Path planning is a critical challenge in the field of intelligent robotics, with significant implications for applications such as automated guided vehicles (AGVs) in smart factories, delivery robots in hotels, and autonomous vehicles. In China, the rapid advancement of artificial intelligence and deep learning has propelled path planning technology to new heights, enabling more efficient and adaptive solutions for complex environments. Traditional algorithms like Dijkstra, A*, Ant Colony Optimization (ACO), and Rapidly-exploring Random Tree (RRT) have been widely used, but they often suffer from issues like excessive path curvature, long route lengths, and redundant sampling points. Among these, the RRT algorithm stands out due to its probabilistic completeness and minimal dependency on global environmental information, making it highly adaptable. However, it still grapples with inefficiencies in sampling and path quality. To address these limitations, this paper proposes an enhanced APF-Bi-RRT* algorithm that integrates dynamic target bias functions, adaptive repulsive coefficients in artificial potential fields, and advanced path smoothing techniques. This approach not only improves planning efficiency but also ensures smoother and safer paths for mobile robots, which is particularly relevant for China’s growing robotics industry, where precision and reliability are paramount.
The Bidirectional RRT* (Bi-RRT*) algorithm builds upon the standard RRT* by initiating two trees—one from the start point and another from the goal point—which expand simultaneously until they connect, thereby reducing path generation time. However, this method often results in random sampling that leads to redundant nodes and suboptimal paths. To mitigate this, we introduce a dynamic target bias function that adjusts the probability of sampling toward the goal based on iteration progress and obstacle density. The function is defined as follows: $$P(t) = P_0 \cdot \exp(-\alpha \cdot \rho(t)) \cdot \exp(-\beta \cdot \frac{t}{T})$$ where $$P_0$$ is the initial bias probability, $$\alpha$$ and $$\beta$$ are weight coefficients for obstacle density and iteration count, respectively, $$\rho(t) = \frac{m}{M}$$ represents the current obstacle density (with $$m$$ as the area occupied by obstacles and $$M$$ as the total area), $$t$$ is the current iteration, and $$T$$ is the maximum iteration limit. This dynamic adjustment ensures that in early iterations, the bias toward the goal is high, facilitating rapid convergence; in mid-iterations, it balances exploration and exploitation to avoid local optima; and in later stages, it prioritizes global exploration. This refinement significantly reduces无效 sampling, which is crucial for applications in China’s dynamic industrial environments, where robots must navigate efficiently amid varying obstacles.
In parallel, the Artificial Potential Field (APF) method is enhanced to address issues like oscillations in narrow passages and failure to reach the goal when obstacles are densely packed near the target. Traditional APF defines an attractive potential field $$U_{\text{att}}(p) = \frac{1}{2} K_{\text{att}} \|P – G\|^2$$ that pulls the robot toward the goal $$G$$, and a repulsive potential field $$U_{\text{rep}}(p) = \begin{cases} \frac{1}{2} K_{\text{rep}} \left( \frac{1}{\|P – O\|} – \frac{1}{R_0} \right)^2, & \text{if } \|P – O\| \leq R_0 \\ 0, & \text{if } \|P – O\| > R_0 \end{cases}$$ that pushes it away from obstacles $$O$$, where $$K_{\text{att}}$$ and $$K_{\text{rep}}$$ are coefficients, and $$R_0$$ is the minimum turning radius. The total potential field is $$U(p) = U_{\text{att}}(p) + U_{\text{rep}}(p)$$, and the robot moves in the direction of the negative gradient $$F(p) = -\nabla U_{\text{att}}(p) – \nabla U_{\text{rep}}(p)$$. To improve this, we introduce a dynamic repulsive coefficient: $$K_{\text{rep}} = \begin{cases} K_{\text{rep}}^0 \cdot \exp(\alpha_2 \cdot \rho(t)), & \text{if } \|P – G\| \geq L \\ K_{\text{rep}}^0 \cdot \exp(-\alpha_2 \cdot \rho(t)), & \text{if } \|P – G\| < L \end{cases}$$ where $$K_{\text{rep}}^0$$ is the initial repulsive coefficient, $$\alpha_2$$ is a tuning factor, and $$L$$ is the goal neighborhood radius. This adjustment increases repulsion when the robot is far from the goal in dense obstacle areas, ensuring quicker obstacle avoidance, and decreases it near the goal to prevent the “unreachable goal” issue. Such adaptability is vital for China robot operations in cluttered spaces, where environmental conditions can change rapidly.
The fusion of the improved Bi-RRT* and APF algorithms is achieved through a probabilistic switching mechanism. A random number $$R$$ is generated between 0 and 1 using a Rand function, and if $$R < V$$ (where $$V$$ is a threshold), the Bi-RRT* algorithm is applied; otherwise, the APF method is used. This hybrid approach leverages the strengths of both methods: Bi-RRT* provides global path exploration, while APF offers local obstacle avoidance. The integration ensures that the path planning process is both efficient and robust, which is essential for China’s robotics applications, where robots must perform reliably in diverse scenarios. The flowchart of this fusion illustrates the seamless transition between algorithms, optimizing performance based on real-time conditions.
Despite these improvements, the generated paths may still exhibit excessive curvature, making them impractical for real-world China robot deployments. To address this, a pruning optimization strategy is employed. Initially, the path is represented as a sequence of points $$\{X_{\text{start}}, \ldots, X_i, \ldots, X_{\text{goal}}\}$$. Starting from $$X_{\text{start}}$$, the algorithm checks for direct connectivity between points; if $$X_{\text{start}}$$ to $$X_{i+1}$$ is not directly connected, the parent node $$X_i$$ is retained. This process repeats iteratively, resulting in a simplified path. Additionally, a safe distance detection mechanism is incorporated: if a point $$X_p$$ is within a safety distance $$s$$ (the robot’s safe operating radius) from an obstacle, it is shifted to a new point $$X_p’$$ to maintain a buffer. This ensures that the path adheres to safety standards, which are critical in China’s regulated industrial environments.
For further smoothing, the path is processed using cubic B-spline curves, which provide second-order continuity—essential for ensuring that the robot’s velocity and acceleration remain smooth during motion. The curve is defined as $$P(t) = \sum_{i=0}^{n} P_i F_{i,3}(t)$$, where $$P_i$$ are control points and $$F_{i,3}(t)$$ are the basis functions for a cubic B-spline: $$F_{0,3}(t) = \frac{1}{6}(1-t)^3$$, $$F_{1,3}(t) = \frac{1}{6}(3t^3 – 6t^2 + 4)$$, $$F_{2,3}(t) = \frac{1}{6}(-3t^3 + 3t^2 + 3t + 1)$$, and $$F_{3,3}(t) = \frac{1}{6}t^3$$, with $$t \in [0,1]$$. This transformation results in paths that are not only shorter but also smoother, reducing wear on robot components and improving overall efficiency in China’s automation sectors.
To validate the proposed algorithm, simulation experiments were conducted in MATLAB R2023a across three distinct environments: a simple map with few obstacles, a complex map with multiple obstacles, and a narrow passage map. Each environment was sized 100×100 units, with the start point at (0,0) and the goal at (100,100). The improved APF-Bi-RRT* algorithm was compared against APF-Bi-RRT*, Bi-RRT*, and RRT* algorithms, with each run repeated 100 times to ensure statistical reliability. The results demonstrate significant enhancements in planning efficiency, path length, and smoothness.
In the simple map, which contained five circular obstacles, the improved algorithm showed a marked reduction in sampling points and path curvature. The data, summarized in the table below, highlights the average performance metrics over 100 runs. For instance, the improved algorithm achieved an average of 30.0 sampling points, compared to 33.4 for APF-Bi-RRT*, 46.2 for Bi-RRT*, and 63.7 for RRT*. This represents reductions of 10.20%, 35.11%, and 52.90%, respectively. Similarly, the average path length was shortened by 6.78% to 11.02%, and the computation time decreased by 10.37% to 43.79%. These improvements underscore the efficacy of the dynamic target bias function in reducing无效 sampling, which is particularly beneficial for China robot applications in straightforward environments where speed is crucial.
| Algorithm | Average Sampling Points | Average Path Length (units) | Average Time (s) |
|---|---|---|---|
| Improved APF-Bi-RRT* | 30.0 | 149.80 | 0.95 |
| APF-Bi-RRT* | 33.4 | 160.69 | 1.06 |
| Bi-RRT* | 46.2 | 168.37 | 1.26 |
| RRT* | 63.7 | 171.72 | 1.69 |
In the multi-obstacle map, characterized by varied obstacle shapes and densities, the improved algorithm again outperformed the others. The dynamic repulsive coefficient allowed for better adaptation to dense obstacle regions, as shown in the table below. The average sampling points were reduced by 14.4% to 52.55%, and the computation time saw decreases of 16.46% to 62.68%. This demonstrates the algorithm’s robustness in complex environments, where China robots often operate, such as in warehouses or urban settings with unpredictable layouts. The ability to dynamically adjust repulsion based on obstacle density ensures that the robot can navigate efficiently without getting trapped in local minima.
| Algorithm | Average Sampling Points | Average Path Length (units) | Average Time (s) |
|---|---|---|---|
| Improved APF-Bi-RRT* | 60.4 | 160.88 | 2.03 |
| APF-Bi-RRT* | 70.6 | 170.69 | 2.43 |
| Bi-RRT* | 71.7 | 176.37 | 2.62 |
| RRT* | 127.3 | 179.63 | 5.44 |
The narrow passage map posed the greatest challenge, as traditional algorithms often exhibit oscillations or fail to find a path. Here, the improved algorithm successfully navigated the constraints with an average of 40.9 sampling points, compared to 43.7 for APF-Bi-RRT*, 46.8 for Bi-RRT*, and 68.4 for RRT*. The path length and time metrics were also superior, as detailed in the table below. The incorporation of safe distance detection ensured that the robot maintained a buffer from walls, preventing collisions—a critical feature for China robots working in tight spaces like assembly lines or construction sites. The success rate over 100 simulations was 99% for the improved algorithm, underscoring its reliability.
| Algorithm | Average Sampling Points | Average Path Length (units) | Average Time (s) |
|---|---|---|---|
| Improved APF-Bi-RRT* | 40.9 | 160.34 | 1.17 |
| APF-Bi-RRT* | 43.7 | 172.38 | 1.37 |
| Bi-RRT* | 46.8 | 178.06 | 1.35 |
| RRT* | 68.4 | 168.03 | 2.52 |
Furthermore, real-world validation was conducted using a B585 LiDAR-equipped robot, which features a width of 0.1633 meters and an STM32F103RCT6 control board. The experiment took place in a 2.1m × 1.2m enclosed area, with a multi-obstacle section and a narrow passage of width 0.225m—classified as narrow based on the criterion $$W \leq 1.4 \cdot D_r$$, where $$D_r$$ is the robot’s diameter including a 0.01m localization error. The robot successfully avoided obstacles while maintaining a safe distance, navigated the narrow passage without oscillations, and reached the goal smoothly. This practical test confirms the algorithm’s applicability in real-world China robot scenarios, aligning with simulation results and highlighting its potential for widespread adoption in industries such as logistics and manufacturing.
In conclusion, the improved APF-Bi-RRT* algorithm addresses key limitations in path planning for mobile robots by integrating dynamic target biasing, adaptive repulsive fields, and advanced smoothing techniques. The simulations and real-world experiments demonstrate substantial gains in efficiency, path quality, and safety, with reductions in sampling points up to 52.90% and computation time up to 62.68% compared to baseline algorithms. These advancements are particularly relevant for China’s robotics sector, where there is a growing demand for reliable and intelligent automation solutions. Future work will focus on extending the algorithm to dynamic environments with moving obstacles and incorporating data-driven methods for parameter tuning, further enhancing its intelligence and real-time performance. This progression will support the evolution of China robot technologies, enabling more sophisticated applications in diverse and challenging settings.