New Algorithm Enables Faster, More Stable Multi-Robot Formations
In a significant advancement for autonomous robotics, researchers have developed a novel control algorithm that dramatically improves the speed and stability of multi-robot formations. The breakthrough, published in the Journal of Nanjing University of Information Science and Technology (Natural Science Edition), introduces a dual-power sliding mode control strategy that allows follower robots to rapidly and precisely align with a leader, maintaining tight formation even during complex maneuvers.
The research, led by Tianlong Li from Zhejiang Institute of Mechanical and Electrical Engineering and Jianjun Bai from Hangzhou Dianzi University, addresses a long-standing challenge in the field of multi-robot systems: achieving fast convergence to a desired formation while ensuring robust stability. As robotic teams are increasingly deployed for tasks in search and rescue, warehouse logistics, and environmental monitoring, the ability to move as a coordinated unit is paramount. A slow or unstable formation can lead to inefficiencies, collisions, or mission failure.
Traditional formation control methods, such as the leader-follower approach, have been widely studied for their theoretical robustness. In this paradigm, one robot acts as the leader, charting the course, while others, the followers, adjust their movements to maintain a specific geometric relationship—defined by a target distance and angle—relative to the leader. While effective, many existing control algorithms suffer from a critical flaw: slow convergence. This means that after a change in the leader’s path or a disturbance, it can take a considerable amount of time for the follower robots to correct their positions and velocities, resulting in a loose and potentially unsafe formation.
To overcome this limitation, the team turned to sliding mode control (SMC), a powerful nonlinear control technique known for its ability to handle system uncertainties and external disturbances. SMC works by forcing the system’s state to “slide” along a predefined surface in the state space, guiding it toward the desired equilibrium point. However, conventional SMC often relies on a linear reaching law, which results in a constant rate of convergence. This can be slow, especially when the system state is far from the target.
The key innovation in the new research is the application of a “dual-power reaching law” to the leader-follower formation problem. This sophisticated mathematical framework combines two distinct power terms in the control law. One term is designed to act with high intensity when the tracking error—the difference between a follower’s actual position and its desired position—is large. This provides a powerful corrective force, rapidly pulling the follower robot back into formation. The second term becomes dominant as the error shrinks, ensuring a smooth and precise convergence to zero without the excessive oscillations, known as “chattering,” that can plague traditional SMC systems.
“Think of it like a driver approaching a parking spot,” explained Dr. Jianjun Bai, the corresponding author of the study. “If you’re far away, you need to accelerate quickly to cover the distance. But if you try to maintain that high speed as you get close, you’ll overshoot. Our controller is intelligent; it knows to apply a strong push when the robot is far off course, but then smoothly transitions to a gentle, precise nudge as it gets closer, ensuring a perfect park every time.”
The researchers meticulously designed separate controllers for the follower robot’s linear (forward) velocity and angular (turning) velocity. By defining a new set of error coordinates that account for the robot’s orientation, they were able to decouple the complex formation problem into two more manageable tracking tasks. The dual-power sliding mode law was then applied to these error dynamics, creating a control signal that commands the robot’s motors.
A critical aspect of the design is the choice of the power indices in the reaching law. The researchers specified that one power must be less than one, and the other must be greater than one. This specific combination is mathematically proven to guarantee that the tracking error will converge to zero in a finite time, a significant improvement over asymptotic convergence, which only approaches zero over an infinite time horizon. This finite-time convergence is what enables the “fast” response touted in the paper.
The theoretical foundation of the work is solid. The team used Lyapunov stability theory, the gold standard for proving the stability of nonlinear systems, to rigorously demonstrate that their control law ensures the system is asymptotically stable. They constructed a Lyapunov function—a scalar function of the system’s state—and showed that its derivative is always negative or zero. This proves that the system’s “energy” is always decreasing, meaning the state will inevitably settle at the desired equilibrium point, where the tracking error is zero.
To validate their theory, the researchers conducted a series of numerical simulations. They modeled a scenario with one leader robot and one follower robot. The leader was given a predefined trajectory with a constant linear speed of 2 meters per second and a constant angular speed of 0.3 radians per second, causing it to move in a circular path. The follower started from a significantly different initial position and orientation, creating a large initial error.
The simulation results were compelling. The graphical output showed that the follower robot’s trajectory quickly converged with the leader’s path, achieving the desired formation—defined by a 1-meter distance and a 150-degree relative angle—within a remarkably short period. The plots of the follower’s linear and angular velocities demonstrated a rapid and smooth transition, closely tracking the leader’s commands without any significant overshoot or oscillation. This visual evidence strongly supports the claim of fast and stable convergence.
The implications of this research extend far beyond a simple two-robot simulation. The algorithm is inherently scalable; the same control law can be applied to each follower in a larger swarm, allowing for the creation of complex, dynamic formations. This scalability is crucial for real-world applications. For instance, in a warehouse, a fleet of autonomous mobile robots (AMRs) could use this algorithm to move in a tight convoy, maximizing space efficiency and reducing the risk of collisions in narrow aisles. In search and rescue operations, a team of drones could maintain a precise grid pattern while scanning a disaster zone, ensuring complete coverage without gaps or overlaps.
The robustness of the sliding mode control also makes it suitable for environments with uncertainty. The algorithm is designed to handle model inaccuracies—differences between the mathematical model used for control and the real-world robot’s behavior—and external disturbances, such as uneven terrain or wind gusts for drones. This resilience is a major advantage over more delicate control strategies that might fail under real-world conditions.
While the paper presents a significant theoretical and simulation-based advance, the path to real-world deployment involves further challenges. The next critical step is experimental validation on physical robot platforms. Simulations are idealized; real robots have sensor noise, actuator delays, and mechanical imperfections. Testing the algorithm on actual hardware will reveal its true performance and any need for tuning or modification. Furthermore, the current model assumes that the follower robot has perfect knowledge of the leader’s position and orientation, likely through a wireless communication network. The impact of communication delays, packet loss, or sensor errors on the formation’s stability would be an important area for future research.
Another consideration is the computational load. The dual-power reaching law involves calculating powers and sign functions, which may be more demanding than simpler control laws. For robots with limited onboard processing power, this could be a constraint. However, modern microcontrollers are increasingly powerful, and the benefits of faster, more stable formation may well outweigh the computational cost.
The research also opens doors for further innovation. One potential direction is the integration of this control strategy with higher-level planning algorithms. For example, a central planner could determine an optimal formation shape for a given task—like a line for perimeter patrol or a circle for area surveillance—and then broadcast the desired distance and angle parameters to each follower. The dual-power sliding mode controllers would then autonomously execute the formation change.
Another exciting avenue is the development of adaptive versions of the controller. The current algorithm uses fixed parameters (the alpha and p/q values). An adaptive controller could learn and adjust these parameters in real-time based on the performance of the formation, potentially achieving even better results in varying conditions.
The work of Li and Bai stands out in a crowded field of robotics research. Many papers propose incremental improvements, but this study offers a clear, demonstrable leap in performance by leveraging a powerful, yet underutilized, control technique. The choice to focus on the leader-follower method is pragmatic; it is a well-understood and widely implemented architecture, making the adoption of their new controller more straightforward for existing robotic systems.
The significance of this contribution is amplified by the growing commercial and industrial interest in multi-robot systems. Companies like Amazon, with its vast network of warehouse robots, and startups developing drone swarms for agriculture and inspection, are constantly seeking ways to make their fleets more efficient and reliable. A control algorithm that can reduce formation settling time by even a few seconds can translate into significant gains in productivity and safety across a large fleet.
In conclusion, the dual-power sliding mode control algorithm presented by Tianlong Li and Jianjun Bai represents a major step forward in multi-robot coordination. By solving the persistent problem of slow convergence, it paves the way for robotic teams that can react swiftly to changes, maintain tighter formations, and operate with greater confidence in dynamic and uncertain environments. As robotics continues to move from isolated machines to collaborative teams, research like this will be the foundation upon which the next generation of intelligent, autonomous systems is built. The successful transition from simulation to real-world application will be the ultimate test, but the theoretical and numerical evidence presented is a strong indicator of its potential to reshape how we think about robotic teamwork.
The research was supported by the National Natural Science Foundation of China, highlighting the national importance placed on advancing robotics and automation technology. The detailed methodology and mathematical proofs provide a solid foundation for other researchers to build upon, fostering further innovation in the global scientific community.
The paper, “Formation control of the multi-robot system based on dual-power sliding mode,” by Tianlong Li and Jianjun Bai, was published in the Journal of Nanjing University of Information Science and Technology (Natural Science Edition), volume 13, issue 1, pages 111-115, with the DOI 10.13878/j.cnki.jnuist.2021.01.015.