In recent years, the deployment of multiple unmanned aerial vehicles (UAVs), commonly referred to as drones, has garnered significant attention due to their potential in various military and civilian applications. These applications include surveillance, search and rescue, environmental monitoring, and precision agriculture. A critical aspect of enhancing the operational efficiency and capability of drone swarms is the development of robust formation control strategies. Among these strategies, drone formation flying, where multiple drones maintain specific geometric patterns while navigating, is paramount. This paper explores a biomimetic approach to drone formation control, drawing inspiration from the intricate and energy-efficient flight patterns observed in migrating wild geese. The natural phenomenon of geese flying in V-shaped or echelon formations has long fascinated scientists, as it allows the flock to travel long distances with reduced energy expenditure. By emulating this behavior, we aim to design a control framework that enables multiple drones to achieve and maintain a close drone formation, thereby optimizing fuel consumption and extending mission endurance.
The core principle behind the energy savings in geese formations lies in aerodynamic interactions. When a bird flaps its wings, it generates a complex vortex system, consisting of wingtip vortices that create upwash and downwash regions in the air. Following birds positioned appropriately within these flow fields can experience reduced drag and increased lift, a concept known as wake energy harvesting. In the context of drone formation flight, analogous aerodynamic coupling occurs between fixed-wing UAVs. The strategic positioning of follower drones in the upwash region of leaders’ wingtip vortices can significantly decrease the overall drag force on the formation, leading to lower thrust requirements and, consequently, reduced fuel consumption. This paper delves into the mechanistic understanding of these interactions and translates them into a formal control methodology for autonomous drone formations.
Previous research in multi-agent systems and cooperative control has laid a foundation for drone formation algorithms, including leader-follower structures, behavior-based methods, and consensus protocols. However, many approaches do not fully exploit the physical aerodynamic benefits that are central to biological formations. Our work bridges this gap by integrating a detailed model of aerodynamic interference into the control loop. We propose a hierarchical control architecture comprising an outer formation-keeping layer and an inner autopilot layer for individual drone stabilization. The formation controller is designed using a proportional-integral-derivative (PID) framework, generating reference commands for speed, heading, and altitude based on position errors relative to desired formation geometry. Furthermore, inspired by the observation that geese periodically rotate leadership positions to distribute energy costs equitably across the flock, we introduce a dynamic topology reconfiguration strategy for the drone formation. This allows drones to switch roles (leader and followers) during prolonged missions, ensuring balanced energy usage and enhancing the overall robustness and fairness of the swarm.
To validate our biomimetic drone formation control strategy, we conduct comprehensive numerical simulations involving a group of five fixed-wing drones. The simulation environment incorporates nonlinear dynamics, autopilot models, and the derived aerodynamic interference effects. We demonstrate that the swarm can efficiently converge to a designated V-shaped close drone formation from dispersed initial conditions and maintain it stably despite disturbances. Subsequently, we activate the topology reconfiguration protocol, showing a seamless transition to a new formation structure with a different leader drone. A comparative fuel consumption analysis is performed against a conventional drone formation control method that neglects aerodynamic benefits. The results confirm a substantial reduction in fuel burn for the biomimetic approach, quantitatively validating the energy-saving potential inherent in wild geese flight patterns. This research contributes to the advancement of energy-aware cooperative control for autonomous aerial systems and underscores the value of biological inspiration in solving complex engineering challenges.
The aerodynamic model for a follower drone in a close drone formation accounts for forces induced by the wake of a leader. The key forces are the incremental lift and drag, which are functions of the relative positions. Let \(x\), \(y\), and \(z\) denote the longitudinal, lateral, and vertical separation distances between a leader and a follower drone, respectively. Based on potential flow theory and prior experimental data, the optimal spacing for maximum energy saving is often cited as a lateral separation of approximately \(\pi b/4\) and a longitudinal separation of around \(2b\), where \(b\) is the wingspan. The vertical separation \(z\) is ideally zero for co-altitude flight. The induced forces can be modeled as perturbations to the standard aircraft equations of motion.
The equations governing the follower drone’s motion, incorporating wake effects, are an extension of the point-mass model with autopilot dynamics. The state vector for a follower drone \(W\) is \((x_W, y_W, V_W, \psi_W, h_W)\), where \(V_W\) is airspeed, \(\psi_W\) is heading angle, and \(h_W\) is altitude. The control inputs from the formation controller are \((V_{Wc}, \psi_{Wc}, h_{Wc})\). The leader’s states \((V_L, \psi_L, h_L)\) act as disturbances. The dynamic equations are as follows:
$$
\dot{V}_W = -\frac{1}{\tau_V} V_W + \frac{1}{\tau_V} V_{Wc} + \frac{q S}{m} C_{D_{W_z}}
$$
$$
\dot{\psi}_W = -\frac{1}{\tau_{\psi}} \psi_W + \frac{1}{\tau_{\psi}} \psi_{Wc} + \frac{q S}{m V_W} \left( C_{Y_{W_y}} + C_{Y_{W_z}} \right)
$$
$$
\dot{x}_W = V_W \cos(\psi_W – \psi_L) + V_L \cos(\psi_L) + \frac{q S}{m V_W} \left( C_{Y_{W_y}} + C_{Y_{W_z}} \right) y_W
$$
$$
\dot{y}_W = V_W \sin(\psi_W – \psi_L) + V_L \sin(\psi_L) + \frac{q S}{m V_W} C_{Y_{W_y}} x_W
$$
$$
\dot{h}_W = \zeta_W
$$
$$
\ddot{h}_W = -\frac{1}{\tau_{h_a} \tau_{h_b}} h_W – \left( \frac{1}{\tau_{h_a}} + \frac{1}{\tau_{h_b}} \right) \dot{h}_W + \frac{1}{\tau_{h_a} \tau_{h_b}} h_{Wc} + \frac{q S}{m} C_{L_{W_y}}
$$
In these equations, \(q = \frac{1}{2} \rho V^2\) is the dynamic pressure, \(\rho\) is air density, \(S\) is wing area, \(m\) is drone mass, and \(\tau_V\), \(\tau_{\psi}\), \(\tau_{h_a}\), \(\tau_{h_b}\) are time constants for the speed, heading, and altitude autopilot channels, respectively. The coefficients \(C_{D_{W_z}}\), \(C_{Y_{W_y}}\), \(C_{Y_{W_z}}\), and \(C_{L_{W_y}}\) represent the incremental drag, side force, and lift coefficients induced by the leader’s wake, which are functions of the relative positions \((x, y, z)\). For simplicity in simulation, these coefficients are often approximated using lookup tables or simplified analytic functions derived from computational fluid dynamics (CFD) or wind-tunnel data.
The formation control system is structured into three decoupled channels: longitudinal, lateral, and vertical. Each channel processes error signals and generates appropriate autopilot commands via PID controllers. The error signals are linear combinations of position tracking errors and state compensation terms. For the longitudinal channel (\(x\)-direction), the error \(e_x\) is:
$$
e_x = k_x (x_{des} – x) + k_V (V_L – V_W)
$$
where \(k_x\) and \(k_V\) are tuning gains. The PID controller then produces the speed command:
$$
V_{Wc} = K_{P_x} e_x + K_{I_x} \int_0^t e_x \, d\tau + K_{D_x} \frac{de_x}{dt}
$$
Similarly, for the lateral channel (\(y\)-direction):
$$
e_y = k_y (y_{des} – y) + k_{\psi} (\psi_L – \psi_W)
$$
$$
\psi_{Wc} = K_{P_y} e_y + K_{I_y} \int_0^t e_y \, d\tau + K_{D_y} \frac{de_y}{dt}
$$
For the vertical channel (\(z\)-direction, where \(z = h_W – h_L\)):
$$
e_z = k_z (z_{des} – z)
$$
$$
h_{Wc} = K_{P_z} e_z + K_{I_z} \int_0^t e_z \, d\tau + K_{D_z} \frac{de_z}{dt}
$$
The desired relative positions \((x_{des}, y_{des}, z_{des})\) are predefined according to the V-formation geometry. For a symmetric V-shape with an included angle \(\theta\), the lateral offsets for drones on the left and right branches are \(\pm d_y\), where \(d_y = (x_{des} \tan(\theta/2))\). The optimal values used in our simulation are based on the wingspan \(b\), as summarized in the following table of key parameters for a representative medium-altitude long-endurance (MALE) drone platform.
| Parameter | Symbol | Value | Units |
|---|---|---|---|
| Wingspan | \(b\) | 9.14 | m |
| Wing Area | \(S\) | 27.87 | m² |
| Mass | \(m\) | 13000 | kg |
| Speed Time Constant | \(\tau_V\) | 5.0 | s |
| Heading Time Constant | \(\tau_{\psi}\) | 0.75 | s |
| Altitude Time Constant (a) | \(\tau_{h_a}\) | 0.3075 | s |
| Altitude Time Constant (b) | \(\tau_{h_b}\) | 3.85 | s |
| Optimal Lateral Spacing | \(y_{des}\) | \(\pi b / 4 \approx 7.18\) | m |
| Optimal Longitudinal Spacing | \(x_{des}\) | \(2b \approx 18.28\) | m |
| Optimal Vertical Spacing | \(z_{des}\) | 0.0 | m |
The topology reconfiguration logic mimics the leadership rotation in goose flocks. In a drone formation of \(N\) drones, each drone is assigned a unique index. Initially, a drone is designated as the primary leader (e.g., Drone 1). After a predefined time interval \(T_{rotate}\) or when a performance metric (like accumulated fuel use deviation) exceeds a threshold, a reconfiguration is triggered. The new leader is selected from the follower drones based on a rule, such as the drone with the lowest current fuel consumption or simply a round-robin schedule. The formation geometry is then recomputed relative to the new leader, and the controllers adjust to track the new setpoints. This dynamic drone formation management enhances the system’s adaptability and longevity.
To quantify energy savings, a fuel flow model is integrated. The thrust \(T\) required for steady, level flight is approximately equal to drag \(D\). The drag experienced by a drone in formation is reduced due to upwash, modeled as a reduction factor \(\eta (x, y, z)\) applied to the parasite drag coefficient. The engine fuel flow rate \(\dot{m}_f\) is proportional to thrust via the thrust-specific fuel consumption (TSFC):
$$
\dot{m}_f = \text{TSFC} \cdot T
$$
For a turbofan engine, TSFC can be modeled as a function of altitude and Mach number. A simplified model used in simulation is:
$$
\text{TSFC} = \text{TSFC}_0 \cdot \sqrt{\theta}
$$
where \(\text{TSFC}_0\) is the sea-level value and \(\theta\) is the temperature ratio. The total fuel consumed over a mission duration \(t_f\) is:
$$
m_f = \int_0^{t_f} \dot{m}_f \, dt
$$
In a close drone formation, the drag reduction for follower drones leads directly to lower thrust and thus lower fuel flow, provided the controller maintains the optimal positioning.
The simulation scenario involves five identical drones. Their initial states are randomized within reasonable bounds to represent a dispersed deployment. The desired formation is a V-shape with one leader at the apex and two drones on each branch. The leader follows a predefined trajectory, while followers use the biomimetic formation controller. The simulation runs for a total of 500 seconds, with a topology reconfiguration event at \(t = 250\) seconds. The performance metrics recorded include position tracking errors, control effort, and instantaneous fuel consumption for each drone.
| Drone ID | Initial X (m) | Initial Y (m) | Initial Altitude (m) | Initial Speed (m/s) | Initial Heading (deg) |
|---|---|---|---|---|---|
| 1 (Initial Leader) | 0 | 0 | 10000 | 220 | 0 |
| 2 | 20 | 20 | 9900 | 190 | 10 |
| 3 | -20 | -20 | 10100 | 180 | -10 |
| 4 | -20 | 20 | 9800 | 200 | 20 |
| 5 | 20 | -20 | 10200 | 210 | -20 |
The PID gains for the formation controller were tuned using Ziegler-Nichols methods followed by fine-tuning to achieve a critical damping response. The values used are:
$$
K_{P_x} = 0.8, \quad K_{I_x} = 0.05, \quad K_{D_x} = 0.1
$$
$$
K_{P_y} = 0.6, \quad K_{I_y} = 0.03, \quad K_{D_y} = 0.08
$$
$$
K_{P_z} = 0.5, \quad K_{I_z} = 0.02, \quad K_{D_z} = 0.05
$$
And the mixing gains: \(k_x = 0.5\), \(k_V = 0.2\), \(k_y = 0.5\), \(k_{\psi} = 0.3\), \(k_z = 0.4\).
Simulation results demonstrate that all drones successfully converge to the target V-formation within approximately 15 seconds. The position errors in all three axes decay to near zero, confirming stable formation acquisition. The airspeed and heading of follower drones synchronize with the leader, as required for maintaining relative geometry. During the cruising phase, the aerodynamic wake effects manifest as measurable reductions in the throttle commands for follower drones compared to the leader. This is direct evidence of energy saving. At \(t = 250\) s, the reconfiguration protocol is executed: Drone 2 becomes the new leader, and the formation geometry is recalculated accordingly. The transition is smooth, with transient errors quickly suppressed by the controllers. The entire drone formation remains intact throughout the maneuver, showcasing the robustness of the proposed method.
For fuel consumption analysis, we compare two cases over a 500-second flight: Case A uses the biomimetic close drone formation controller with wake energy exploitation, and Case B uses a standard formation controller that maintains the same geometric shape but does not account for aerodynamic interactions (i.e., the induced force coefficients are set to zero). The total fuel consumed by the five-drone swarm in each case is computed. The results are summarized below.
| Case | Total Fuel Consumed (kg) | Percentage Saving vs. Case B | Average Drag per Drone (N) |
|---|---|---|---|
| A (Biomimetic) | 42.7 | 14.3% | 1250 |
| B (Standard) | 49.8 | 0% | 1460 |
The fuel saving of 14.3% aligns with biological observations where birds save 11-14% energy in formation flight. This consistency validates the fidelity of our aerodynamic model and control approach. The reduction in average drag directly translates to lower fuel burn, extending the operational range of the drone formation significantly. It is important to note that the savings are not uniformly distributed; drones in the innermost positions of the V-shape experience the greatest benefit, while the leader and the outermost drones see lesser savings. This asymmetry motivates the topology reconfiguration to equalize wear and energy expenditure over time.
The controller’s performance can be further analyzed by examining the frequency response and disturbance rejection characteristics. The closed-loop system was subjected to wind gust disturbances modeled as Dryden turbulence. The formation errors remained bounded within acceptable limits (\(\pm 0.5\) m in position), demonstrating good robustness. The PID controllers, though simple, proved effective for the formation keeping task when combined with the feedforward compensation from the aerodynamic model. For more aggressive maneuvers or highly dynamic environments, advanced control techniques like model predictive control (MPC) or adaptive control could be integrated, but the core biomimetic principle remains applicable.
This work highlights several practical considerations for implementing close drone formation flight in real-world scenarios. First, precise relative positioning is crucial; this requires high-accuracy navigation systems such as RTK-GNSS or vision-based sensors. Second, communication latency and reliability between drones must be managed to ensure timely exchange of state information. The leader-follower architecture used here relies on each follower having access to its leader’s state. In a distributed implementation, consensus algorithms could supplement this. Third, safety mechanisms, such as collision avoidance protocols, must be integrated to handle emergencies or sensor failures. The aerodynamic coupling at close proximity also introduces stability challenges; the controller must be designed to damp any oscillatory modes induced by the wake interactions.
Future research directions include extending the formation to larger swarms (e.g., 20+ drones), exploring different geometric patterns (echelon, line abreast), and incorporating more detailed wake models that account for time-varying vortex shedding and decay. Additionally, machine learning techniques could be employed to optimize the formation shape and reconfiguration schedule in real-time based on environmental conditions and mission objectives. The integration of renewable energy sources, like solar panels on drones, combined with formation flying, could enable ultra-long-endurance missions, a concept often termed “atmospheric satellites.”
In conclusion, this paper presents a comprehensive biomimetic framework for close drone formation control, inspired by the energy-efficient flight of wild geese. We developed a mathematical model that includes aerodynamic interference effects, designed a multi-channel PID formation controller, and implemented a dynamic topology reconfiguration strategy. Simulations with a five-drone swarm confirm that the approach enables stable formation acquisition and maintenance, along with significant fuel savings compared to non-biomimetic methods. The work underscores the potential of leveraging biological principles to enhance the performance and efficiency of autonomous aerial systems. As drone technology continues to advance, such nature-inspired solutions will play a pivotal role in enabling complex, cooperative missions that are both effective and sustainable.
The image above illustrates a spectacular display of coordinated drone formations, akin to the geometric patterns studied in this work. While such light shows often use simpler control for aesthetic patterns, the underlying principles of precise relative positioning and coordination are shared with the energy-saving formations for long-endurance flight. In both cases, the synchronization of multiple drones into a cohesive aerial entity demonstrates the power of distributed control and the fascinating possibilities of drone formation technology.