In the rapidly evolving field of robot technology, autonomous navigation in complex environments remains a critical challenge. Path planning, a fundamental aspect of robot technology, ensures that mobile robots can efficiently and safely traverse from a start point to a goal while avoiding obstacles. Traditional global path planning algorithms, such as the ant colony optimization (ACO), often suffer from slow convergence and poor path quality, while local methods like the artificial potential field (APF) are prone to local minima and target inaccessibility issues. To address these limitations in robot technology, we propose a novel fusion algorithm that integrates an improved ant colony algorithm (IACO) with an enhanced artificial potential field method (IAPF). This approach leverages the global optimality of IACO and the dynamic obstacle avoidance capabilities of IAPF, resulting in efficient, smooth, and collision-free paths for mobile robots in both static and dynamic environments. Through extensive simulations and real-world experiments, we demonstrate the superiority of our method in terms of path length, smoothness, and computational efficiency, highlighting its potential for advancing robot technology in practical applications.
The integration of robot technology into various domains, such as logistics, manufacturing, and exploration, demands robust path planning solutions. Global path planning algorithms provide a high-level route, whereas local planners handle real-time adjustments. However,单一 algorithms often fall short in complex scenarios. For instance, ACO, inspired by ant foraging behavior, exhibits strong robustness but tends to converge slowly and produce suboptimal paths. On the other hand, APF, known for its computational efficiency, struggles with local optima and unreachable targets when obstacles surround the goal. Our work focuses on overcoming these drawbacks by innovatively combining IACO and IAPF, thereby pushing the boundaries of robot technology. We optimize ACO’s search strategy, pheromone update rules, and heuristic information, while modifying APF’s repulsive potential field and introducing sub-goals to enhance performance. The fusion algorithm not only maintains global path optimality but also ensures adaptive local navigation, making it a significant contribution to robot technology.
Environment modeling is a crucial step in robot technology for simplifying complex spaces. We employ a grid-based map, where each cell represents either free space or an obstacle. For a 20 m × 20 m area, the grid is sequentially numbered, and Cartesian coordinates are derived using mathematical transformations. Let $n$ denote the grid index, and $(x_n, y_n)$ represent its coordinates. The relationship is defined as:
$$ x_n =
\begin{cases}
a(\text{mod}(n, G_x) – 0.5), & \text{if } \text{mod}(n, G_x) \neq 0 \\
a(G_x + \text{mod}(n, G_x) – 0.5), & \text{otherwise}
\end{cases} $$
$$ y_n = a(G_y – \lceil n / G_y \rceil + 0.5) $$
where $G_x$ and $G_y$ are the grid dimensions, $a$ is the cell length, $\text{mod}()$ is the modulo operation, and $\lceil \cdot \rceil$ denotes the ceiling function. This modeling approach efficiently reduces environmental complexity, facilitating path planning in robot technology.
In traditional ACO, ants move based on state transition probabilities and pheromone trails. The probability $P_{ij}^k(t)$ of ant $k$ moving from node $i$ to $j$ at time $t$ is given by:
$$ P_{ij}^k(t) = \frac{[\tau_{ij}(t)]^\alpha \cdot [\eta_{ij}(t)]^\beta}{\sum_{j \in A_k} [\tau_{ij}(t)]^\alpha \cdot [\eta_{ij}(t)]^\beta} \quad \text{for } j \in A_k $$
where $\tau_{ij}(t)$ is the pheromone concentration, $\eta_{ij}(t)$ is the heuristic information, $\alpha$ and $\beta$ are parameters, and $A_k$ is the set of feasible neighbors. The heuristic is typically inversely proportional to the distance $d_{ij}$ between nodes $i$ and $j$: $\eta_{ij}(t) = 1 / d_{ij}$. Pheromone update involves evaporation and reinforcement:
$$ \tau_{ij}(t+1) = (1 – \rho) \tau_{ij}(t) + \Delta \tau_{ij}(t) $$
$$ \Delta \tau_{ij}(t) = \sum_{k=1}^{M} \Delta \tau_{ij}^k(t) $$
with $\Delta \tau_{ij}^k(t) = Q / L_k(t)$ if ant $k$ traverses the path, where $\rho$ is the evaporation rate, $M$ is the number of ants, $Q$ is a constant, and $L_k(t)$ is the path length. However, this approach often leads to inefficiencies in robot technology applications.
To enhance ACO for robot technology, we introduce several improvements. First, the search strategy is expanded to include additional neighborhoods, increasing the step sizes to $\{1, \sqrt{2}, 2, \sqrt{5}, 2\sqrt{2}\}$. A local coordinate system is established based on the start point, and the search direction is determined by the relative position of the goal, as defined by:
$$ R_s = \begin{cases}
\text{First quadrant}, & \text{if } (E_x > S_x \text{ and } E_y > S_y) \text{ or } (E_x > S_x \text{ and } E_y = S_y) \\
\text{Second quadrant}, & \text{if } (E_x < S_x \text{ and } E_y > S_y) \text{ or } (E_x = S_x \text{ and } E_y > S_y) \\
\text{Third quadrant}, & \text{if } (E_x < S_x \text{ and } E_y < S_y) \text{ or } (E_x < S_x \text{ and } E_y = S_y) \\
\text{Fourth quadrant}, & \text{if } (E_x > S_x \text{ and } E_y < S_y) \text{ or } (E_x = S_x \text{ and } E_y < S_y)
\end{cases} $$
where $(S_x, S_y)$ and $(E_x, E_y)$ are the start and goal coordinates. This modification broadens the search scope, reducing deadlocks and improving path diversity in robot technology.
Second, we revise the pheromone initialization and update rules. Instead of a constant initial value, we use a distance-based distribution: $\tau_{ij}(0) = c$ and $\tau_{ij_{\text{initial}}} = 1 / d(i,j) + \tau_{ij}(0)$, where $c$ is a constant and $d(i,j)$ is the Euclidean distance. For pheromone increment, a reward-penalty mechanism is incorporated based on path quality:
$$ \Delta \tau_{ij}^k(t) = \begin{cases}
\frac{Q}{L_k} \cdot \frac{L_w + L_b}{3L_m} \cdot L_c, & \text{if } L_k = L_b \\
\frac{Q}{L_k}, & \text{if } L_b < L_k < L_m \\
\frac{Q}{0.5 L_k L_c}, & \text{if } L_m \leq L_k < L_w \\
\frac{Q}{L_k L_c}, & \text{if } L_k = L_w
\end{cases} $$
where $L_b$, $L_w$, and $L_m$ are the best, worst, and average path lengths in the current iteration, and $L_c$ is the number of non-deadlock ants. This approach emphasizes high-quality paths and accelerates convergence, crucial for efficient robot technology.
Third, the heuristic information is modified to consider the distance from neighbors to the goal, with an adaptive factor $\sigma$: $\eta_{ij}(t) = 1 / (d_{jE}^\sigma)$, where $d_{jE}$ is the distance from node $j$ to the goal, and $\sigma = \exp(-3 K_c / K)$. Here, $K_c$ is the current iteration, and $K$ is the maximum iterations. This adjustment reduces the risk of local optima and enhances global search capability in robot technology.
Finally, a path node optimization strategy is implemented to eliminate redundant nodes. For a path with nodes $N_i$ ($i=1,2,\ldots,n$), the angle $\theta$ between consecutive nodes is computed:
$$ \theta = \cos^{-1} \left( \frac{\overrightarrow{AB} \cdot \overrightarrow{BC}}{|\overrightarrow{AB}| |\overrightarrow{BC}|} \right) \cdot \frac{180}{\pi} $$
If $\theta = 180^\circ$, the intermediate node is removed; otherwise, obstacle detection is performed along the segment. This results in smoother and shorter paths, aligning with the demands of advanced robot technology.
For local path planning, traditional APF defines attractive and repulsive potentials. The attractive potential $U_{\text{att}}(P) = \frac{1}{2} \eta d^2(P, P_g)$ yields a force $F_{\text{att}}(P) = \eta d(P, P_g)$, where $P$ is the robot position, $P_g$ is the goal, and $\eta$ is a gain. The repulsive potential $U_{\text{rep}}(P)$ is:
$$ U_{\text{rep}}(P) = \begin{cases}
\frac{1}{2} \omega \left( \frac{1}{d(P, P_{\text{obs}})} – \frac{1}{d_0} \right)^2, & \text{if } d(P, P_{\text{obs}}) \leq d_0 \\
0, & \text{otherwise}
\end{cases} $$
with a corresponding force $F_{\text{rep}}(P)$. The total force $F(P) = F_{\text{att}}(P) + F_{\text{rep}}(P)$ guides the robot. However, this method often fails in robot technology due to local minima and unreachable goals.
Our IAPF addresses these issues by incorporating the relative distance to the goal into the repulsive potential. The modified repulsive potential $U_{\text{rep}}'(P)$ is:
$$ U_{\text{rep}}'(P) = \begin{cases}
\frac{1}{2} \omega \left( \frac{1}{d(P, P_{\text{obs}})} – \frac{1}{d_0} \right)^2 d^m(P, P_{\text{stp}}), & \text{if } d(P, P_{\text{obs}}) \leq d_0 \\
0, & \text{otherwise}
\end{cases} $$
where $d(P, P_{\text{stp}})$ is the distance to a sub-goal, and $m$ is a parameter. The repulsive force $F_{\text{rep1}}(P)$ is derived as the negative gradient, and an additional attractive force $F_{\text{rep2}}(P)$ towards the sub-goal is introduced:
$$ F_{\text{rep2}}(P) = \frac{m}{2} \omega \left( \frac{1}{d(P, P_{\text{obs}})} – \frac{1}{d_0} \right)^2 d^{m-1}(P, P_{\text{stp}}) $$
The total repulsive force $F_{\text{rep}}'(P) = F_{\text{rep1}}(P) + F_{\text{rep2}}(P)$. This ensures that the attraction dominates near the goal, resolving target inaccessibility. Moreover, sub-goals from the IACO global path help escape local minima, significantly improving the reliability of robot technology in dynamic environments.
The fusion algorithm, IACO-IAPF, combines the strengths of both methods. Initially, IACO generates a global optimal path, whose nodes serve as sub-goals for IAPF. During execution, IAPF performs real-time obstacle avoidance while following the global path. This hybrid approach ensures that the robot adheres to the optimal route while adapting to unforeseen obstacles, a key advancement in robot technology.
To validate our methods, we conducted simulations in various environments. For IACO, we compared it with traditional ACO, A*, Dijkstra, and an existing improved ACO (IACO-TAC) in 20 m × 20 m and 30 m × 30 m grid maps with obstacle densities of 25% and 30%, respectively. Parameters were set as: maximum iterations $K=100$, ants $M=50$, $Q=1$, $\alpha=0.9$, $\beta=9$, $\rho=0.3$. Each algorithm was run 30 times independently. The results are summarized in the following tables:
| Map | Algorithm | Min Path Length (m) | Avg Path Length (m) | Std Dev | Avg Turning Points | Avg Iterations |
|---|---|---|---|---|---|---|
| Map1 (20×20) | ACO | 37.41 | 37.82 | 1.14 | 14.10 | 33.16 |
| IACO-TAC | 29.21 | 29.21 | 0.00 | 8.00 | 15.50 | |
| A* | 29.21 | 29.21 | 0.00 | 8.00 | — | |
| Dijkstra | 29.21 | 29.21 | 0.00 | 10.00 | — | |
| IACO | 28.50 | 28.52 | 0.08 | 6.23 | 10.56 | |
| Map2 (30×30) | ACO | 60.00 | 70.30 | 11.31 | 30.66 | 47.90 |
| IACO-TAC | 46.52 | 48.20 | 1.65 | 20.90 | 30.55 | |
| A* | 45.70 | 45.70 | 0.00 | 20.00 | — | |
| Dijkstra | 45.70 | 45.70 | 0.00 | 21.00 | — | |
| IACO | 44.26 | 44.96 | 0.43 | 15.20 | 23.70 |
IACO achieved a 26.23% reduction in optimal path length, 60.00% fewer turning points, and 73.75% higher search efficiency compared to traditional ACO, demonstrating its superior performance in robot technology. The path smoothness and convergence speed were notably improved, as visualized in the simulations.
For IAPF, we optimized parameters through simulation analysis. The obstacle influence range $d_0$ was set to 1.2 m, and the step size $L$ to 0.1 m. Using a 20 m × 20 m map, we tested gravitational gain $\eta$ and repulsive gain $\omega$. The best parameters were $\eta=5$ and $\omega=15$, balancing path quality and safety. Comparisons with DWA and APF in a U-shaped obstacle environment showed that IAPF successfully reached the goal while others failed due to local minima. The results are summarized below:
| Algorithm | Path Length (m) | Time (s) |
|---|---|---|
| DWA | Failed | Failed |
| APF | Failed | Failed |
| IAPF | 26.69 | 58.69 |
This confirms IAPF’s effectiveness in addressing traditional limitations, enhancing its applicability in robot technology.
The fusion algorithm IACO-IAPF was evaluated in dynamic and static environments. In static scenarios with randomly added obstacles, IACO-IAPF was compared to A*-DWA. The results for 0, 1, and 3 static obstacles are shown below:
| Obstacles | Algorithm | Optimal Path Length (m) | Time (s) |
|---|---|---|---|
| 0 | A*-DWA | 30.17 | 83.34 |
| IACO-IAPF | 28.89 | 61.78 | |
| 1 | A*-DWA | 30.49 | 85.60 |
| IACO-IAPF | 29.10 | 64.69 | |
| 3 | A*-DWA | 31.21 | 90.32 |
| IACO-IAPF | 29.71 | 68.19 |
IACO-IAPF reduced path length by up to 4.81% and time by 24.50%, showcasing its efficiency in robot technology. In dynamic environments with multiple moving obstacles, IACO-IAPF outperformed APF and ACO-APF, successfully navigating complex scenarios where others failed. For instance, in a 20 m × 20 m map with static and dynamic obstacles, IACO-IAPF achieved a path length of 32.46 m in 83.24 s, demonstrating robust obstacle avoidance capabilities essential for real-world robot technology.
Experimental validation involved a real mobile robot equipped with LiDAR, IMU, and cameras. In an indoor setting, IACO planned a path of 2.89 m, shorter than ACO (3.43 m) and A* (3.10 m), confirming its practical utility in robot technology. Additionally, in Gazebo simulations, IACO-IAPF effectively avoided static obstacles while following the global path, verifying the algorithm’s feasibility and performance in robot technology applications.
In conclusion, our fusion of IACO and IAPF represents a significant advancement in robot technology for path planning. The improvements in ACO enhance global path quality and search efficiency, while the modifications to APF resolve local minima and target inaccessibility. The integrated approach ensures smooth, collision-free navigation in complex environments, as validated through simulations and experiments. Future work will focus on optimizing computational overhead and extending the method to multi-robot systems, further contributing to the evolution of robot technology.