Microrobots—tiny robots less than a millimeter in size—are useful in a variety of applications that require tasks to be completed at scales far too small for other tools, such as targeted drug-delivery or micro-manufacturing. However, the researchers and engineers designing these robots have run into some limitations when it comes to navigation. A new study, published in Nature, details a novel solution to these limitations—and the results are promising.
Too small to be ‘smart’
The biggest problem when dealing with microrobots is the lack of space. Their tiny size limits the use of components needed for onboard computation, sensing and actuation, making traditional control methods hard to implement. As a result, microrobots can’t be as “smart” as their larger cousins.
Researchers have tried to cover this limitation already. In particular, two methods have been studied. One method of microrobot control uses external feedback from an auxiliary system, usually with something like optical tweezers or electromagnetic fields. This has yielded precise and adaptable control of small numbers of microrobots, beneficial for complex, multi-step tasks or those requiring high accuracy, but scaling the method for controlling large numbers of independent microrobots has been less successful.
On the other hand, a method referred to as “reactive control” has shown promise in controlling larger numbers of microrobots. The study authors explain, “Rather than relying on continuous external feedback, they use on-robot sensory inputs to immediately modulate the robot’s actions in response to a global control field. This approach is minimalist and well suited to microrobots that often lack sophisticated sensing or computation due to their small size.
“Common examples are stimuli-responsive micromotors that achieve taxis, artificial potential fields that coordinate motion through attractive and repulsive forces, and microrobot swarms whose behavior emerges through collective interactions.”
However, reactive control methods have so far been limited to simple behaviors. Researchers have faced difficulties with behaviors like navigating structured environments or making robots independently converge at a desired location by guiding them from differing trajectories.
A solution inspired by general relativity
Surprisingly, the researchers found that the robots’ motion is formally identical to the path light takes in general relativity, which allowed them to develop a mathematical framework mapping robot motion to geodesics in a curved spacetime defined by a control field—as in other reactive control methods. The team used conformal transformations to map complex environments to simple virtual spaces, then designed control fields and mapped them back. They refer to the resulting geometric framework as “artificial spacetimes.”
Using artificial spacetimes, the team found that they were able to have the robots perform more complicated tasks. They explain, “First, we present metrics that generate primitive behaviors in unobstructed environments. These include navigating to specific locations, confining, diverging, or turning in prescribed ways. We then extended these results to spaces with boundaries by exploiting the invariance of geodesic motion under conformal transformations.”
Their method successfully allowed them to prevent robot collisions with walls and give instructions for navigation, patrolling, turning, or dispersion without the need for on-robot computation. They tested out the approach with both simulations and experiments using silicon microrobots and projected light fields. The experimental robots had two motors, each made up of arrays of silicon photovoltaics, and moved at speeds proportional to the incident light intensity.
Microrobots of the future
Ultimately, this new framework offers a new, scalable way to control large numbers of simple robots—opening up possibilities in the realms of medicine, environmental remediation, and micro-manufacturing. The study authors already see ways to improve the current model, which is currently limited to 2D and specific robot types. They say “there are several promising paths towards generalization,” such as extending the metrics to vary in time.
“Work along this route might target robot-to-robot collision avoidance or sequential exploration of space by causing individual robots to speed up or slow down upon arriving at specific spacetime locations, or be cloaked from one another when in proximity,” they say.
Other possibilities include branching out in terms of the robot hardware or to even allow robots to generate their own control fields, enabling emergent swarm behaviors.
Written for you by our author Krystal Kasal, edited by Gaby Clark, —this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive.
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More information:
William H. Reinhardt et al, Artificial spacetimes for reactive control of resource-limited robots, npj Robotics (2025). DOI: 10.1038/s44182-025-00058-9
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