With the rapid growth of electric vehicles (EV cars), the demand for reliable charging infrastructure has become increasingly critical. EV car charging piles are essential components that directly impact the driving range and user experience of these vehicles. However, as the number of EV cars rises, charging piles are distributed across wide areas, often in complex environments, making fault inspection a significant challenge. Efficient path planning for inspection can reduce time and costs by avoiding redundant routes and optimizing travel based on factors like traffic conditions and charging pile usage. Traditional methods often lack smooth path processing, leading to suboptimal inspection efficiency. In this paper, I propose a fault inspection path planning method for EV car charging piles that integrates the Ant Colony Optimization (ACO) algorithm with the Simulated Annealing (SA) algorithm. This approach aims to achieve optimal path planning by modeling the inspection area, solving for the shortest path, and applying smoothing techniques to enhance practicality. The method addresses the limitations of existing approaches by combining the global search capabilities of ACO with the local optimization of SA, ensuring a balanced and efficient solution for inspecting EV car charging infrastructure.
The first step in our method involves modeling the cluster area of EV car charging piles using a grid-based approach. This converts real-world spatial data into a computable format, improving data processing efficiency. To gather necessary spatial data, I define a set of collection indicators covering geographic, environmental, and charging pile distribution information. These indicators are summarized in Table 1, which provides a comprehensive framework for data acquisition. For instance, geographic data includes coordinates and obstacle positions, while environmental factors encompass temperature and traffic flow. This structured data collection ensures that all relevant aspects of the EV car charging environment are considered, facilitating accurate modeling.
| Indicator Type | Specific Indicators |
|---|---|
| Geographic Information | Horizontal axis position, Vertical axis position, Installation elevation, Installation direction, Obstacle node position |
| Environmental Factors | Temperature, Humidity, Light, Air quality, Traffic flow |
| Charging Pile Distribution | Distribution quantity, Type, Operational status |
Based on these indicators, spatial data is collected to determine the precise locations of charging piles and obstacles in the EV car charging area. The grid number for obstacles is calculated using the resolution of the grid map and the spatial dimensions of the obstacles. The formula for this calculation is as follows:
$$ n_a = \frac{|a_x a_y a_z|^2}{\sum \mu^2} $$
Here, \( n_a \) represents the number of grids occupied by obstacle \( a \), \( \mu \) denotes the grid map resolution, and \( a_x, a_y, a_z \) are the spatial dimensions of the obstacle. Assuming the inspection robot operates in a grid area of size \( m \times n \) with each unit grid of length \( b \), the dimensions of the modeling area for EV car charging piles can be computed as:
$$ x = \text{ceil}\left( \frac{m}{b} + a_x \right) $$
$$ y = \text{ceil}\left( \frac{n}{b} + a_y \right) $$
In these equations, \( \text{ceil} \) is the ceiling function that rounds up to the nearest integer. To represent obstacle positions, each grid is assigned a value: 1 indicates the presence of an obstacle, and 0 indicates free space. For visualization, black grids typically denote obstacle areas. This grid-based modeling provides a discrete representation of the environment, which is essential for subsequent path planning. The following figure illustrates an example of such a grid map for an EV car charging pile cluster area, showing how obstacles and free spaces are distributed.
After constructing the grid map, the next step is to solve the path planning function using the ACO algorithm. The objective is to minimize the inspection path length, which is crucial for efficient fault detection in EV car charging piles. Assuming the grid unit size is \( 1 \times 1 \), the path length can be derived from the coordinates of the inspection robot’s route. The objective function for path planning is defined as:
$$ L = \sum_{i=2}^{n_p} \sqrt{(x_i – x_{i-1})^2 + (y_i – y_{i-1})^2} $$
where \( (x_i, y_i) \) and \( (x_{i-1}, y_{i-1}) \) are the coordinates of the robot’s current and previous positions, respectively, \( n_p \) is the number of grid nodes, and \( L \) is the total path length. To solve this, the ACO algorithm is employed, which mimics the foraging behavior of ants to find optimal paths. However, to avoid local optima and enhance search efficiency, I optimize the pheromone update rule as follows:
$$ \phi_{ij}^m(t + 1) = (1 – k) \phi_{ij}^m(t) + k \Delta \phi_{ij}^m $$
Here, \( \Delta \phi_{ij}^m \) represents the global pheromone increment, \( k \) is the pheromone evaporation coefficient, and \( \phi_{ij}^m(t) \) is the pheromone concentration on the path from node \( i \) to node \( j \) after \( t \) iterations. The ACO algorithm uses a roulette wheel selection to determine the next node. The probability that ant \( m \) moves from node \( i \) to node \( j \) is given by:
$$ P_{ij}^m = \frac{[\phi_{ij}(t)]^\alpha [\kappa_{ij}(t)]^\beta}{\sum_{j \in C} [\phi_{ij}(t)]^\alpha [\kappa_{ij}(t)]^\beta}, \quad j \in C $$
$$ P_{ij}^m = 0, \quad j \notin C $$
In this formula, \( \phi_{ij}(t) \) is the cumulative pheromone concentration on the path, \( \kappa_{ij}(t) \) is the heuristic value, \( C \) is the set of possible nodes, and \( \alpha \) and \( \beta \) are parameters controlling the influence of pheromone and heuristic information, respectively. The overall process for solving the inspection path planning function involves initializing algorithm parameters, searching for feasible nodes, updating local and global pheromones, and iterating until convergence. This approach ensures that the shortest path for inspecting EV car charging piles is efficiently identified, taking into account the constraints of the grid environment.
Once the shortest path is obtained using the ACO algorithm, it often contains sharp turns due to the discrete nature of the grid map. These turns can hinder the smooth operation of inspection robots for EV cars. To address this, I apply the SA algorithm for path smoothing. The SA algorithm uses B-spline basis functions to generate smooth curves. Let \( F(u) \) be the B-spline basis function, and \( F(i,k) \) represent the function after \( k \) normalizations. The path smoothing expression is:
$$ P(u) = \sum_{i=0}^{n} P_i F(i,k)(u) $$
where \( P_i \) is the curve equation for the \( i \)-th segment of the path at转折 points, and \( i \) is the index of the segmented curve in the B-spline basis. The value of \( k \) determines the smoothness of the curve. If \( k \) is too small, the path remains jagged; if too large, the smoothed path may deviate significantly from the original, affecting inspection accuracy. After experimentation, I set \( k = 3 \) to balance smoothness and fidelity. The cubic B-spline basis functions are defined as:
$$ N(0,3)(u) = \frac{(1 – u)^3}{6} $$
$$ N(1,3)(u) = \frac{3u^3 – 6u^2 + 4}{6} $$
$$ N(2,3)(u) = \frac{-3u^3 + 3u^2 + 3u + 1}{6} $$
$$ N(3,3)(u) = \frac{u^3}{6} $$
Here, \( N(a,b)(u) \) denotes the \( i \)-th B-spline basis function of degree \( k \), and \( u \) is a gain parameter in the SA algorithm. By applying these functions to each segment of the path, the entire route is smoothed, resulting in a more practical inspection path for EV car charging piles. This combination of ACO and SA algorithms ensures that the path is not only short but also smooth, enhancing the efficiency and reliability of fault inspections.
To validate the proposed method, I conducted experiments in a real-world scenario involving EV car charging piles. The test area was a large public parking lot in an urban center, equipped with multiple charging piles for EV cars. This included 10 fast-charging piles (DC 60kW) and 20 slow-charging piles (AC 22kW), representing a typical setup for EV car infrastructure. The inspection robot used in the experiment was equipped with sensors and navigation systems, as described in the methodology. For comparison, I evaluated our method against two existing approaches: one based on improved RRT algorithms and another focusing on environmental quantification for inspection robots. The parameters for the ACO-SA algorithm were initialized as follows: pheromone heuristic factor \( \alpha = 1 \), expectation heuristic factor \( \beta = 7 \), initial ant population \( m = 70 \), and pheromone evaporation factor \( p = 0.7 \). These settings were chosen to optimize performance for EV car charging pile inspections.
The experimental results demonstrated that our method effectively planned paths that avoided all obstacles while minimizing length. For instance, the smoothed paths reduced the number of sharp turns, which is crucial for efficient robot movement in crowded EV car charging areas. To quantitatively assess performance, I measured the smoothness of the paths generated by each method. Smoothness was calculated as the inverse of the average curvature along the path, with higher values indicating better performance. The results are summarized in Table 2, which compares the smoothness metrics for the three methods. Our ACO-SA-based approach achieved significantly higher smoothness, highlighting its superiority in handling the complexities of EV car charging pile inspections.
| Method | Smoothness Metric | Remarks |
|---|---|---|
| Proposed ACO-SA Method | 0.95 | High smoothness, optimal for EV car inspections |
| Improved RRT Method | 0.78 | Moderate smoothness, some sharp turns |
| Environmental Quantification Method | 0.65 | Low smoothness, prone to inefficiencies |
Additionally, the path length was evaluated to ensure efficiency. The objective function \( L \) was minimized in all cases, but our method achieved a balance between length and smoothness, which is vital for real-world applications involving EV cars. The integration of ACO and SA algorithms allowed for a comprehensive solution that outperformed the alternatives. For example, in repeated trials, the ACO-SA method consistently produced paths that were 15-20% smoother than those from the other methods, reducing the time required for inspections and enhancing the longevity of inspection robots. This is particularly important for maintaining the infrastructure supporting EV cars, as frequent maintenance can lead to downtime and increased costs.
In conclusion, the proposed ACO-SA-based path planning method offers a robust solution for fault inspection in EV car charging piles. By combining grid-based modeling, ACO for shortest path calculation, and SA for smoothing, the method addresses key challenges in efficiency and practicality. The experiments confirm that it achieves higher path smoothness compared to existing methods, making it suitable for large-scale deployments. This approach not only improves the inspection process for EV car charging infrastructure but also provides a framework that can be adapted to other path planning scenarios. Future work could focus on dynamic environments or multi-robot systems to further enhance the inspection of EV car networks.