In this paper, we investigate the trajectory planning problem for China UAV in complex environments. Traditional ant colony optimization (ACO) algorithms suffer from slow convergence, numerous turning points, and vulnerability to local optima. To address these issues, we propose an enhanced ACO algorithm that integrates multiple strategies. The key contributions include: (1) employing an artificial potential field to initialize the global pheromone distribution, reducing the blindness in early search; (2) introducing an elite ant colony with larger movement space and more sensitive pheromone update rules to improve exploration and convergence speed; (3) modifying the heuristic function by incorporating the distance from candidate nodes to the target node, inspired by the A* algorithm, to strengthen the guidance for ants. Extensive simulations demonstrate that the proposed method yields superior performance in terms of path length, iteration count, and trajectory smoothness, which is critical for China UAV operational efficiency.
1. Introduction
The rapid advancement of China UAV technology has significantly enhanced its application in military reconnaissance, logistics delivery, agricultural spraying, disaster rescue, and power line inspection. Path planning – the process of generating an optimal or feasible flight route from a start point to a destination while satisfying constraints such as obstacle avoidance, fuel consumption, battery limits, and time windows – is a core technology for autonomous flight. Numerous algorithms have been developed for this task. Classical approaches like A*, artificial potential field (APF), and Dijkstra are efficient for simple models but struggle in complex environments. Swarm intelligence algorithms such as ant colony optimization (ACO), particle swarm optimization (PSO), and grasshopper optimization have shown strong adaptability for NP-hard problems, yet they often converge slowly and tend to fall into local optima.
Several recent studies have attempted to overcome these limitations. For example, hybrid methods combining A* with neighborhood matrix search improve safety at the cost of path length. Other works integrate RRT* with heuristic ideas from A* and APF to reduce redundant nodes. In the context of China UAV low‑altitude airspace, researchers have used improved PSO to enhance flight safety while sacrificing some path quality. Pareto approaches for energy‑distance trade‑offs, neural network‑enhanced PSO, and hybrid ACO‑PSO frameworks have also been reported. However, these methods often require careful parameter tuning and may not guarantee global optimality in highly cluttered environments. In this paper, we focus on the specific challenges faced by China UAV during battlefield penetration or urban missions, where radar threats, no‑fly zones, and sharp turns must be simultaneously avoided.
We propose a novel improved ant colony algorithm that fuses several advanced techniques. The algorithm is designed to accelerate convergence, reduce path length, and improve trajectory smoothness for China UAV missions. The remainder of the paper is organized as follows: Section 2 formulates the path planning model including cost functions. Section 3 details the proposed algorithm, covering differential pheromone initialization, elite ant colony, improved heuristic function, and adaptive evaporation coefficient. Section 4 presents simulation results and comparisons. Section 5 concludes the paper.
2. Problem Formulation
We consider a two‑dimensional mission area where a China UAV must fly from a start point to a target point while avoiding threats (e.g., radar detection zones and obstacles). The overall flight cost consists of three components: path length cost, radar threat cost, and turning cost.
2.1 Path Length Cost
The total flight distance is assumed to be composed of N−1 segments connecting N waypoints. The path length cost FJ is given by:
$$
F_J = \sum_{g=1}^{N-1} c \, L_{\text{path},g}
$$
$$
L_{\text{path},g} = \sqrt{(x_{g+1} – x_g)^2 + (y_{g+1} – y_g)^2}
$$
where (xg, yg) are the coordinates of the g‑th waypoint, and c is a weight coefficient.
2.2 Radar Threat Cost
The detection probability of a ground radar r on the UAV is modeled using the classical distance‑attenuation function:
$$
P_r(L) =
\begin{cases}
0, & L > R_{r,\max} \\
1, & L < R_{r,\min} \\
\left( \frac{R_{r,\max} – L}{R_{r,\max} – R_{r,\min}} \right)^4, & R_{r,\min} \le L \le R_{r,\max}
\end{cases}
$$
To avoid underestimating threat on a single segment, we divide each segment into four equal parts and evaluate five sampling points. The radar threat cost Jr for radar r over the whole trajectory is:
$$
J_r = \sum_{g=1}^{N} P_r(L_g)
$$
where Lg is the distance from the midpoint of the g‑th segment to radar r. The total radar threat cost is:
$$
J_R = \sum_{r=1}^{Rn} \alpha_r J_r
$$
with Rn being the number of radars and αr the threat coefficient of radar r.
2.3 Turning Cost
Maneuvering a China UAV consumes extra energy and may increase exposure. The turning cost at the z‑th waypoint is defined as:
$$
J(\theta_z) =
\begin{cases}
\theta_z / \theta_{\max}, & \theta_z \le \theta_{\max} \\
\varepsilon \cdot \theta_z / \theta_{\max}, & \theta_z > \theta_{\max}
\end{cases}
$$
$$
J_\theta = \sum_{z=1}^{N-1} J(\theta_z)
$$
where θz is the turning angle at waypoint z, θmax is the maximum allowable turning angle, and ε is a penalty coefficient.
2.4 Overall Objective Function
The composite cost function that drives the ant colony search is:
$$
f = \omega_1 F_J + \omega_2 J_R + \omega_3 J_\theta
$$
where ω1, ω2, ω3 are weighting factors satisfying ω1 + ω2 + ω3 = 1.
3. Proposed Improved Ant Colony Algorithm
3.1 Differential Pheromone Initialization via Artificial Potential Field
In standard ACO, the initial pheromone distribution is uniform, leading to aimless exploration in early iterations. To mitigate this, we borrow the concept of artificial potential field (APF). The target point creates an attractive field, while obstacles and threat zones create repulsive fields. The initial pheromone value at a grid point q is set as:
$$
U_{\text{att}}(q) = \xi \, d(q, q_{\text{goal}})^2
$$
where ξ is the attractive gain coefficient and d(q, qgoal) is the Euclidean distance from q to the target. This initialization biases pheromone deposition so that ants near the start are guided toward the target from the very beginning, reducing early‑stage blindness.
3.2 Elite Ant Colony Strategy
We divide the total m ants into two groups: elite ants and ordinary ants, with a 1:2 ratio. Ordinary ants use an 8‑neighborhood movement pattern, while elite ants are allowed a larger 24‑neighborhood movement pattern. The expanded neighborhood enables elite ants to discover shorter or safer detours that ordinary ants might miss. The elite ants also follow a more aggressive pheromone update rule to accelerate convergence.
3.3 Improved Heuristic Function
The standard heuristic function ηij in ACO is often the inverse of the Euclidean distance dij. We enhance it by adding a term related to the distance from the candidate node j to the target node, similar to the A* heuristic. The improved heuristic function is:
$$
\eta_{ij} = \lambda \cdot \frac{1}{d_{ij}} + \frac{1}{h(j)}
$$
where h(j) is the estimated distance from node j to the target, and λ is a guidance weight. This formulation strengthens the attraction toward the target while still considering local distance, effectively reducing search space and accelerating convergence.
3.4 Adaptive Evaporation Coefficient for Elite Ants
For ordinary ants, the evaporation coefficient ρ remains constant. For elite ants, we employ an exponential decay scheme to balance exploration and exploitation:
$$
\rho(x) = R e^{-\lambda x}
$$
where x is the iteration number, R = 1/λ is a scaling factor, and λ controls the decay rate. Clamping is applied to keep ρ(x) ∈ [0.2, 0.6]. This strategy allows elite ants to retain higher pheromone levels early on for broad exploration and gradually reduce them to focus on promising paths.
The pheromone update for all ants follows the standard global rule:
$$
\tau_{ij}(t+1) = (1 – \rho) \tau_{ij}(t) + \Delta\tau_{ij}
$$
$$
\Delta\tau_{ij} = \sum_{k=1}^{m} \Delta\tau_{ij}^k
$$
$$
\Delta\tau_{ij}^k =
\begin{cases}
Q / L_k, & \text{if ant } k \text{ traverses edge } (i,j) \\
0, & \text{otherwise}
\end{cases}
$$
where Q is the pheromone intensity and Lk is the total cost of path traveled by ant k.
4. Simulation Results
We conducted simulations using a 50×50 grid environment to compare the proposed improved ACO with the standard ACO for China UAV path planning. The hardware platform was an Intel Core i7 CPU (2.6 GHz) with 16 GB RAM, running Python. The simulation parameters are listed in Table 1.
Table 1: Simulation Parameters
| Parameter | Value |
|---|---|
| Start point coordinates | (5,5) |
| Target point coordinates | (45,45) |
| Radar center coordinates | (25,25) |
| Radar maximum detection range | 10 |
| Obstacle 1 center | (20,16) |
| Obstacle 2 center | (35,32) |
| Obstacle radius | 5 |
| Pheromone factor α | 1 |
| Pheromone intensity Q | 1 |
| Heuristic factor β | 2 |
| Number of ants | 30 |
| Maximum iterations | 100 (simple) / 200 (complex) |
4.1 Simple Environment Results
Figure 1 (above) illustrates the planned trajectories. The yellow point is the start, blue is the target. We ran 10 independent simulations for each algorithm and selected the run with the minimum overall cost.
The cost evolution over iterations is shown in Figure 2. Table 2 summarizes the comparison results for the simple environment.
Table 2: Algorithm Comparison – Simple Environment
| Algorithm | Iterations | Best Iteration | Path Cost |
|---|---|---|---|
| Improved ACO | 100 | 51 | 58.66 |
| Standard ACO | 100 | 61 | 67.25 |
The improved ACO reduces the path cost by 12.7% and reaches the optimal solution 16.3% faster compared to standard ACO. The trajectory generated by our method is also smoother, with fewer sharp turns. This is attributed to the APF‑based initialization that reduces early search blindness, and the elite ants with improved heuristic function that accelerate convergence.
4.2 Complex Environment with Multiple Threats
To further validate the algorithm, we extended the map size and increased the number of obstacles and radar threat zones. The environment became more cluttered. Again, we performed 10 runs for each algorithm. Table 3 and Figure 3 present the results.
Table 3: Algorithm Comparison – Complex Environment
| Algorithm | Iterations | Best Iteration | Path Cost |
|---|---|---|---|
| Improved ACO | 200 | 83 | 185.72 |
| Standard ACO | 200 | 91 | 231.08 |
In the complex environment, the improved ACO achieves a path cost reduction of 19.6% and a faster convergence (best iteration at 83 vs. 91). Standard ACO often failed to find a feasible solution in early iterations, whereas our method generated a reasonable path from the first few iterations. The robustness of the improved algorithm stems from the elite ant strategy that explores a larger neighborhood, and the adaptive evaporation coefficient that maintains a good balance between exploration and exploitation.
The effectiveness of our approach is evident for China UAV operations where quick replanning and smooth flight are essential. The algorithm can be applied to both static and moderately dynamic environments, and it paves the way for future integration with 3D path planning and multi‑UAV coordination.
5. Conclusion
We have presented an improved ant colony algorithm tailored for China UAV path planning in threat‑rich environments. By initializing pheromone distribution using an artificial potential field, introducing elite ants with an extended neighborhood and adaptive evaporation factor, and refining the heuristic function with target‑distance guidance, our method significantly enhances convergence speed and solution quality. Simulation results in both simple and complex settings demonstrate that the proposed algorithm reduces path cost by 12–20% and requires fewer iterations to reach optimal solutions compared to the standard ACO. The resulting trajectories are smoother and more practical for real‑world China UAV missions. Future work will extend our approach to three‑dimensional space and consider cooperative path planning for multiple China UAVs.