Embodying mechanical intelligence from geometrical frustration

Recently, metamaterials have been used to process information [1] by exploiting their ability to change shape and stiffness, conform to different bodies, and complement binary-based mechanical computing by introducing concurrent information processing and memory formation, similar to the processes in physical reservoir computers. A specific class of metamaterials featuring dome-shaped units [2,3] exhibit order-dependent or non-Abelian deflections reminiscent of spin glasses [4], a type of condensed matter exhibiting strong state degeneracy (multiple energy minima), the mechanics of which enable in-material memory and computation [5]. This state degeneracy stems from the inability to simultaneously minimize all the local interactions due to deformation incompatibilities or constraints, a phenomenon known as geometrical frustration. Appropriate design of geometrical frustration allows for accommodating these local incompatibilities, whereby the accumulated collective deflections result in substantial three-dimensional reshaping while maintaining low strains.

We show how exploiting the interplay between geometry and constraints allows for leveraging the resulting strong state degeneracy in dome-patterned structures to embody intelligence into morphing systems purely from mechanics. We illustrate intelligence from geometrical frustration via pneumatically actuated soft systems with encoded multiple accessible, stable states that offer a route to open-loop shape reconfiguration. Informed by the mechanics of multistable metamaterials, we design coexisting states resembling different actuation modes in soft structures. We achieve this by leveraging distinct path-dependent activation sequences to access desired coexisting states. We demonstrate how to describe this system as a temporal finite-state machine that yields different output shapes depending on the recorded sequence. Our strategy offers a new route for controlling soft robots, exploiting the nonlinear mechanics of multistable structures to the designer's advantage, thus opening the avenue for embodying finite-state machine-based control strategies without closed-loop feedback [6] for soft structures.