Inspired by how brainless lifeforms such as starfish and slime moulds move around, physicists at the University of Amsterdam have constructed ‘odd’ objects that autonomously roll, crawl and wiggle over unpredictable terrain, including uphill and over obstacles placed in their way. This solves a key problem of robotic locomotion.

Locomotion, the ability of moving from one place to another, is an essential survival strategy for a large variety of living systems. Adapting to the unpredictable terrain they run into, cells, fungi and microorganisms autonomously move and change shape to explore their environments, while animals run, crawl, slither, roll and jump.

Despite advances in computing power and AI, human-made robots still struggle to imitate this movement, especially in new and unpredictable terrain. This prompts the question: what does it take to recreate the same adaptive locomotion capabilities that animals and other lifeforms have?

In answer to this question, physicists from the University of Amsterdam and the University of Chicago showcase a series of ‘odd’ objects – each a type of so-called ‘active metamaterial’ – that are remarkably good at moving across any terrain they encounter. Each object is made from the same motorised building blocks, which can sense forces and exert them on one another. Crucially, these building blocks interact with one another in an uneven or ‘odd’ way: building block A reacts to its neighbouring building block B differently than how B reacts to A.

A wormlike ‘odd chain’ of linked building blocks will wiggle through a bendy tunnel and over uneven ground. Loop a chain into an ‘odd wheel’ and it will bouncily roll itself forward, including uphill and over bumpy terrain. Similarly, an ‘odd ball’ made of the building blocks connected in a hexagonal grid will roll on flat terrain but changes to a crawling gait to move uphill.

Brainless motion from odd elasticity
Impressively, the odd objects achieve all their motion autonomously, without steering or being controlled by a central processing unit or ‘brain’. The motion comes from the unusual interactions between the objects’ motorised building blocks.
PhD student Jonas Veenstra, first author of the publication, explains: “The building blocks exert forces that are nonsymmetric and nonreciprocal. When connected together by elastic springs, they collectively form an energy-consuming ‘active’ solid that deforms in an odd and counterintuitive way: these materials shear when compressed, but extend when sheared.”

Unlike ordinary elastic materials, which compress along the same direction as an applied force and bulge out in the perpendicular direction, the objects made of these building blocks always stretch diagonally at a fixed angle. This strange response was recently formulated and dubbed ‘odd elasticity’.

A cycle emerges where the terrain deforms the object, which the object’s building blocks sense and respond to in an odd way, thereby deforming the object further so that it moves forward and encounters new terrain.
Take the example of an odd wheel on a surface. With gravity pulling downwards, the wheel stretches diagonally, thereby tipping and rotating. After rotating, gravity again causes it to stretch at an angle and the process repeats. And thanks to the ‘wiggliness’ of the wheel’s forward motion, the odd wheel can easily overcome bumps or other unevenness on the road.

While the odd objects might look a bit silly as they move, don’t confuse their wiggly motion for randomness. Their locomotion is reliable and robust thanks to their decentralised nature – each building block contributing to the movement – and thanks to the fact that the solids actively sense and respond to their environment.

The future of odd materials
“I hope our research inspires new design principles for robotics and other active materials,” says Veenstra. “Supported by the wonderful people of the Technology Centre at the University of Amsterdam, we are already working on generalising our current two-dimensional designs to three-dimensional structures of various sizes that can be used in other settings.”

The research connects to the broader theme of the university’s Machine Materials Lab, where researchers attempt to bridge the gap between materials and machines. Lab leader Corentin Coulais comments: “Active matter has long held the promise of having useful applications, but active materials have proven difficult to tame. Our new designs make active solids functional, enabling a paradigm shift in robot locomotion.
“Investigating and wielding the intriguing mechanics of active solids will help us design and create materials and objects that form patterns, can learn and change shape. We can encode all that functionality in their structure.”

Publication
Jonas Veenstra, Colin Scheibner, Martin Brandenbourger, Jack Binysh, Anton Souslov, Vincenzo Vitelli and Corentin Coulais, 2025, 'Adaptive locomotion of active solids'. In: Nature, DOI: 10.1038/s41586-025-08646-3

Contact
Jonas Veenstra, J.C.Veenstra@uva.nl, +31 6-36325192
Corentin Coulais, C.J.M.Coulais@uva.nl, +31 20-5257224