Swarm robotics continues to learn from nature’s seamless coordination, whether it’s birds flocking or fish schooling. A recent study in Proceedings of the National Academy of Sciences introduces a geometric parameter; “curvity”as a key to guiding synthetic swarms more naturally and efficiently.
The international research team, which included NYU scientists Mathias Casiulis and Stefano Martiniani, from New York University and Radboud University proposes a simple mechanical rule: assign each robot a signed “curvity,” akin to an electric charge, to control its trajectory under external forces.
Casiulis, M., Arbel, E., van Waes, C., Lahini, Y., Martiniani, S., Oppenheimer, N., & Zion, M. Y. ben. (2025). A geometric condition for robot-swarm cohesion and cluster–flock transition. Proceedings of the National Academy of Sciences, 122(37). https://doi.org/10.1073/pnas.2502211122
Matan Yah Ben Zion from Radboud University stated,
“One of the great challenges of designing robotic swarms is finding a decentralized control mechanism’.
Negative or positive curvity causes robots to curve in opposite directions. When two robots interact, their curvity values determine whether they are drawn together into clusters or steer apart to maintain flocking patterns. What is notable is the rule’s scalability; from simple pairs to swarms of thousands.
The researchers backed their theory with both simulations and physical trials. The results confirm that curvity can reliably tune collective patterns across scales, and that it can be built directly into the robot’s structure without added computational demands.
As assistant professor Matan Yah Ben Zion points out, this design rule could inform future industrial or medical fleets; think delivery drones or microscopic agents for targeted drug treatments. The elegance lies in its reliance on elementary mechanics, which simplifies real-world deployment.
- Acoustic Signaling in Microrobots
A parallel development uses sound waves for communication among microscopic robots. These “acoustic swarms” align and adapt collectively and even self-repair after damage—all driven by local sound-based interaction rather than curvature-based guidance. - Link-Bots: Geometry Without Sensors
Another study presents “link-bots”; robots connected in V-shaped chains that self-propel on vibrating surfaces. Coordinated behaviors emerge purely from geometry and mechanical design, without sensors or controllers.
While curvity provides a geometric way to direct interactions within a swarm, it is not the only emerging approach. Acoustic swarms use sound waves to drive communication, enabling adaptability and even self-healing behaviors. Link bots, by contrast, rely on simple physical connections and geometry to produce coordinated motion without sensors or computation. All three strategies reduce reliance on centralized control and heavy processing. Curvity emphasizes mechanical curvature, acoustic swarms emphasize signaling, and link bots emphasize structural design. Together, they highlight a broader trend: the future of swarm robotics may lie in leveraging simple, scalable physical principles rather than complex algorithms.
The curvity framework marks a fresh take on decentralized swarm control. It reimagines swarm design as a problem of mechanics and geometry, rather than software and network coordination. Given its simplicity and effectiveness, curvity could soon find its way into real world robotic systems; from compact delivery teams to targeted medical agents.
At the same time, acoustic communication and purely mechanical designs like link bots demonstrate that nature-inspired behaviors need not be computationally intensive. As these ideas continue to mature, the next generation of swarm systems may be as elegant as they are capable.
Adrian graduated with a Masters Degree (1st Class Honours) in Chemical Engineering from Chester University along with Harris. His master’s research aimed to develop a standardadised clean water oxygenation transfer procedure to test bubble diffusers that are currently used in the wastewater industry commercial market. He has also undergone placments in both US and China primarely focused within the R&D department and is an associate member of the Institute of Chemical Engineers (IChemE).
