In recent years, the field of robot technology has witnessed significant advancements, particularly in applications such as autonomous navigation and delivery services in high-risk environments. Path planning is a critical component of mobile robot technology, enabling robots to traverse from a start point to a goal while avoiding obstacles efficiently. Among various algorithms, the A* algorithm stands out due to its heuristic search capabilities, which combine the strengths of Dijkstra’s algorithm and breadth-first search. However, traditional A* algorithms suffer from issues like prolonged computation time, excessive inflection points, and large turning angles in complex environments. These limitations can hinder the practical deployment of robot technology in real-world scenarios, such as indoor navigation for delivery robots. To address these challenges, we propose an enhanced A* algorithm that extends the search neighborhood, dynamically adjusts heuristic weights, and incorporates concave obstacle detection. This improvement aims to optimize path planning for robot technology by reducing path length, minimizing inflection points, and enhancing overall efficiency.
The core of our approach lies in modifying the estimation function of the A* algorithm to adapt to dynamic path conditions, expanding the search neighborhood to 24 directions for finer angular resolution, and integrating a detection mechanism for concave obstacles. These enhancements not only accelerate the search process but also produce smoother paths, which are crucial for the stability and performance of mobile robot technology. Through simulations in grid-based environments with varying obstacle densities, we demonstrate that our method outperforms traditional A* and other variants in key metrics such as path length, number of searched nodes, computation time, and total turning angle. This contribution is particularly relevant for advancing robot technology in complex, obstacle-rich settings, where efficient and reliable path planning is essential.
Path planning in robot technology involves generating a collision-free trajectory from a start to a goal point, often categorized into global and local planning. Global methods, like the A* algorithm, rely on complete environmental knowledge, while local methods handle dynamic obstacles. The A* algorithm uses an estimation function \( f(n) = g(n) + h(n) \), where \( g(n) \) is the actual cost from the start node to the current node \( n \), and \( h(n) \) is the heuristic estimate from \( n \) to the goal. Typically, Euclidean distance is employed for \( h(n) \), calculated as \( D(X) = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are coordinates of two points. Although A* guarantees optimal paths under certain conditions, its performance degrades in complex environments due to excessive node expansions and rigid angular constraints from limited search neighborhoods (e.g., 4 or 8 directions). This can lead to paths with numerous sharp turns, which are impractical for robot technology that requires smooth maneuvers. Our work builds on existing research, such as weighted heuristics and expanded neighborhoods, but introduces a novel 24-neighborhood search that reduces the minimum turning angle to approximately \( \pi/20 \) radians, compared to \( \pi/4 \) in traditional 8-neighborhood searches. Additionally, we address the issue of concave obstacles, which often trap the algorithm into inefficient searches, by incorporating a detection function that penalizes nodes within such regions. These innovations collectively enhance the applicability of A* in modern robot technology.
To elaborate on the improved estimation function, we redefine \( f(n) \) as \( f^*(n) = g(n) + L(d) \cdot h(n) \), where \( L(d) \) is a dynamic weight function that adjusts based on the proximity to the goal. Specifically, \( L(d) = 1 + \beta \cdot \ln(1 + \frac{d_x}{D_x}) \), with \( d_x \) being the absolute difference in x-coordinates between the current node and the goal, \( D_x \) the total x-distance from start to goal, and \( \beta \) a weight parameter optimized between 0.4 and 0.6 (we use 0.5 in our experiments). This adjustment allows the heuristic to dominate early in the search, speeding up node expansion, and then recede near the goal to ensure path optimality. Such dynamic weighting is vital for robot technology, as it balances exploration and exploitation in path planning. For the 24-neighborhood search, we extend the traditional 8 directions to 24, covering angles as small as \( \pi/20 \) radians, which significantly reduces inflection points and turning angles. The search process involves evaluating 24 neighboring nodes, sorting them by \( f^*(n) \), and excluding those blocked by obstacles. This expansion not only improves path smoothness but also decreases the number of nodes searched, enhancing computational efficiency for robot technology applications. Furthermore, the concave obstacle detection function scans a 7×7 cell area around the current node, comparing it to a pre-defined library of concave shapes. If a match is found, nodes within the concave region are penalized by adding a large value \( \sigma \) (set to 10, representing infinity) to their \( f^*(n) \), thus steering the search away from traps. This function is integrated into the A* algorithm’s main loop, ensuring that paths avoid inefficient detours common in complex environments.
The simulation setup for validating our approach uses a grid map of 35×35 cells, with obstacle coverages of 10% and 20%, representing typical challenges in robot technology. We compare our improved A* algorithm with the traditional A* and a 24-neighborhood A* variant from literature. The results, summarized in the table below, show that our method reduces path length by 2-3%, searched nodes by 66-73%, computation time by 6-8%, and total turning angle by 40-60%. These improvements are crucial for robot technology, as they translate to faster, more energy-efficient, and smoother navigation. The algorithm’s flowchart, though not depicted here, outlines steps like initializing open and closed lists, dynamic \( f^*(n) \) calculation, 24-neighborhood expansion, and obstacle checks. In conclusion, our enhanced A* algorithm addresses key limitations in path planning for robot technology, offering a robust solution for global navigation in complex settings. Future work could focus on integrating this with local planners to handle dynamic obstacles, further advancing the capabilities of mobile robot technology.
| Algorithm | Obstacle Ratio | Path Length | Searched Nodes | Search Time (s) | Total Turning Angle (°) | Optimization (%) |
|---|---|---|---|---|---|---|
| Traditional A* | 10% | 41.0 | 360 | 0.70 | 315 | — |
| Traditional A* | 20% | 42.8 | 496 | 0.91 | 405 | — |
| 24-Neighborhood A* | 10% | 40.8 | 336 | 0.68 | 225 | Length: 0.5, Nodes: 6.7, Time: 2.9, Angle: 28.6 |
| 24-Neighborhood A* | 20% | 44.0 | 402 | 0.89 | 251.6 | Length: -2.8, Nodes: 19.0, Time: 2.2, Angle: 37.9 |
| Improved A* (Ours) | 10% | 40.1 | 112 | 0.65 | 186 | Length: 2.2, Nodes: 68.9, Time: 7.1, Angle: 41.0 |
| Improved A* (Ours) | 20% | 41.6 | 144 | 0.85 | 72 | Length: 2.8, Nodes: 70.9, Time: 6.6, Angle: 82.2 |
The mathematical formulation of our improved estimation function is central to the algorithm’s performance. We define the dynamic weight \( L(d) \) as follows: $$ L(d) = 1 + \beta \cdot \ln\left(1 + \frac{d_x}{D_x}\right) $$ where \( \beta = 0.5 \), \( d_x = |x_{\text{current}} – x_{\text{goal}}| \), and \( D_x = |x_{\text{start}} – x_{\text{goal}}| \). This function ensures that the heuristic \( h(n) \) contributes more heavily when the robot is far from the goal, reducing unnecessary node expansions. For the 24-neighborhood search, the minimum turning angle \( \theta_{\text{min}} \) is given by \( \theta_{\text{min}} = \frac{\pi}{20} \), which is derived from the angular resolution of the expanded directions. The Euclidean distance for any two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is computed as: $$ D(X) = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} $$ This metric is used in both \( g(n) \) and \( h(n) \) calculations. The concave obstacle detection involves a function \( \text{concave}(n) \) that returns a set of nodes within concave regions, and the penalty is applied as \( f^*(n) = f^*(n) + \sigma \) for those nodes, with \( \sigma = 10 \). These equations collectively enhance the A* algorithm’s efficiency, making it more suitable for advanced robot technology.
In terms of implementation, the improved A* algorithm follows a structured workflow. First, parameters such as open list, closed list, obstacle list, and the concave function library are initialized. The start node is set as the current node and added to the open list. While the current node is not the goal, the algorithm checks for concave obstacles in a 48-node neighborhood around the current node. If detected, nodes within concave regions are marked with a penalty. Then, the 24 neighboring nodes’ \( f^*(n) \) values are computed and added to the open list. After removing any nodes that match obstacles, the algorithm selects the node with the minimum \( f^*(n) \) from the open list, verifies if it is obstacle-free along the path, and moves it to the closed list. This process repeats until the goal is reached. The resulting path is generated from the closed list, ensuring optimality and smoothness. This method significantly reduces computational overhead and improves path quality, which are critical factors in robot technology for real-time applications.
Our simulations confirm the superiority of the improved A* algorithm in robot path planning. For instance, in a 10% obstacle environment, the path length decreased from 41.0 to 40.1, searched nodes dropped from 360 to 112, and total turning angle reduced from 315° to 186°. Similarly, in a 20% obstacle scenario, the improvements were even more pronounced, with a 82.2% reduction in turning angle. These results highlight the algorithm’s ability to handle complex environments efficiently, making it a valuable tool for robot technology. The expansion to 24 search directions allows for more natural and continuous paths, reducing the need for post-processing smoothing techniques. Moreover, the dynamic weighting in the estimation function adapts to the path’s progression, optimizing the trade-off between speed and accuracy. As robot technology continues to evolve, such enhancements in path planning algorithms will play a pivotal role in enabling autonomous systems to operate reliably in diverse settings.
In conclusion, we have presented an extended search neighborhood A* algorithm that addresses key challenges in robot path planning. By dynamically adjusting the heuristic weight, expanding the search directions, and incorporating concave obstacle detection, our method produces shorter, smoother, and more efficient paths. These advancements are essential for the progression of robot technology, particularly in applications requiring precise and reliable navigation. Future research could explore the integration of this global planner with local methods, such as dynamic window approaches, to further enhance the adaptability of robot technology in dynamic environments. Overall, this work contributes to the ongoing development of intelligent robotic systems, paving the way for more sophisticated and efficient autonomous operations.