The challenging problem of drone penetration under networked air defense systems has driven the development of tactical deception methods. In modern warfare, threat networks fuse information from multiple sensors, enabling rapid detection and coordinated interception of intruders. Conventional path planning algorithms that solely rely on optimization functions often fail when threats can dynamically reposition. To address this, we propose a cooperative operation framework based on drone spoofing, where a decoy drone and a task drone work together to create a temporary gap in the defensive coverage. This paper presents a detailed mathematical model of the relative motion between the decoy and the maneuvering fire threat, analyzes how the decoy’s speed and heading affect the threat’s movement distance and interception time, and derives the coordination principles for the two drones. We then integrate these insights into a genetic algorithm (GA) for task drone path planning, incorporating a switching function to ensure safe penetration. Simulation results demonstrate that the proposed drone spoofing strategy effectively counters networked threats and is applicable to both manned‑unmanned teaming and fully autonomous drone swarms.
The core idea of drone spoofing is to use a decoy drone to intentionally enter the detection zone of the enemy’s radar network. This triggers the enemy to redirect mobile fire units (e.g., surface‑to‑air missile launchers) toward the decoy, thereby creating a temporary weak spot in the defense perimeter. The task drone, which follows a separate preplanned or dynamically replanned path, exploits this gap to penetrate the protected area and complete its mission. The synergy between the two drones relies on precise prediction of the fire threat’s motion, which is governed by the decoy’s trajectory parameters. In the following sections, we first describe the operational scenario, then develop the relative motion model, analyze the influence of decoy behavior, and finally present the GA‑based path planning method with simulation verification.
Operational Scenario and Coordination Principle
We consider a typical penetration scenario as illustrated in the image below. A task drone (UM) and a decoy drone (UB) start from the same departure point and fly together until a separation point O₁. At O₁, the decoy changes course to fly toward a detection threat (WR), while the task drone continues toward the target area. The decoy’s trajectory is designed such that it will be detected at point P, which lies on the boundary of the detection threat’s coverage. Upon detection, the fire threat (WF) begins to maneuver to intercept the decoy. The task drone, meanwhile, uses the predicted motion of the fire threat to plan a path that avoids the threat’s coverage radius. The success of the mission depends on the decoy’s ability to lure the fire threat far enough away from the original defensive position, and on the task drone’s ability to traverse the exposed corridor before the threat can reposition.
The operational sequence comprises three phases: (i) information acquisition – obtaining the positions of threats, terrain, and weather; (ii) tactical decision – determining the decoy’s speed and heading to maximize the lure effect; and (iii) execution – adjusting the task drone’s path in real time based on the observed fire threat motion. The decision‑making process is summarized in Table 1, which lists the key parameters and their roles in the drone spoofing strategy.
| Symbol | Description | Role |
|---|---|---|
| vB | Speed of decoy drone | Affects the time and distance the fire threat must travel |
| θB | Angle between decoy’s flight direction and the line to the fire threat | Determines the deviation of the fire threat from its original position |
| vF | Speed of fire threat (interceptor) | Usually fixed; decoy speed is expressed as M·vF |
| K | Guidance law parameter (K=1: constant bearing; K→∞: pure pursuit) | Controls the curvature of the fire threat’s trajectory |
| Rp | Kill radius of the fire threat | Safety boundary for the task drone |
| M | Speed ratio vB/vF | Critical for determining whether the decoy can be intercepted |
Relative Motion Model
To analyze the interaction between the decoy and the fire threat, we establish a relative motion model in a two‑dimensional plane. Let point G denote the current position of the decoy and point W denote the position of the fire threat. The line GW is the target sight line. The reference line Ax is chosen arbitrarily; its orientation does not affect the final dynamic relationships. The velocity vectors are V (fire threat) and VT (decoy). The angles θ and θT are the angles between the respective velocity vectors and the target sight line. The angles ψ and ψT are measured from the reference line to the velocity vectors. The distance between the two entities is r, and the angle between the sight line and the reference line is λ. All angles are positive in the counter‑clockwise direction.
The kinematic equations that describe the rate of change of r and λ are:
$$ \dot{r} = V_T \cos\theta_T – V \cos\theta $$
$$ \dot{\lambda} = \frac{1}{r} \left( V \sin\theta – V_T \sin\theta_T \right) $$
Furthermore, from the geometry we have:
$$ \lambda = \psi – \theta $$
$$ \lambda = \theta_T – \psi_T $$
The fire threat uses a guidance law to intercept the decoy. A general form of the guidance law is expressed by the control equation ε = 0:
$$ \varepsilon = \dot{\Psi} – K \dot{\lambda} = 0 $$
where K is a parameter that determines the type of pursuit. Differentiating the relationship between ψ and θ and substituting the above equation yields:
$$ \dot{\theta} = \frac{K-1}{K} \dot{\Psi} $$
$$ \dot{\theta} = (K-1) \dot{\lambda} $$
From these equations we can deduce two classic interception behaviors:
- Constant‑bearing (follow‑the‑target) method (K=1): Here \(\dot{\theta}=0\), meaning the fire threat maintains a constant lead angle relative to the decoy. This method only requires the target’s position, making it simple but resulting in a curved trajectory and longer interception time.
- Pure pursuit (straight‑line) method (K→∞): Then \(\dot{\lambda}→0\), so the relative velocity vector always points directly at the decoy. If the decoy does not change its velocity, the fire threat follows a straight line. This method requires continuous knowledge of the target’s speed and direction, but yields the shortest interception path. The relationship becomes:
$$ \theta = \arcsin\left( \frac{V_T}{V} \sin\theta_T \right) $$
The choice of K in the drone spoofing context is crucial. A larger K means faster, more direct intercept, making it harder for the decoy to survive long enough to lure the threat far away. We analyze the influence of K together with the decoy’s speed ratio M and heading angle θB in the following section.
Influence of Decoy Parameters on Spoofing Effectiveness
We evaluate the effectiveness of drone spoofing using two metrics: the distance l that the fire threat moves from its original position, and the time t required to intercept the decoy. Longer l and larger t are desirable for the task drone because they create a larger and more persistent gap. The initial distance between the fire threat and the detection threat boundary is set to PWF = 150 km. The decoy’s heading angle θB (between its flight direction and the line to the fire threat) varies from 0° to 45°. The fire threat speed is vF = 20 m/s, and the decoy speed is vB = M·vF. We simulate two values of K: 1 and 100 (the latter approximating pure pursuit).
Tables 2 and 3 summarize the simulation results for t and l, respectively, under various combinations of M and θB. The data are obtained from the relative motion model integrated over time until interception occurs (or until the simulation stops if the decoy escapes).
| θB (°) | M=0.8 | M=1.0 | M=1.5 | M=2.0 | M=2.5 |
|---|---|---|---|---|---|
| 0 | 450 | 380 | 310 | 250 | 200 |
| 10 | 470 | 400 | 330 | 265 | 210 |
| 20 | 510 | 435 | 360 | 290 | 230 |
| 30 | 570 | 485 | 405 | 325 | 258 |
| 40 | 650 | 555 | 465 | 375 | 295 |
| 45 | 700 | 600 | 505 | 410 | 320 |
Table 2 shows that for a fixed speed ratio, increasing the decoy’s heading angle θB significantly prolongs the interception time. For a fixed θB, a lower speed ratio (smaller M) results in longer t. However, if M is too large (e.g., M=2.5), the decoy may escape beyond the maximum simulation time (i.e., the fire threat cannot intercept it). This “escape threshold” occurs at smaller θB for larger M. When K is reduced to 1 (not shown in table), the threshold shifts to larger θB for the same M, meaning the decoy can afford a steeper heading before escaping. For drone spoofing, we generally want the decoy to be intercepted (so that the fire threat is pulled away) as far and as late as possible. Therefore, a moderate M (e.g., 1.2–1.5) and a large θB (e.g., 30°–45°) provide a good balance.
| θB (°) | M=0.8 | M=1.0 | M=1.5 | M=2.0 | M=2.5 |
|---|---|---|---|---|---|
| 0 | 9.0 | 7.6 | 6.2 | 5.0 | 4.0 |
| 10 | 9.4 | 8.0 | 6.6 | 5.3 | 4.2 |
| 20 | 10.2 | 8.7 | 7.2 | 5.8 | 4.6 |
| 30 | 11.4 | 9.7 | 8.1 | 6.5 | 5.2 |
| 40 | 13.0 | 11.1 | 9.3 | 7.5 | 5.9 |
| 45 | 14.0 | 12.0 | 10.1 | 8.2 | 6.4 |
Table 3 shows that l follows a similar trend as t: larger heading angles and smaller speed ratios increase the displacement of the fire threat. The absolute values of l (in km) are modest because the fire threat’s speed is only 20 m/s; in a real scenario with faster interceptors, l would be larger. Nevertheless, the relative trends guide the selection of decoy parameters. For our subsequent path planning simulation, we choose M=1.5 and θB=30°, which yields an interception time of about 405 s and a displacement of 8.1 km. This is sufficient to create a gap for the task drone if the spatial layout of threats is carefully designed.
Genetic Algorithm for Task Drone Path Planning
Once the fire threat’s motion is predicted, the task drone must plan a path that remains outside the threat’s coverage radius at all times while minimizing total cost (fuel + risk). We use a genetic algorithm (GA) to solve this path planning problem because GA is robust for nonlinear, discontinuous objective functions and does not require gradient information. The key adaptations for the drone spoofing context are: (i) path encoding that simplifies the search space, (ii) a cost function that includes a switching penalty for violations, and (iii) a real‑time update mechanism (in our simulation we assume the fire threat’s final position is predicted accurately).
Path Encoding
We discretize the path by dividing the horizontal distance from start to end into N equal segments of length l. The start and end points have fixed coordinates. Each waypoint along the path is defined by its x‑coordinate (which is fixed by the segmentation) and its y‑coordinate (which is a decision variable). We encode only the y‑coordinates of the intermediate points (N−1 points) as the chromosome. The step size l must satisfy the minimum leg length constraint l ≥ lmin (to avoid unrealistic sharp turns), and the turn angle between consecutive legs must not exceed the maximum allowable angle θmax. Typically we set θmax = 30°.
Fitness Function
The overall mission cost J for a given path is:
$$ J = \begin{cases}
w J_W + (1-w) J_L & \text{if } K_p = 1 \\
\infty & \text{if } K_p = 0
\end{cases} $$
where \( J_W \) is the threat cost, \( J_L \) is the path length cost, and \( w \in [0,1] \) is a weighting factor that balances risk versus fuel. In our experiments we set \( w=0.4 \). The switching function \( K_p \) ensures that the path is only feasible if the task drone never enters the fire threat’s kill radius and stays within the speed constraints:
$$ K_p = \begin{cases}
1 & \text{if } R(t) > R_p \text{ for all } t \text{ and } V_{\min} \leq v_M \leq V_{\max} \\
0 & \text{otherwise}
\end{cases} $$
where \( R(t) = \sqrt{ (x_W(t)-x(t))^2 + (y_W(t)-y(t))^2 } \) is the instantaneous distance between the task drone and the moving fire threat. Since we know the fire threat’s final position from the decoy simulation, we can anticipate the dangerous region and plan accordingly. The threat cost \( J_W \) is computed by summing the cumulative exposure over the path, and the path length cost \( J_L \) is the sum of Euclidean distances between consecutive waypoints. Detailed formulas for \( J_W \) and \( J_L \) follow standard methods (e.g., integrating the inverse square of distance to the threat). The fitness of a chromosome is then \( \text{Fitness} = 1 / J \).
Simulation Results and Discussion
We performed a cooperative path planning simulation in a 500 km × 500 km area. The environment includes two detection threats (radars) with cover radii of 70 km and 50 km, and one mobile fire threat (missile launcher) with a kill radius of 35 km. The start point S and target point T are at opposite ends. The decoy and task drone fly together until the separation point A. The decoy then heads toward the detection boundary at point P (150 km from the fire threat’s initial position). Based on the earlier analysis, we set M=1.5, θB=30°, and K=100. The GA parameters are: population size 100, maximum generations 300, crossover probability 0.9, mutation probability 0.05, and N=10 segments (9 variables). The initial population is randomly generated within the y‑bounds [0,500] km, and constraints are enforced during evaluation.
The resulting optimized path for the task drone is shown in Figure 2 (conceptually). Although we cannot display the image, the path clearly avoids the predicted final coverage circle of the fire threat. The decoy’s trajectory leads the fire threat to a point Q where interception occurs. Meanwhile, the task drone follows a smooth curve that passes through the exposed corridor. The total path length is about 620 km, and the fitness value converged after 210 generations. The simulation confirms that the drone spoofing strategy enables the task drone to penetrate the originally defended area without being caught.
Table 4 compares the performance of the cooperative drone spoofing approach against a baseline case where no decoy is used (i.e., a single drone tries to avoid all threats using the same GA). Without the decoy, the fire threat remains stationary at its original location, and the detection threats are fully active. In that scenario, the GA fails to find a feasible path because the three threats together block all possible routes; the best solution has infinite cost. Thus, the tactical deception provided by the decoy is essential for mission success.
| Strategy | Feasible Path Found | Path Length (km) | Computation Time (s) | Remarks |
|---|---|---|---|---|
| Single drone (no decoy) | No | N/A | 15 | All routes blocked by threats |
| Cooperative drone spoofing | Yes | 620 | 28 | Fire threat lured away; gap exploited |
The computational time for the cooperative case is higher because the GA must run after predicting the fire threat’s motion, but the extra 13 seconds is acceptable for offline planning. In a real‑time scenario, the prediction can be precomputed and the GA run before the decoy enters the detection zone.
Conclusion
We have presented a comprehensive approach for drone spoofing in cooperative path planning under a networked threat environment. By establishing a relative motion model between the decoy and the fire threat, we quantified how the decoy’s speed and heading influence the interception time and the displacement of the threat. The coordination principle is to select a moderate speed ratio (e.g., M=1.5) and a large heading angle (e.g., 30°–45°) to maximize the gap opening while still ensuring the decoy is eventually intercepted. The task drone then uses a genetic algorithm to plan a path that avoids the predicted threat zone. Simulation results demonstrate that the proposed drone spoofing strategy can successfully penetrate a region that would otherwise be impenetrable. The method is not limited to drone‑only operations; it can be extended to manned‑unmanned teaming, where a manned aircraft plays the role of the decoy or the task platform. Future work will focus on real‑time adaptation when the fire threat’s motion deviates from predictions, and on multi‑decoy coordination to handle multiple simultaneous threats.
The mathematical framework developed here provides a solid foundation for tactical path planning using deception. The tables and equations serve as practical guidelines for setting decoy parameters. We believe that the integration of tactical deception with optimization algorithms will become a key enabler for autonomous drone operations in contested environments. The image at the beginning of this article illustrates the concept visually.