Imagine a swarm of robots rushing to complete an urgent task, like cleaning up an oil spill or assembling a complex machine. Initially, adding robots will speed up the process. However, after a certain point, the space becomes crowded and robots begin to interfere with each other, slowing down overall progress.
This raises a simple but important question. How many robots can we deploy in a limited area before efficiency starts to decline? Researchers at Harvard University believe they have found a clear answer.
Simple ideas to increase efficiency
New research from the lab of L. Mahadevan, Laura Englund de Valpine Professor of Applied Mathematics, Bio-Evolutionary Biology, and Physics, shows that adding a controlled amount of randomness to the way robots move can reduce crowding and improve performance in crowded environments.
The research combines mathematical modeling, computer simulations, and real-world experiments. This shows how basic local movement rules can lead to organized and efficient results at scale. The findings could have implications for how robot fleets are designed, and could also apply to human crowd management and traffic flow. The research was published in the Proceedings of the National Academy of Sciences and was led by Applied Mathematics Ph.D. student Lucy Liu, supervised by SEAS Senior Researcher Justin Warfel.
Why randomness helps predict complex behavior
Dense crowds are difficult to study. This is because individuals can take an infinite number of possible paths and interact in unpredictable ways, Liu explained. To simplify the problem, the researchers treated each robot as a basic unit with small, adjustable variations in movement.
“This may be counterintuitive, because does randomness make things easier?” Liu said. “But in this case, high randomness allows you to take averages like average distance, average time, average behavior, etc. This makes predictions much easier.”
Simulation of a group of moving robots
To explore this idea, the team created a computer simulation of a group of robots called agents. Each agent started at a random location and was assigned a random destination. Once a goal was reached, it immediately received a new goal, mimicking continuous task assignment in real-world systems.
Each agent moved toward its goal with an adjustable amount of variation called “noise.” There was no noise and the agent moved in a straight line. The high noise made the path unstable and inefficient. But this wandering also helped them avoid each other.
Finding the “Goldilocks Zone” of noise
The simulations revealed a clear pattern. When the agents traveled in a perfectly straight path, they quickly formed dense clusters and created traffic jams that halted progress. If movement becomes too random, traffic jams will be alleviated, but efficiency will decrease due to increased wandering.
Researchers have identified a sweet spot between these extremes. At this range, the agents occasionally bumped into each other, forming short-lived clusters, but still managed to slip through and keep moving. This balance allowed the system to maintain a steady flow.
From simulation to mathematical models
Using these insights, the team developed a formula to estimate “goal completion rate,” or how much of a destination is reached over time. These equations made it possible to determine the ideal combination of crowd density and movement randomness to maximize performance.
Test your theory on real robots
To confirm their findings, Liu collaborated with physicist Federico Toschi of Eindhoven University of Technology in the Netherlands. Together, they set up experiments on small wheeled robots in a lab equipped with overhead cameras.
Each robot is equipped with a QR code that allows its location to be tracked and updated with new destinations. The physical robot moved slower and less precisely than the simulated agent, but the overall pattern was the same.
Simple rules, complex results
This experiment confirmed the important idea that highly complex coordination does not require high intelligence or centralized control. Instead, effective group behavior can be generated by simple local rules, at least within certain density limits.
“Understanding how active matter, whether a swarm of ants, a swarm of animals, or a group of robots, functions and uses principles of self-organization to perform tasks in crowded environments is relevant to many questions in behavioral ecology,” Mahadevan said. “Our study suggests a much broader strategy than the instantiation we have focused on.”
Impact beyond robotics
Liu said he has long been interested in designing safer and more efficient crowded spaces. This research points to a future where the movement of large groups of people, including robots, vehicles, and humans, can be predicted and optimized using mathematical tools.
The results suggest that introducing controlled variability in movement patterns has the potential to improve the flow of many real-world systems, from the factory floor to the street.
Important points
- Researchers at Harvard SEAS have found that when large numbers of robots operate in the same space, introducing a controlled amount of randomness into their movements can significantly improve efficiency.
- This study highlights that simple, local movement rules can generate surprisingly complex and well-coordinated group behavior without the need for central control.
- The mathematical model developed in this study could help optimize the design of robot swarms and improve how crowded environments such as cities, transportation systems, and public spaces are managed.
Research funding was provided by the National Science Foundation Graduate Research Fellowship Program under grant number DGE 2140743, along with grants from the Simons Foundation and Henri Seydoux Foundation.
