The development of a mechanical metamaterial, wherein the energy required to drive its movements is derived solely from its individual components, without reliance on external forces, indicates the presence of an inherent self-sustaining physics within robots.

In future robotic systems, abilities such as movement, signal transmission, and environmental perception might emerge from the interactions between the individual units that make up the machine rather than being controlled by a central system.

This prospect is particularly pertinent in the context of soft robotics and its applications, which involve robots constructed from small, soft, deformable, and flexible materials. These robots are designed to seamlessly integrate into highly complex and unstructured natural settings, such as the depths of the oceans and outer space.

In terms of deformable and flexible materials, recent advancements in soft robotics have led to the development of “metamaterials“. As defined in “Focus on Metamaterials in Robotics and Intelligent Structures” by Materials Research Express, these are «a class of materials whose properties are derived more from their internal microstructures than from their chemical composition. They are artificially engineered to possess properties not found in naturally occurring materials».

Notably, mechanical metamaterials demonstrate advanced functionalities, including energy absorption, minimal rigidity, and inherent mechanical logic.

Revisiting our initial question, a study by the University of Amsterdam, detailed in “Non-reciprocal topological solitons in active metamaterials” (Nature, March 20, 2024), provides a fascinating response based on the behavior of “topological solitons” in robotic metamaterials. Let’s delve into this concept and explore how, in the future, this discovery might revolutionize the mechanisms of motion control, communication, and perception in robots.

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TAKEAWAYS

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What are topological solitons?

The Dutch study investigates the so-called “topological solitons,” analysing their significance and their role within interactions among components of robotic metamaterials. The research team explains, «a topological soliton is a type of wave driven by external fields, behaving like a particle. Unlike typical particles, however, it can move without expanding or dissipating, which contrasts with, for instance, a ripple on the surface of water».

The authors’ originality resides in integrating the unique properties of topological solitons – specifically, their ability to move while preserving their form without disappearing abruptly – with what are termed in physics as “non-reciprocal interactions.” In these interactions, «agent A reacts to agent B differently than agent B reacts to agent A».

The motivation behind their research choice, beyond addressing the physics community’s current undervaluation of non-reciprocal interactions (despite their established dynamics in human groups and complex living systems), hinges on these interactions «existing solely in non-equilibrium systems».

Their intent is to embed such interactions in materials, aiming – as emphasised by the team – to blur the “boundary” between materials and machines, thus creating «animated materials or those that are as lifelike as possible».

The relationship between topological solitons and non-reciprocal interactions in robotic metamaterials

The robotic metamaterial devised by the authors consists of a chain of small robotic units (mechanical rotors), each comprising pairs of rotating rods joined by elastic bands and mounted on an electric motorthat exerts a slight force on each rod. The interactions between the rods are managed by the motors, the magnetic fields on the rods (attracted, in turn, by magnets adjacent to the robotic units), and the elastic bands (refer to the opening image, above).

The researchers noted that in a state of perfect equilibrium, all pairs of rotating rods assume the same position, either tilted left or right. When the left rod of a pair is pushed to rotate in the opposite direction, the right rod also rotates (reciprocal interaction). Conversely, when the right rod of the pair is turned from one orientation to another, the left rod does not mirror this movement, and both eventually revert to their original orientation (non-reciprocal interaction).

Another noteworthy observation is made when, within the specially engineered robotic metamaterial, the pairs of rotating rods are connected in a sequence to form a chain and are disrupted by a force.

It is precisely in the mobile space at the boundary that forms between two adjacent pairs – where the first is entirely tilted to the left and the second entirely to the right – that the topological soliton emerges. Conversely, in the space between pairs where the first is entirely tilted to the right and the second to the left, an “anti-soliton” forms.

What dynamics lead to these two observed behaviour patterns?

Magnetic fields and the domino effect

To address the question, we recall that prior research on this robotic metamaterial demonstrated that, in a linear state – where the movement of robotic units produces waves characterized by straightforward linear relationships – the behaviour of the assembly exhibits wave-like properties.

In the current study, however, the team purposefully imposed restrictions on the wave-like movement of the robotic units by integrating magnetic fields (positioned on the rotating rods and alongside each unit), «thus introducing significant non-linearity into the system». This represents the innovation. More specifically:

«… the magnetic fields established pairs of potential energy wells, leading to two stable states: one where pairs of rotating rods are uniformly inclined either left or right, and another where each pair maintains its orientation, effectively ‘at rest’»

This complexity, as the research group notes, significantly complicates the system to the extent that the emergent behaviour of the metamaterial cannot easily be correlated with the actions of its individual components.

In this particular scenario, the movement of topological solitons is likened to «a sequence of domino tiles falling, each one precipitating the next. However, the pivotal difference unlike dominoes, the non-reciprocal interactions introduced by the researchers ensure that the ‘tipping’ occurs in only one direction».

Historically, various research has explored the movement of topological solitons in response to external forces. To date, it has been observed that solitons and anti-solitons move in opposite directions.

The desire to regulate such movements, to orchestrate them, necessarily involves guidance that “directs” both solitons and anti-solitons towards the same direction. The implementation of non-reciprocal interactions within the metamaterial has led to this breakthrough by the University of Amsterdam. More specifically:

«… when the motors within the chain of robotic units are switched off, the solitons and anti-solitons can be manually pushed either right or left, indiscriminately. However, once the motors are activated – and thus the reciprocal interactions commence – the solitons and anti-solitons automatically glide along the chain, moving in the same direction at a velocity dictated by the non-reciprocity of the motors»

Glimpses of Futures

The innovative element of the research presented involves the development of a mechanical metamaterial where the energy needed to drive soliton motion is autonomously supplied by the robotic units themselves, obviating the need for manual intervention. This establishes that robots are endowed with an inherent physics, extending beyond their central processing capabilities. This insight opens new avenues for exploring the autonomy and control mechanisms of machines.

Expanding on this idea and with an eye to forecasting future developments, we seek to delineate – through the STEPS framework – the potential impacts that studying the behavior of non-reciprocal topological solitons in robotic metamaterials could have on several fronts.

S – SOCIAL: in the robotic metamaterial under discussion, there are no external forces at play. This independence is essential for a robust analysis of the social implications that arise from mechanisms propelling solitons and anti-solitons in a unified direction via non-reciprocal guidance. The impetus within this metamaterial springs from this very non-reciprocity, which imposes local directives on the robotic units. This foretells the potential emergence of non-reciprocal solitons that could independently offer an effective guidance system for robotic movement, as well as foster the development of autonomously functional materials, free from external energy dependencies. Such technologies could revolutionize applications ranging from space exploration to navigating complex marine or ice-covered oceanic environments, facilitating the emergence of more agile and lighter soft robots. These advancements imply robots could perform more efficiently without the need for onboard sensors and actuators, having their locomotive functions seamlessly integrated within their structural mechanics and powered by topological solitons.

T – TECHNOLOGICAL: one aspect of the evolving study into the behaviour of non-reciprocal topological solitons may, in future, require further exploration of non-reciprocity mechanisms within increasingly sophisticated robotic metamaterials. This includes examining collective robotic movements which, in some instances, lead to collisions between machines or the absorption of impacts among them. Furthermore, looking ahead, the forces propelling solitons and anti-solitons in the same direction could potentially be harnessed in fields beyond robotics to manage, for instance, the non-linear dynamics prevalent in soft materials (such as polymers, colloids, gels, and foams), biological systems, and driven nanomechanical devices.

E – ECONOMIC: as has already been seen at an institutional level within the European Union in another study area of topological solitons [“Topological solitons in ferroics for unconventional computing“], the future application of non-reciprocal topological soliton mechanisms to robotic metamaterials will necessitate the creation of tailored training programmes. These are essential to support the designers and builders of robotic devices in fully harnessing the potential of solitons and anti-solitons travelling in the same direction and addressing the challenges of a sector that holds significant technological and economic promise but is still in its infancy regarding research and development.

P – POLITICAL: regarding mechanisms for robotic locomotion and autonomous functional materials that require no external energy sources, collaborative research from 2022, led by the University of Amsterdam, Université Libre de Bruxelles, Aix-Marseille Université, and the University of Chicago – entitled “Limit cycles turn active matter into robots” – already shed light on the darker aspects, highlighting how the presence of intrinsic energy sources «is what renders the material prone to dynamic instabilities, thus making it challenging to control. »Shifting focus from soft robotics to collaborative robotic systems, in a future scenario where applying non-reciprocal topological soliton mechanisms to robotic metamaterials becomes a reality, the risk of movement instabilities and difficulties in machine control could pose real dangers to people interacting with these systems in workplace or domestic settings. In this regard, the new EU Regulation 2023/1230 on machinery (published on 29 June 2023 and effective from 20 January 2027), which supersedes the established Machinery Directive 2006/42/EC, mandates manufacturers to introduce new safety components and requires users to adhere to heightened protection standards in human-machine collaboration, introducing the “EU Conformity Declaration” in lieu of the former CE conformity declaration, aligning with the new legislative framework.

S – SUSTAINABILITY: in the future, robotic metamaterials devoid of sensors and actuators, which operate independently of external forces and where the necessary energy for movement primarily arises from non-reciprocal interactions among the units composing them, are set to advance the development of sustainable soft robotics. These innovations are expected to yield significant environmental and economic benefits, stemming from reduced resource and production costs, widespread distribution, and the disposal of obsolete components and devices, which are no longer essential for the functionality of soft machines, thanks to the adoption of multifunctional metamaterials.