In the field of robot technology, path planning is a critical component that enables autonomous navigation and efficient task execution. As mobile robots become increasingly integrated into various applications, from industrial automation to service robotics, the demand for robust and optimized path planning algorithms has grown. Traditional methods often struggle with convergence issues, local optima, and computational inefficiency, especially in complex environments. To address these challenges, we propose an enhanced version of the dragonfly algorithm (DA), which incorporates chaotic mapping, sine-cosine strategies, and Lévy flight mechanisms. This improved approach aims to enhance convergence accuracy, path quality, and overall performance in robot technology applications. By integrating these elements, our method not only accelerates the search process but also ensures more reliable and shorter paths for mobile robots operating in dynamic settings.
The dragonfly algorithm is a metaheuristic optimization technique inspired by the swarming behaviors of dragonflies, including static and dynamic patterns that correspond to exploration and exploitation phases. In robot technology, such algorithms are vital for solving multi-objective optimization problems, such as finding the shortest path while avoiding obstacles. The basic DA involves five key behaviors: separation, alignment, cohesion, attraction to food sources, and avoidance of enemies. These behaviors are mathematically represented to guide the search process. For instance, the separation behavior prevents collisions between individuals and is defined as:
$$ S_i = -\sum_{j=1}^{N} (X – X_j) $$
where $S_i$ is the separation for the $i$-th individual, $X$ is the current position, and $X_j$ is the position of the $j$-th neighbor. Alignment ensures velocity matching among neighbors:
$$ A_i = \frac{\sum_{j=1}^{N} V_j}{N} $$
where $A_i$ is the alignment, and $V_j$ is the velocity of the $j$-th neighbor. Cohesion drives individuals toward the center of mass:
$$ C_i = \frac{\sum_{j=1}^{N} X_j}{N} – X $$
Attraction to food and avoidance of enemies are given by:
$$ F_i = X_{\text{food}} – X $$
$$ E_i = X_{\text{enemy}} – X $$
where $F_i$ and $E_i$ represent the attraction and avoidance forces, respectively. The step vector $\Delta X$ and position update are computed as:
$$ \Delta X_{t+1} = (s S_i + a A_i + c C_i + f F_i + e E_i) + w \Delta X_t $$
$$ X_{t+1} = X_t + \Delta X_{t+1} $$
Here, $s$, $a$, $c$, $f$, and $e$ are weights for each behavior, and $w$ is the inertia weight. When no neighbors are present, Lévy flight is used for random walk:
$$ X_{t+1} = X_t + \text{Lévy}(d) \cdot X_t $$
where $\text{Lévy}(d)$ is defined as:
$$ \text{Lévy}(\beta) = \frac{\mu \cdot \sigma}{|v|^{1/\beta}} $$
with $\mu$ and $v$ as random variables, and $\sigma$ calculated using the Gamma function. This foundation allows DA to be applied in robot technology for path planning, but it often faces limitations in convergence and path quality, which our improvements aim to overcome.
To enhance the dragonfly algorithm for robot technology, we introduce several key modifications. First, we employ chaotic mapping for population initialization to ensure a more uniform distribution of potential solutions in the search space. Specifically, we use the Fuch’s chaotic map, which replaces random initialization and reduces the risk of premature convergence to local optima. The chaotic sequence is generated as:
$$ x_{n+1} = \begin{cases}
\frac{x_n}{\alpha} & \text{if } 0 \leq x_n \leq \alpha \\
\frac{1 – x_n}{1 – \alpha} & \text{if } \alpha < x_n \leq 1
\end{cases} $$
where $\alpha$ is a parameter set to 0.7. This approach diversifies the initial population, improving global exploration capabilities. Second, we integrate the sine-cosine algorithm (SCA) and Lévy flight into the position update process. When neighbors are present, SCA is used to update positions, leveraging the periodicity of sine and cosine functions to balance exploration and exploitation. The position update in SCA is given by:
$$ X_{t+1}^i = \begin{cases}
X_t^i + r_1 \cdot \sin(r_2) \cdot |r_3 P_t – X_t^i| & \text{if } r_4 < 0.5 \\
X_t^i + r_1 \cdot \cos(r_2) \cdot |r_3 P_t – X_t^i| & \text{otherwise}
\end{cases} $$
where $r_1$, $r_2$, $r_3$, and $r_4$ are random parameters generated using chaotic mapping, and $P_t$ is the best solution. This enhances search efficiency and helps avoid local optima. For scenarios without neighbors, Lévy flight provides a random walk with heavy-tailed steps, facilitating broader exploration. These strategies collectively improve the algorithm’s performance in robot technology applications by increasing convergence speed and solution quality.
In robot technology, the environment representation is crucial for path planning. We utilize grid-based maps with 16-direction 24-neighborhood searches, expanding beyond the traditional 8-direction approach to cover a wider search area and reduce the number of search iterations. This is particularly beneficial in complex environments where obstacle density is high. Additionally, we implement a diagonal obstacle mechanism to prevent infeasible paths through diagonal barriers. For example, if a robot is adjacent to obstacles in both the right and upper directions, it cannot move to the upper-right cell, ensuring realistic navigation. The table below summarizes the comparison between traditional and our improved search methods in terms of path length and search iterations, demonstrating the advantages of our approach in robot technology.
| Search Method | Average Path Length | Average Search Iterations |
|---|---|---|
| 8-Direction | 20.5 | 15 |
| 16-Direction | 18.2 | 10 |
To evaluate the performance of our improved dragonfly algorithm in robot technology, we conducted experiments using benchmark functions and simulation environments. The benchmark functions include unimodal and multimodal types, such as Sphere, Rosenbrock, and Ackley functions, which test convergence and global search capabilities. The functions are defined as follows:
$$ f_1(x) = \sum_{i=1}^{n} x_i^2 $$
$$ f_2(x) = \sum_{i=1}^{n-1} [100(x_{i+1} – x_i^2)^2 + (1 – x_i)^2] $$
$$ f_3(x) = -20 \exp(-0.2 \sqrt{\frac{1}{n} \sum_{i=1}^{n} x_i^2}) – \exp(\frac{1}{n} \sum_{i=1}^{n} \cos(2\pi x_i)) + 20 + e $$
We compared our algorithm with the standard DA, an adaptive genetic algorithm, and a sparrow search algorithm with tabu search. The population size was set to 50, and maximum iterations to 1000. The results, averaged over 50 independent runs, are presented in the table below, highlighting the superior performance of our method in terms of minimum values, average values, and computation time.
| Function | Metric | Standard DA | Adaptive GA | Sparrow Search | Our Algorithm |
|---|---|---|---|---|---|
| $f_1$ | Min Value | 1.25e-3 | 2.15e-2 | 1.08e-3 | 0.0 |
| Avg Value | 1.95e-2 | 1.11e-2 | 8.88e-3 | 5.55e-3 | |
| Time (s) | 0.22 | 0.17 | 0.15 | 0.10 | |
| $f_2$ | Min Value | 1.12e-1 | 1.45e-1 | 3.78e-1 | 1.02e-1 |
| Avg Value | 2.11e-1 | 1.87e-1 | 1.27e-1 | 1.42e-1 | |
| Time (s) | 0.18 | 0.16 | 0.15 | 0.11 | |
| $f_3$ | Min Value | 1.42e-1 | 2.24e-1 | 7.82e-1 | 0.0 |
| Avg Value | 1.67e-1 | 4.51e-1 | 2.84e-1 | 1.53e-1 | |
| Time (s) | 0.19 | 0.22 | 0.11 | 0.14 |
For path planning in robot technology, we simulated both simple and complex environments using grid maps. In simple environments with sparse obstacles, our algorithm demonstrated faster convergence and shorter paths compared to other methods. The average path length was reduced by approximately 5.3%, and the convergence time decreased by 25.8% relative to the standard DA. In complex environments with high obstacle density, the improvements were even more pronounced, with a 30.5% reduction in planning time and a 7.2% shorter average path length. The convergence curves for these experiments show that our algorithm reaches the optimal solution more quickly, thanks to the chaotic initialization and sine-cosine strategies. This makes it highly suitable for real-time applications in robot technology, where efficiency and reliability are paramount.
Furthermore, we validated our algorithm in a real-world robot technology scenario using a mobile robot equipped with LiDAR, encoders, and ultrasonic sensors. The robot was tasked with navigating from a start to a goal point in an indoor environment. The results confirmed that our improved DA outperformed other algorithms in terms of path smoothness and stability, with an average path length of 12.47 meters and a convergence time of 1.50 seconds, compared to 15.21 meters and 3.21 seconds for the standard DA. This practical validation underscores the applicability of our method in advancing robot technology, particularly in autonomous navigation systems.
In conclusion, our enhanced dragonfly algorithm addresses key limitations in path planning for robot technology by incorporating chaotic mapping, sine-cosine strategies, and Lévy flight. These improvements lead to higher convergence accuracy, better path quality, and reduced computational time, as evidenced by benchmark tests and real-world experiments. The use of 16-direction searches and diagonal obstacle mechanisms further enhances the practicality of the algorithm in diverse environments. As robot technology continues to evolve, such optimized algorithms will play a crucial role in enabling efficient and intelligent mobile robot operations. Future work could focus on adapting this approach to multi-robot systems or dynamic environments, further expanding its impact on robot technology.