Chaos to coordination: vibrating material organises itself into a single rhythm

Scientists have developed a material that can grow and coordinate its own movement until the entire structure pulses in unison, paving the way for versatile robots that behave more like living systems.

Publishing their findings today (14 Oct) in Nature, engineers from the University of Birmingham working with the Universities of Amsterdam, Lyon, Delft, Leiden and Cambridge reveal that they have created a mechatronic metamaterial that behaves as a ‘time crystal’. Time crystals are an unusual form of matter in which particles endlessly move in regular, repeating cycles. But here, the “particles” were not the atoms of molecules: they were robots.

The scientists’ experimental material combines elastic structures, sensors, electronics, and actuators so that neighbouring components can influence one another. The key ingredient to generate the time-crystalline state was making the interactions between components ‘non-reciprocal’, meaning that one component's response to another does not have to be mirrored in reverse.

When reciprocity was broken in the material, individual vibrations initially appeared at short wavelengths, but then progressively grew in wavelength, period, and amplitude - resulting in a globally synchronised state that the researchers demonstrate is a time crystal. The team describe the process they have discovered as ‘wave coarsening’.

Co-lead author Dr Jack Binysh, from the University of Birmingham, started working on the project at the University of Amsterdam. He said: “Our research is a beautiful example of what robotics can teach us about physics, and vice-versa. It’s also a showcase for combining fundamental physical concepts about different states of matter with outstanding technical expertise in mechatronic fabrication.”

“Our research provides a striking example of spontaneous organisation - tiny vibrations organising themselves until an entire material moves in a coordinated way. Like musicians gradually finding the same beat, individual parts of an active material can organise their movements until the whole structure moves together.”

“Wave coarsening could be exploited as a way of controlling shape changes and directed motion – proving useful in robotics, active matter and optomechanics. Our discovery could form a key step towards the development of biology-inspired multifunctional robots.”

2D honeycomb material

The researchers first constructed a 2D honeycomb material made from 37 active units. When pushed beyond a stability threshold, individual units began self-oscillating at around 30 Hz. Gradually, longer waves came to dominate until the entire material oscillated collectively.

They then constructed an elastic ring containing 24 motorised units. Initially, higher-frequency deformation patterns appeared around the ring. These progressively combined into larger patterns until the ring settled into a slow collective cycle.

Crucially, the experiments as well as the model show that random disturbances do not destroy the collective order as the size of the material is increased – the repeating pattern is very stable.

Co-lead author Jonas Veenstra was a PhD student at Amsterdam when the research started and is now a postdoctoral fellow at ENS Lyon. He said: “With applications in mind, we have also started to think about making one material support several distinct, stable patterns of motion. Could we switch between these patterns and use each one for a different robotic function, such as a different shape change or direction of movement?

“Instead of designing a separate structure for every task, we could then use the different modes of a single material to achieve different behaviours, leading to remarkably simple but highly multifunctional robots. Our aim is a biology-inspired form of robotics where coordinated behaviour emerges from carefully designed interactions between building blocks, rather than instructions from a central controller.”

The research originated in the Amsterdam group led by Dr Corentin Coulais and the experimental metamaterials incorporated more than 100 sensors and actuators alongside 3D-printed components and custom-made Lorentz actuators that convert electrical energy into mechanical motion.

Dr Corentin Coulais said: “Like the materials themselves, the research team that produced them consisted of many moving and interacting parts. There was enormous help from the university’s Technology Centre in Amsterdam. We had interns assembling the metamaterials with more than 100 sensor and actuators embedded, where each actuator needed more than 20 points of glue. There were 3D printed parts with varied materials, and an in-house custom-made Lorentz actuator that converts electrical energy into mechanical motion.”

Researchers aim to develop 3D active materials which could provide many more ways for components to interact, including shearing, bending, and twisting. They hope to understand how wave coarsening behaves in three dimensions and how it could be harnessed to control changes in the shape of self-supporting materials.