As a researcher in the field of underwater robotics, I have long been fascinated by the potential of bionic robots to revolutionize ocean exploration and resource development. The inherent challenges of underwater environments—complex obstacles, limited energy, and dynamic conditions—demand solutions that draw inspiration from nature itself. Bionic robots, with their ability to mimic the morphology and behaviors of aquatic organisms, offer a promising path forward. However, single bionic robots often face constraints in task execution due to energy limitations and restricted sensing capabilities. This has led me to investigate multi-bionic robot systems, where collaborative strategies can enhance efficiency and robustness. In this article, I present a comprehensive approach to the cooperative formation capture of targets using multiple bionic robots, addressing both formation strategy and path planning in unknown underwater settings. My work builds on existing research but introduces novel elements to overcome common pitfalls, such as inefficient task allocation and suboptimal path planning. Through detailed modeling, algorithm development, and simulation, I aim to demonstrate a strategy that enables bionic robots to perform effectively in challenging underwater scenarios.
The core problem I address is the collaborative formation capture task, where a group of bionic robots must locate and encircle a moving target in an environment with obstacles. This task is critical for applications like underwater surveillance, resource monitoring, or rescue operations. Previous studies have explored various formation and path-planning methods, but many rely on greedy allocation principles or computationally intensive algorithms that may not suit small-scale bionic robots with limited processing power. For instance, angle-based or distance-based allocation strategies can lead to deadlocks or asynchronous arrival times, reducing overall mission efficiency. Similarly, path-planning algorithms like neural networks or sampling-based methods may incur high computational costs or fail to guarantee optimal paths. My contribution lies in integrating a secure domain negotiation strategy for capture point allocation with an improved ant colony algorithm for adaptive path planning. This combination ensures that bionic robots coordinate their movements efficiently, minimize time disparities, and navigate around obstacles intelligently. In the following sections, I will describe the problem formulation, detail my proposed methods, and present simulation results that validate the approach’s effectiveness. Along the way, I will emphasize the role of bionic robots as agile, bio-inspired agents capable of thriving in underwater realms.
To frame the problem, I consider a bounded underwater environment $X$ populated with obstacles. Within $X$, there are $n$ search robots, denoted as $R = \{R_1, R_2, …, R_n\}$, tasked with capturing a mobile target $u$ whose initial position is unknown. The capture is deemed successful when the bionic robots either distribute themselves uniformly around the target’s detection zone or confine the target to the environment’s boundary. This setup mirrors real-world scenarios where bionic robots must cooperate to isolate a dynamic entity, such as a pollutant source or a lost asset. The motion of each bionic robot and the target is governed by kinematic equations. At time $t$, the position $(x(t), y(t))$ of a robot or target is expressed as:
$$ \begin{align*}
\dot{x}(t) &= v(t) \cos \theta(t), \\
\dot{y}(t) &= v(t) \sin \theta(t), \\
\dot{\theta}(t) &= \omega(t),
\end{align*} $$
where $v(t)$ is the velocity, $\theta(t)$ is the heading angle, and $\omega(t)$ is the angular velocity. For simplicity, I assume a constant nominal speed $v$ for normal travel, but the target can switch to an escape speed of $1.1v$ upon detecting a bionic robot within its perception range. This escape behavior adds complexity, as premature exposure of a bionic robot could trigger evasive maneuvers, hindering capture. To mitigate this, I introduce the concept of a secure domain (SD) around the target. The SD is a circular region centered at the target’s position $(x_m, y_m)$ with radius $d$, representing the detection range:
$$ SD = \{(x, y) \mid (x – x_m)^2 + (y – y_m)^2 < d^2 \}. $$
Bionic robots are prohibited from entering the SD individually until all assigned capture points are occupied, preventing the target from fleeing prematurely. This secure domain is pivotal for coordinating the bionic robots’ approach and ensuring a synchronized encirclement.
Once a bionic robot detects the target, it generates a set of desired capture points on the boundary of the secure domain. These points serve as positions where bionic robots should station themselves to form a cohesive enclosure. The first capture point $m_1$ is placed at the intersection of the secure domain boundary and the line opposite the target’s velocity direction. This placement minimizes the risk of the target escaping along its current path. Subsequent points $m_i$ for $i = 2, 3, …, n$ are evenly spaced clockwise around the circle. Mathematically, the coordinates of capture point $m_i$ are given by:
$$ \begin{align*}
x_{m_i} &= x_u + d \cos(\theta_u + \alpha_i – \pi), \\
y_{m_i} &= y_u + d \sin(\theta_u + \alpha_i – \pi), \\
\alpha_i &= 2\pi \cdot (i – 1) / n,
\end{align*} $$
where $(x_u, y_u)$ is the target’s position, $\theta_u$ is its velocity direction, and $\alpha_i$ is the angular offset from $m_1$. This configuration ensures that the bionic robots surround the target uniformly, maximizing coverage. However, assigning these points to the bionic robots efficiently is nontrivial. Common strategies, such as minimizing the angle between the robot-target line and the target-capture point line, or minimizing the Euclidean distance, can lead to issues like deadlock or uneven arrival times. For example, if two bionic robots have identical angles, angle-based allocation may stall, while distance-based allocation might cause some bionic robots to reach their points much later than others, reducing coordination. To address this, I propose a secure domain negotiation strategy that balances total path length and synchronization. The goal is to assign capture points such that the time difference among bionic robots’ arrivals is minimized while keeping the overall travel distance short. This is achieved by evaluating all possible permutations of assignments and selecting the one that optimizes a cost function incorporating both distance and time estimates. The algorithm proceeds as follows: upon target detection, each bionic robot computes the expected time to reach each capture point based on its current position and obstacle avoidance needs. These times are shared among the group, and an assignment matrix is constructed. The optimal assignment minimizes the maximum arrival time difference and the sum of distances. This negotiation process ensures that bionic robots act as a cohesive unit, enhancing the likelihood of successful capture.
Path planning for bionic robots in obstacle-rich environments requires an algorithm that is both efficient and adaptable. Traditional ant colony optimization (ACO) has been used for path planning due to its ability to find near-optimal paths through pheromone-based learning. However, standard ACO can converge slowly or get trapped in local optima, which is unsuitable for dynamic underwater tasks. I enhance ACO by dynamically adjusting heuristic information and incorporating obstacle-aware mechanisms. In my improved ant colony algorithm, each bionic robot plans its path from its current location to its assigned capture point while avoiding obstacles. The environment is discretized into a grid for simplicity, but the algorithm operates in continuous space by considering directional steps. At each step, an ant (representing a path candidate) selects the next position $j$ from the current position $i$ based on a probability $P_{ij}$:
$$ P_{ij} = \frac{[\tau_{ij}]^\alpha \cdot [H_{ij}]^\beta}{\sum_{k \in N_i} [\tau_{ik}]^\alpha \cdot [H_{ik}]^\beta}, $$
where $\tau_{ij}$ is the pheromone concentration on the edge from $i$ to $j$, $H_{ij}$ is the heuristic information, $\alpha$ and $\beta$ are weighting parameters, and $N_i$ is the set of neighboring positions (typically eight directions). The heuristic information $H_{ij}$ is defined as the inverse of the distance $D_{ij}$ between $i$ and $j$, encouraging shorter paths:
$$ H_{ij} = \frac{1}{D_{ij}}. $$
To adapt to obstacles, I modify the heuristic to penalize directions that lead near obstacles, effectively guiding bionic robots away from collisions. Pheromone updates are performed after each ant completes a path, with evaporation to avoid stagnation:
$$ \tau_{ij} \leftarrow (1 – \rho) \cdot \tau_{ij} + \sum_{k=1}^{m} \Delta \tau_{ij}^k, $$
where $\rho$ is the evaporation rate, $m$ is the number of ants, and $\Delta \tau_{ij}^k$ is the pheromone deposited by ant $k$ if it used edge $(i,j)$. This deposit is proportional to the path’s quality—shorter paths receive more pheromone. Additionally, I introduce a dynamic adjustment of $\beta$ based on obstacle density: in cluttered areas, $\beta$ is increased to give more weight to heuristic information, facilitating quicker obstacle avoidance. This adaptive mechanism allows bionic robots to navigate complex environments efficiently. The path-planning algorithm runs in real-time, enabling bionic robots to replan if obstacles are detected or if the target moves. By integrating this improved ant colony algorithm with the secure domain negotiation strategy, bionic robots can collaboratively approach their capture points along optimized, collision-free paths.
To validate my approach, I conducted simulation experiments in both obstacle-free and obstacle-rich environments. The scenarios involved four bionic robots ($n=4$) and one target. The bionic robots were modeled as circular agents with a radius of 10 meters, moving at a speed of 10 m/s, while the target had an escape speed of 11 m/s. The detection range $d$ for the secure domain was set to 20 meters. In the obstacle-free case, the environment spanned 400 m × 400 m, with bionic robots initially positioned at (150,150), (250,150), (150,350), and (250,350), and the target at (100,50). For obstacle-rich environments, I used an 800 m × 800 m area with randomly placed circular obstacles of varying sizes. The simulation update rate was 25 Hz. Parameters for the improved ant colony algorithm were set as follows: $\alpha = 1.0$, $\beta = 12.0$, $\rho = 0.1$, and pheromone increment $Q = 10.0$. These values were tuned through preliminary trials to balance exploration and exploitation. The bionic robots performed random search until one detected the target, triggering the secure domain negotiation and path planning. I compared my method with a baseline using an improved artificial potential field (APF) algorithm for path planning, keeping the same secure domain strategy for fairness.
The results demonstrated the efficacy of my approach. In obstacle-free environments, both algorithms achieved capture, but my method yielded shorter paths and faster convergence. For instance, the average formation time for my improved ant colony algorithm was 2.068 seconds, compared to 2.847 seconds for APF. This efficiency stems from the ant colony’s ability to find near-optimal paths without oscillatory behaviors common in potential fields. In obstacle-rich environments, the advantages became more pronounced. My algorithm successfully guided bionic robots around obstacles, as shown in trajectory plots, whereas APF sometimes led to local minima or longer detours. To quantify performance, I measured the average capture time and success rate over 40 simulation runs. A capture was considered failed if it exceeded 25 seconds. The results are summarized in Tables 1 and 2.
| Planning Algorithm | Environment | Average Time (s) |
|---|---|---|
| Improved Ant Colony | Obstacle-Free | 2.068 |
| Improved APF | Obstacle-Free | 2.847 |
| Improved Ant Colony | Obstacle-Rich | 4.510 |
| Improved APF | Obstacle-Rich | 6.263 |
| Planning Algorithm | Environment | Success Rate (%) |
|---|---|---|
| Improved Ant Colony | Obstacle-Free | 100 |
| Improved APF | Obstacle-Free | 100 |
| Improved Ant Colony | Obstacle-Rich | 85 |
| Improved APF | Obstacle-Rich | 70 |
These tables highlight that my improved ant colony algorithm consistently outperforms APF in both time and success rate, especially in complex settings. The higher success rate for bionic robots using my method—85% versus 70%—underscores its robustness in handling obstacles. The secure domain negotiation also played a key role: by minimizing arrival time differences, it ensured that bionic robots enclosed the target simultaneously, preventing escape opportunities. Visualizations of the trajectories revealed smooth, coordinated movements among bionic robots, with no deadlocks or collisions. This synergy between allocation and path planning is crucial for real-world applications where bionic robots must operate in unpredictable underwater domains.
In conclusion, I have presented a collaborative formation capture strategy for multiple bionic robots that integrates secure domain negotiation and an improved ant colony algorithm. This work addresses common challenges in multi-robot systems, such as inefficient task allocation and suboptimal path planning, by introducing a synchronized approach tailored for underwater environments. The secure domain negotiation ensures that bionic robots assign capture points in a way that balances distance and time, promoting coordinated arrival. The improved ant colony algorithm enables adaptive, obstacle-aware path planning with low computational overhead, making it suitable for small-scale bionic robots. Simulation results in both obstacle-free and obstacle-rich settings confirm the strategy’s effectiveness, showing faster formation times and higher success rates compared to baseline methods. These findings contribute to the growing body of research on bionic robots, highlighting their potential for collaborative tasks in marine exploration, environmental monitoring, and defense. Future work will extend this strategy to three-dimensional environments and implement it on physical bionic robot platforms to validate real-world performance. Additionally, incorporating machine learning for dynamic parameter tuning could further enhance adaptability. As bionic robots continue to evolve, such cooperative strategies will be essential for unlocking their full potential in the vast, uncharted underwater world.
Throughout this article, I have emphasized the role of bionic robots as versatile, bio-inspired agents. Their ability to mimic natural organisms lends them unique advantages in underwater mobility and sensing. By leveraging these traits through intelligent algorithms, we can deploy fleets of bionic robots for complex missions that single robots cannot accomplish. The secure domain concept, for instance, mimics predator-prey dynamics in nature, where hunters coordinate to isolate prey. Similarly, the ant colony algorithm draws inspiration from social insects’ collective intelligence. This bio-inspired paradigm not only improves technical performance but also aligns with sustainable, energy-efficient designs. As I refine these strategies, I envision bionic robots becoming integral to oceanographic studies, underwater infrastructure maintenance, and even search-and-rescue operations. The journey toward autonomous, collaborative bionic robots is challenging, but with continued innovation in formation control and path planning, we can overcome the hurdles of underwater environments and harness the ocean’s resources responsibly.