In the field of robot technology, path planning is a critical component for autonomous navigation, especially in complex environments such as industrial inspection, emergency rescue, and space exploration. Traditional path planning methods often struggle with non-flat terrains, where storage efficiency and terrain adaptability become significant challenges. This article presents an improved A* algorithm based on a dual-resolution hierarchical grid map, designed to address these issues by optimizing map representation and path planning strategies. The approach integrates high-resolution obstacle layers and low-resolution elevation layers to balance computational load and environmental accuracy, enhancing the overall performance of robot technology in unstructured scenarios.
The dual-resolution hierarchical grid map consists of two distinct layers: an obstacle layer and an elevation layer. The obstacle layer uses binary representation to identify rigid obstacles like rocks and steep slopes, while the elevation layer employs a digital elevation model (DEM) to quantify terrain undulations. This hierarchical structure allows for efficient data storage and retrieval, reducing memory usage compared to traditional 3D grid maps. The mathematical representation of a grid node is given by:
$$ \text{Node}(x, y) = \{\text{Map}_A(x, y) \in \{0, 1\}, \text{Map}_B(x, y) = z\} $$
where $\text{Map}_A$ denotes the obstacle layer with binary values (0 for free, 1 for occupied), and $\text{Map}_B$ stores elevation values $z$. This formulation enables seamless integration of spatial and topographical data, which is essential for advanced robot technology applications.
To further enhance path planning, the A* algorithm is modified by reconstructing its cost function. The traditional cost function $f(n) = g(n) + h(n)$ is extended to incorporate terrain-specific constraints, such as slope, energy consumption, and safety factors. The improved cost function is defined as:
$$ f_{\text{cost}}(n) = x \cdot g_{\text{cost}}(n) + (1 – x) \cdot h_{\text{cost}}(n) $$
Here, $x$ is a dynamic weight factor adjusted based on the distance to the goal, $g_{\text{cost}}(n)$ represents the mobility cost considering terrain坡度, and $h_{\text{cost}}(n)$ is the heuristic function that integrates spatial distance, slope root mean square, and terrain risk. The mobility cost is computed as:
$$ g_{\text{cost}}(n) = \alpha \cdot d(n) + \beta \cdot \max\left(\frac{\Delta z(n, n_{\text{parent}})}{d(n, n_{\text{parent}})}\right) $$
where $d(n)$ is the cumulative移动距离, $\Delta z$ is the elevation difference between nodes, and $\alpha$, $\beta$ are weights for energy consumption and slope safety. The heuristic function is expanded to a multimodal evaluation:
$$ h_{\text{cost}}(n) = \gamma_1 \cdot h_{\text{dist}}(n) + \gamma_2 \cdot h_{\text{slope}}(n) + \gamma_3 \cdot h_{\text{risk}}(n) $$
with $\gamma_1 + \gamma_2 + \gamma_3 = 1$. The distance component $h_{\text{dist}}(n)$ uses Euclidean distance, while $h_{\text{slope}}(n)$ calculates the root mean square of slopes along the path to discourage steep ascents/descents. The dynamic weight $x(n)$ is regulated by a Sigmoid function for smooth transitions between global and local planning:
$$ x(n) = \frac{1}{1 + \exp\left(-k \cdot \frac{h_{\text{dist}}(n)}{D_{\text{max}}}\right)} $$
where $k$ is a decay coefficient (set to 2.5 in experiments), and $D_{\text{max}}$ is the maximum path length. This adaptive mechanism ensures that robot technology can efficiently navigate varying terrains without compromising safety or performance.
Experimental validation was conducted through simulations, real-world robot tests, and engineering applications. In simulation, the dual-resolution map demonstrated a 61.7% reduction in storage load compared to 3D grid maps over a 700 m × 700 m area. The improved A* algorithm achieved a 38.9% decrease in elevation standard deviation of planned paths, indicating smoother and safer routes. Real robot experiments in outdoor environments confirmed the method’s ability to avoid steep slopes and obstacles, while engineering tests in oilfield inspection scenarios showed a 62% reduction in memory usage and path planning response times under 6.9 seconds. These results underscore the practicality of this approach in large-scale, unstructured environments for robot technology.
The following table summarizes the performance comparison of different path planning algorithms in terms of key metrics:
| Algorithm | Expansion Nodes | Path Length (m) | Planning Time (s) | Elevation Standard Deviation |
|---|---|---|---|---|
| A* Algorithm | 76 | 25.4 | 4.32 | 29.73 |
| 3D A* Algorithm | 724 | 31.8 | 41.70 | 23.56 |
| Dynamic Weighted A* | 68 | 26.1 | 4.85 | 27.45 |
| Improved A* with DWA | 115 | 28.9 | 12.34 | 18.72 |
| Dual-Resolution Improved A* | 83 | 34.2 | 5.24 | 11.43 |
Another table compares memory usage for different map types, highlighting the efficiency of the dual-resolution approach:
| Map Type | Memory Usage (MB) |
|---|---|
| 2D Grid Map | 436.4 |
| Dual-Resolution Hierarchical Grid Map | 518.2 |
| 3D Grid Map | 1351.6 |
The implementation of the dual-resolution map involves specific algorithms for each layer. For the obstacle layer, a Bayesian filtering framework updates grid occupancy probabilities using sensor data. The logarithmic odds update is given by:
$$ l_{t,i} = l_{t-1,i} + \log\left(\frac{p(m_i | z_t, x_t)}{1 – p(m_i | z_t, x_t)}\right) – l_0 $$
where $l_{t,i}$ is the log-odds at time $t$, $z_t$ is sensor data, $x_t$ is the robot pose, and $l_0$ is the initial log-odds. This ensures robust obstacle detection in dynamic environments. For the elevation layer, DEM data is projected onto a 2D grid, with each cell’s elevation computed as the weighted mean of point cloud data within its area. The resolution of the elevation layer is adaptively set based on robot kinematics:
$$ R_h = \frac{L_{\text{robot}}}{2} \cdot \tan(\theta_{\text{max}}) $$
where $L_{\text{robot}}$ is the robot length and $\theta_{\text{max}}$ is the maximum climbable slope. This design minimizes data redundancy while preserving essential terrain features for robot technology.
In conclusion, the dual-resolution hierarchical grid map and improved A* algorithm provide a comprehensive solution for path planning in non-flat terrains, advancing robot technology by optimizing storage, safety, and efficiency. Future work will focus on integrating multimodal environmental parameters to enhance robustness in dynamic scenarios. The consistent emphasis on robot technology throughout this research highlights its transformative potential in autonomous systems.