In the era of rapid automation and artificial intelligence, robot technology has become a strategic driver of technological revolution and industrial transformation. Path planning is a critical component in robotics, focusing on generating collision-free paths from a start to a goal position. Traditional algorithms, such as simulated annealing and artificial potential fields, often struggle in complex environments. In contrast, bio-inspired algorithms like the ant colony algorithm exhibit higher feasibility due to their positive feedback, parallelism, and robustness. However, the ant colony algorithm faces challenges like prolonged search times and susceptibility to local optima. To address these issues, we propose an improved ant colony hybrid algorithm that integrates elements from particle swarm optimization and artificial potential field methods. This approach enhances path smoothness, reduces redundancy, and improves convergence speed, making it more suitable for real-world applications in robot technology.
We begin by modeling the robot’s environment using a grid-based approach, where the workspace is divided into $G \times G$ grid cells. Each grid cell is assigned a unique index $S$, and its coordinates $(X, Y)$ are calculated as follows: $$ X = \mod\left(\frac{S-1}{G}\right) + 0.5 $$ $$ Y = G + 0.5 – \text{ceil}\left(\frac{S}{G}\right) $$ White grids represent free space, while black grids denote obstacles. This modeling method simplifies the environment for efficient path planning in robot technology applications.
The core of the ant colony algorithm mimics ant foraging behavior, where ants deposit pheromones to guide others. The transition probability from node $i$ to $j$ for ant $k$ is given by: $$ P_{ij}^k = \begin{cases} \frac{\tau_{ij}^\alpha(t) \eta_{ij}^\beta(t) \mathbf{F}(t)}{\sum_{s \in A} \tau_{is}^\alpha(t) \eta_{is}^\beta(t) \mathbf{F}_{iS}(t)}, & j \in A \\ 0, & \text{otherwise} \end{cases} $$ where $\tau_{ij}(t)$ is the pheromone concentration, $\eta_{ij}(t)$ is the heuristic function, $\alpha$ and $\beta$ are tuning parameters, and $A$ is the set of feasible next nodes. The pheromone update rule is: $$ \tau_{ij}(t+1) = (1 – \rho) \tau_{ij}(t) + \Delta \tau_{ij} $$ with $\Delta \tau_{ij} = \sum_{k=1}^{M} \Delta \tau_{ij}^k$ and $\Delta \tau_{ij}^k = \frac{Q}{L_k}$ if ant $k$ traverses path $(i,j)$, where $L_k$ is the path length and $Q$ is a constant.
To improve the algorithm, we first introduce an initial pheromone distribution strategy that reduces early search blindness. Instead of uniform distribution, we use a weakly heuristic function: $$ \text{TAU} = T \left( \left| \sin\left(\frac{2\pi x}{G}\right) \right| + \left| \sin\left(\frac{2\pi y}{G}\right) \right| \right) $$ This function increases pheromone concentration near the line connecting start and goal points, encouraging exploration in promising regions without over-concentration, thus enhancing efficiency in robot technology implementations.
Next, we enhance the transition probability by incorporating an angle factor and a potential field heuristic function. The improved distance heuristic function is: $$ \eta_{ij} = \frac{a \cos \theta_1}{d_{ij} + d_{jN}} $$ where $a$ is a constant, $\theta_1$ is the angle between current and next nodes to promote smooth paths, and $d_{jN}$ is the Euclidean distance to the goal. The potential field function, derived from artificial potential field algorithms, introduces attractive and repulsive forces: $$ U_{\text{att}}(x) = \frac{1}{2} k_t D^2(x, x_d) $$ $$ \mathbf{F}_{\text{att}}(\mathbf{x}) = -k_a D(x, x_d) $$ $$ U_{\text{rep}}(x) = \begin{cases} \frac{1}{2} k_r \left( \frac{1}{D(x, x_0)} – \frac{1}{D_{x_0}} \right)^2, & D(x, x_0) \leq D_{x_0} \\ 0, & \text{otherwise} \end{cases} $$ $$ \mathbf{F}_{\text{rep}}(\mathbf{x}) = \begin{cases} k_r \left( \frac{1}{D(x, x_0)} – \frac{1}{D_{x_0}} \right) \frac{1}{(D(x, x_0))^2}, & D(x, x_0) \leq D_{x_0} \\ 0, & \text{otherwise} \end{cases} $$ The total force is $\mathbf{F}(\mathbf{x}) = \mathbf{F}_{\text{att}}(\mathbf{x}) + \mathbf{F}_{\text{rep}}(\mathbf{x})$, and we incorporate it into the heuristic with a decay factor $\chi = 1 – \frac{k}{k_{\text{max}}}$: $$ \mathbf{F} = b \chi \mathbf{F}(\mathbf{x}) \cos \theta_2 $$ where $b$ is a constant and $\theta_2$ is the angle between the force and the next node. This helps robots avoid local optima in dense obstacle scenarios, a common issue in robot technology.
For pheromone updating, we integrate concepts from particle swarm optimization to enhance convergence. The new update rule includes a local information exchange term $\gamma$: $$ \Delta \tau_{ij}^k = \omega \left( \frac{Q}{L_k} \right) + c_1 r_1 \left( \frac{L_b}{L_k} \right) + c_2 r_2 (L_{\text{above}} – L_k) + \gamma $$ where $\gamma = \exp\left( \frac{\text{tran}}{L_k} \right) – 1$, $L_b$ is the shortest path length in the iteration, $L_{\text{above}}$ is the average path length, and $\text{tran}$ is the number of turns. The inertia weight $\omega$ is dynamically adjusted: $$ \omega = \omega_{\text{star}} – (\omega_{\text{star}} – \omega_{\text{end}}) \left( \frac{k}{k_{\text{max}}} \right)^2 $$ This ensures that path length dominates early updates, while smoothness (via $\gamma$) becomes influential later, optimizing paths for robot technology applications.
Finally, we perform secondary path optimization to remove redundant turns. Starting from the first node, we check triplets of nodes: if the line between the first and third nodes does not intersect obstacles, the middle node is deleted. This process iterates until no further optimizations are possible, resulting in smoother paths.
We evaluated our algorithm through simulations in MATLAB 2022b, using $20 \times 20$ and $30 \times 30$ grid environments. Performance was assessed based on path length, number of turns, and convergence iterations. In the $20 \times 20$ environment, our algorithm achieved a shortest path of 29.2 cm, with 7 turns and convergence in 17 iterations, outperforming other methods. For the $30 \times 30$ environment, it produced a path of 47.4 cm with 7 turns and 12 iterations, demonstrating robustness in complex scenarios. The results confirm that our hybrid algorithm excels in reducing path redundancy and improving smoothness, key for advancing robot technology.
| Algorithm | Shortest Path (cm) | Number of Turns | Best Iteration |
|---|---|---|---|
| Reference [6] | 30.1 | 10 | 25 |
| Reference [14] | 29.8 | 7 | 24 |
| Our Algorithm | 29.2 | 7 | 17 |
| Algorithm | Shortest Path (cm) | Number of Turns | Best Iteration |
|---|---|---|---|
| Reference [15] | 48.3 | 10 | 19 |
| Reference [16] | 52.0 | 13 | 21 |
| Our Algorithm | 47.4 | 7 | 12 |
In conclusion, our improved ant colony hybrid algorithm addresses key limitations of traditional methods by integrating innovative pheromone distribution, heuristic enhancements, and dynamic updates. It demonstrates superior performance in various environments, reducing path length and turns while accelerating convergence. This makes it highly suitable for real-world robot technology applications, such as autonomous navigation and logistics. Future work could extend this approach to multi-robot systems and 3D path planning, further advancing the capabilities of robot technology.