In modern warfare, China drone has become a symbol of advanced military capability, demonstrating immense value in reconnaissance, strike, electronic warfare, and other fields. The trajectory planning algorithm is a key technology for autonomous flight of China drone. It plans an optimal or feasible flight route from the starting point to the destination while satisfying various constraints such as obstacle avoidance, fuel consumption, power limitation, and time restrictions. This technology is widely used in military reconnaissance, logistics delivery, geological survey, agricultural spraying, disaster rescue, and power inspection.
Extensive research has been conducted on trajectory planning algorithms for China drone. Traditional algorithms like A*, artificial potential field method, and Dijkstra’s algorithm have high computational efficiency and ease of implementation for simple models, but they struggle to meet the requirements of complex environments. Swarm intelligence optimization algorithms such as ant colony algorithm, particle swarm algorithm, and grasshopper algorithm are suitable for solving complex environmental NP problems with strong adaptability. However, their drawbacks include long convergence time and a tendency to fall into local optima.
To address these issues, I propose an improved ant colony algorithm for China drone path planning in complex environments. This algorithm enhances the traditional ant colony optimization (ACO) by incorporating the artificial potential field method for initial pheromone distribution, introducing elite ant colonies with larger movement ranges and more sensitive pheromone update rules, and improving the heuristic function by borrowing ideas from the A* algorithm. Simulation results demonstrate that the improved algorithm provides superior solutions in terms of path length, iteration count, and trajectory smoothness.
1. Trajectory Optimization Model
1.1 Flight Cost Evaluation
1.1.1 Path Length Evaluation Function
The fuel consumption of a China drone is proportional to the flight distance. Assuming the total path consists of N waypoints, the path length evaluation function $F_J$ is expressed as:
$$
F_J = \sum_{g=1}^{N-1} L_{\text{path},g}
$$
$$
L_{\text{path},g} = \sqrt{(x_{g+1} – x_g)^2 + (y_{g+1} – y_g)^2}
$$
where $(x_g, y_g)$ are the coordinates of the g-th waypoint, $L_{\text{path},g}$ is the length cost between waypoints g and g+1, and a weight coefficient $c$ can be applied to represent the path cost.
1.1.2 Radar Threat Evaluation Function
Radar threat assessment is critical for evaluating the detection and strike threat of enemy air defense radar against a China drone. The classic distance attenuation model is used to quantify the radar threat cost. To avoid misjudgment caused by evaluating only two endpoints, each segment between waypoints is divided into 4 equal parts, and 5 sampling points are taken. The threat cost of the entire path is approximated by the sum of the threat costs of these sampling points.
The detection probability $P_r(L)$ of ground radar r against a China drone is:
$$
P_r(L) =
\begin{cases}
0, & L \geq R_{r,\text{max}} \\
1, & L \leq R_{r,\text{min}} \\
\frac{R_{r,\text{max}}^4}{L^4}, & R_{r,\text{min}} < L < R_{r,\text{max}}
\end{cases}
$$
where $L$ is the distance between the China drone and radar r, $R_{r,\text{max}}$ is the maximum detection range, and $R_{r,\text{min}}$ is the reliable detection range.
The threat cost $J_r$ of radar r on the entire path is:
$$
J_r = \sum_{g=1}^{N} P_r(L_g)
$$
where $L_g$ is the distance between the midpoint of the path segment from waypoint g to g+1 and the radar. The total radar threat cost $J_R$ is:
$$
J_R = \sum_{r=1}^{R_n} \alpha_r J_r
$$
where $R_n$ is the total number of radars and $\alpha_r$ is the threat coefficient of the r-th radar.
1.1.3 Turning Cost Evaluation Function
A China drone consumes energy for steering during turns. The turning cost at the z-th waypoint $J(\theta_z)$ is:
$$
J(\theta_z) =
\begin{cases}
\varepsilon \cdot \frac{\theta_z}{\theta_{\text{max}}} / 2, & \theta_z \leq \theta_{\text{max}} / 2 \\
\varepsilon \cdot \frac{\theta_z}{\theta_{\text{max}}}, & \theta_{\text{max}} / 2 < \theta_z \leq \theta_{\text{max}}
\end{cases}
$$
$$
J_\theta = \sum_{z=1}^{N-1} J(\theta_z)
$$
where $\theta_{\text{max}}$ is the maximum turning angle, $\theta_z$ is the actual turning angle at the z-th waypoint, and $\varepsilon$ is the turning weight coefficient.
Considering fuel consumption and radar threat, the objective function is:
$$
f = \omega_1 F_J + \omega_2 J_R + \omega_3 J_\theta
$$
where $\omega_1, \omega_2, \omega_3$ are weight coefficients satisfying $\omega_1 + \omega_2 + \omega_3 = 1$.
2. Ant Colony Algorithm and Improvement
2.1 Traditional Ant Colony Algorithm
The ant colony algorithm simulates the foraging behavior of ants. Ants release pheromones during movement, which evaporate over time. Ants choose the path with the highest pheromone concentration, thereby finding the shortest path between the nest and the food source. The key mechanisms are the pheromone update mechanism and the transition probability mechanism. The probability of moving from position i to position j is:
$$
P_{ij}^k(t) =
\begin{cases}
\frac{[\tau_{ij}(t)]^\alpha \cdot [\eta_{ij}(t)]^\beta}{\sum_{j \in \text{allow}} [\tau_{ij}(t)]^\alpha \cdot [\eta_{ij}(t)]^\beta}, & j \in \text{allow} \\
0, & \text{otherwise}
\end{cases}
$$
where $\tau_{ij}(t)$ is the pheromone on the path from i to j at time t, $\alpha$ is the pheromone factor, $\beta$ is the heuristic factor, $\eta_{ij}(t)$ is the heuristic function, and allow is the set of feasible positions from i.
The pheromone update formula is:
$$
\tau_{ij}(t+1) = (1 – \rho) \cdot \tau_{ij}(t) + \Delta \tau_{ij}
$$
$$
\Delta \tau_{ij} = \sum_{k=1}^m \Delta \tau_{ij}^k
$$
$$
\Delta \tau_{ij}^k =
\begin{cases}
Q / L_k, & \text{if ant k visits edge (i,j)} \\
0, & \text{otherwise}
\end{cases}
$$
where $\rho$ is the evaporation constant ($0 < \rho < 1$), $m$ is the total number of ants, $Q$ is the pheromone intensity, and $L_k$ is the total path length of the k-th ant.
2.2 Algorithm Improvements
2.2.1 Differentiated Initial Pheromone Distribution
In traditional ACO, the pheromone distribution is uniform, leading to blind initial search. I borrow the idea of the artificial potential field method: treat the destination as an attractive field and obstacles as repulsive fields. The initial pheromone value at position q is:
$$
U_{\text{att}}(q) = \frac{1}{2} \xi \cdot d(q, q_{\text{goal}})^2
$$
where $d(q, q_{\text{goal}})$ is the Euclidean distance from position q to the goal, and $\xi$ is the attraction gain coefficient.
2.2.2 Elite Ant Colony
I divide the total m ants into two groups in a 1:2 ratio: elite ants and ordinary ants. Elite ants have a larger movement range. Ordinary ants have an 8-neighbor movement range, while elite ants have a 24-neighbor movement range. This increases the search diversity and accelerates convergence.
The movement ranges are summarized in the following table:
| Ant Type | Neighborhood Type | Number of Movable Directions |
|---|---|---|
| Ordinary Ant | 8-neighbor | 8 |
| Elite Ant | 24-neighbor | 24 |
2.2.3 Improved Heuristic Function
Traditional ACO uses a fixed heuristic function $\eta_{ij} = 1/d_{ij}$. This leads to blind selection of the next node. By borrowing the heuristic idea from the A* algorithm, I introduce the distance from node j to the goal:
$$
\eta_{ij} = \frac{1}{d_{ij}} + \frac{\lambda}{h(j)}
$$
where $h(j)$ is the estimated distance from node j to the goal, $d_{ij}$ is the distance between i and j, and $\lambda$ is a guidance coefficient.
2.2.4 Improved Evaporation Factor
The evaporation factor $\rho$ controls the volatilization speed of pheromones. For ordinary ants, $\rho$ is constant. For elite ants, $\rho$ follows an exponential distribution to adaptively adjust the exploration-exploitation balance:
$$
\rho(x) = \frac{1}{\lambda} e^{-x/\lambda}
$$
Limited to the range [0.2, 0.6] to avoid extreme values, where $R$ is the self-adjustment coefficient.
3. Simulation Results
The simulation environment uses an Intel Core i7 CPU (2.6 GHz), 16 GB RAM, Windows 10, and Python. The environmental space is 50×50. The parameters are listed in the table below.
| Parameter | Value |
|---|---|
| Start point | (5,5) |
| Goal point | (45,45) |
| Radar center | (25,25) |
| Radar max detection range | 10 |
| Obstacle 1 center | (20,16) |
| Obstacle 2 center | (35,32) |
| Obstacle radius | 5 |
| Pheromone factor $\alpha$ | 1 |
| Heuristic factor $\beta$ | 5 |
| Evaporation coefficient $\rho$ (ordinary) | 0.3 |
| Evaporation coefficient $\rho$ (elite) | 0.2~0.6 (exponential) |
| Pheromone intensity $Q$ | 1 |
| Number of ants | 30 |
| Maximum iterations | 100 |
I compared the improved ACO with traditional ACO. Ten simulation runs were performed, and the run with the minimum path cost was selected. The path cost convergence curves are shown in the following figure (noting that the actual figure is represented by the hyperlink inserted below).
The comparison of cost over iterations for the simple environment is shown in the table below:
| Algorithm | Total Iterations | Optimal Iteration | Path Cost |
|---|---|---|---|
| Improved ACO | 100 | 51 | 58.66 |
| Traditional ACO | 100 | 61 | 67.25 |
In the simple environment, the improved ACO reduces the path cost by approximately 12.7% compared to traditional ACO and reaches the optimal solution in 16.3% fewer iterations. The algorithm’s improvements—differentiated initial pheromone, elite ant colonies, and enhanced heuristic—reduce initial blind search and accelerate convergence.
Next, I expanded the environment by increasing obstacles and radar threat zones. The map size remained 50×50. The comparison results for the expanded environment are as follows:
| Algorithm | Total Iterations | Optimal Iteration | Path Cost |
|---|---|---|---|
| Improved ACO | 200 | 83 | 185.72 |
| Traditional ACO | 200 | 91 | 231.08 |
In the complex environment, the improved ACO achieves a path cost reduction of approximately 19.6% compared to traditional ACO. The improved algorithm obtains a feasible solution earlier in the iteration process and converges faster to the global optimum. This demonstrates that the improved ACO is particularly effective for China drone path planning in complex environments with multiple threats.
The enhanced heuristic function, elite ant colony strategy, and adaptive evaporation factor collectively contribute to superior performance. The algorithm balances exploration and exploitation, avoiding local optima while maintaining fast convergence.
4. Conclusion
I proposed an improved ant colony algorithm for China drone path planning. By modifying the initial pheromone distribution using the artificial potential field method, introducing elite ant colonies with expanded search ranges, and refining the heuristic function with A*-inspired guidance, the algorithm enhances the search capability and convergence speed. Simulation results confirm that the improved ACO outperforms traditional ACO in path length, iteration number, and trajectory smoothness while ensuring flight safety.
Future work will extend this research to 3D space and multi-China drone cooperative path planning, which are more challenging and practical for real-world missions.