Vic” to a “Line Abreast,” and finally to a “Trail” formation. Throughout these transitions and the intervening turning maneuvers, the controllers effectively drive each wingman to its new setpoint, maintaining stable and collision-free relative trajectories. This validates the controller’s adaptability and its suitability for complex, multi-phase drone formation missions requiring in-flight reconfiguration.
In conclusion, a structured approach to the design of formation control laws for small fixed-wing UAVs has been presented and validated. By decomposing the problem into forward, lateral, and vertical channels and employing a cascaded control architecture, effective decoupling and control of the 3D relative motion is achieved. The linearized dynamic models provide a sufficient basis for inner-loop controller design, while the outer-loop laws are derived from formation kinematics. Simulations confirm that the proposed control laws ensure stable formation keeping in the presence of initial errors and during aggressive leader maneuvers. Furthermore, the leader-follower communication topology is shown to be superior for multi-vehicle formations, and the system capably executes planned formation changes. This work provides a foundational control framework that is both practically implementable and robust, paving the way for advanced drone formation applications in surveillance, mapping, and cooperative transport. Future work will integrate trajectory planning for obstacle avoidance, investigate fault-tolerant formation reconfiguration strategies, and explore distributed estimation techniques to reduce dependence on continuous leader state communication.