Safety-Protected Formation–Containment Control for Nonlinear Multi-Agent Systems via Interval Type-2 Fuzzy Sliding Mode and Smooth-Switching Collision Avoidance

In the vast and unpredictable expanse of the ocean, the future of maritime travel is shifting from human crews to autonomous vessels. These self-governing ships are designed to navigate hazardous waters, carrying out complex missions while reducing the risk to human life. However, a single ship operating alone is rarely enough for large-scale tasks like defense or escort operations. To handle these challenges, engineers are developing systems where multiple ships work together as a coordinated team. This concept, known as multi-agent control, relies on vessels communicating with one another to share information and move in unison. The goal is for a group of ships to maintain a specific shape, or formation, while ensuring that every member stays within the safe boundaries defined by the leaders of the group. Yet, the ocean is not a static environment. It is filled with sudden obstacles, shifting currents, and the wear and tear of saltwater that can confuse a ship's sensors. The central challenge for researchers is to create a control system that is not only smart enough to keep the fleet in formation but also robust enough to react instantly to danger without losing its way.

A team of researchers from universities in Taiwan and China has addressed this challenge by developing a new control method for nonlinear autonomous multi-ship systems. Their approach combines several advanced techniques to ensure that a fleet of ten ships can move together safely, even when faced with unexpected obstacles and environmental disturbances. The researchers focused on a specific problem: how to keep a group of ships in a precise formation while allowing them to avoid collisions with other objects or each other. In their proposed system, four ships act as leaders, tasked with defining the path and maintaining the overall shape of the group. The remaining six ships act as followers, which must stay within the area bounded by the leaders. This arrangement, called formation-containment coordination, allows the leaders to handle complex navigation tasks while the followers focus on their specific roles, creating a hierarchy that improves efficiency and safety.

The core of this new method lies in how the ships process information and make decisions. Traditional control systems often struggle with the uncertainties of the marine environment, such as the gradual corrosion of a ship's hull or the unpredictable force of wind and waves. To overcome this, the researchers utilized a mathematical framework known as an interval type-2 fuzzy model. Unlike simpler models that rely on fixed rules, this system is designed to handle ambiguity and uncertainty more effectively. It allows the ship's computer to understand that a sensor reading might not be a single, exact value but rather a range of possibilities. By using this flexible approach, the system can make more reliable decisions even when the data it receives is imperfect or noisy. This is crucial for maintaining stability when the ships are subjected to the constant, random jostling of the ocean.

To ensure the ships stay on course despite these disturbances, the researchers integrated a technique called sliding mode control. This method acts as a powerful corrective force, constantly adjusting the ship's thrusters to counteract any deviation from the desired path. It is particularly effective at handling external forces like sudden gusts of wind or strong currents. However, simply staying on a pre-planned path is not enough when a collision is imminent. The researchers developed a new collision avoidance algorithm that works in tandem with the formation control. This algorithm uses a concept known as an artificial potential field, which creates a virtual landscape around the ship. In this landscape, obstacles act like repulsive forces, pushing the ship away, while the destination acts like an attractive force, pulling it forward.

What makes this new algorithm unique is its ability to switch smoothly between different avoidance strategies. The researchers combined two types of virtual forces: a vortex force that guides the ship to circle around an obstacle, and a source force that pushes the ship directly away. Using fuzzy logic, the system evaluates the situation in real-time and blends these two forces together. This prevents the ship from getting stuck in a deadlock, a scenario where it might circle an obstacle endlessly or stop directly in front of it. Instead, the ship can navigate around the danger and then seamlessly return to its original formation path. This smooth switching capability ensures that the entire fleet can react to a sudden hazard without breaking their coordinated shape or causing panic among the followers.

The researchers tested their system through detailed computer simulations involving a fleet of ten ships. In these virtual scenarios, the four leader ships were tasked with maintaining a triangular formation while navigating toward a destination. The six follower ships were required to stay within the boundaries created by the leaders. The simulations introduced various challenges, including random disturbances to mimic the effects of wind and waves, as well as the sudden appearance of obstacles in the ships' paths. The results demonstrated that the proposed control method successfully guided the leaders to track their target trajectories while maintaining the triangular formation. When obstacles appeared, the leaders were able to switch to avoidance mode, maneuvering around the danger and then returning to their original path. Crucially, the follower ships remained safely contained within the leaders' formation throughout these maneuvers, never straying too far or colliding with the obstacles.

The study also highlighted the importance of the specific mathematical tools used. By extending analysis methods originally designed for linear systems to these more complex nonlinear systems, the researchers were able to prove that their control strategy would work without needing extra, unrealistic assumptions. They showed that the system could effectively dampen the effects of disturbances, ensuring that the ships remained stable and on course. The integration of the collision avoidance logic directly into the formation controller meant that the ships did not need to switch between different control modes in a jarring way. Instead, the transition from normal navigation to obstacle avoidance was fluid and continuous, preserving the integrity of the entire fleet.

This work represents a significant step forward in the development of autonomous maritime systems. It moves beyond the theoretical possibility of ships working together to a practical framework that accounts for the messy, uncertain reality of the ocean. By combining robust disturbance rejection with intelligent, smooth-switching collision avoidance, the researchers have provided a blueprint for how future fleets of autonomous vessels might operate safely in crowded or hazardous waters. The simulations suggest that this approach is viable for real-world applications, offering a way to keep ships coordinated and safe even when the environment tries to pull them apart. As autonomous technology continues to mature, methods like these will be essential for deploying fleets that can handle the full complexity of the open sea.