Turning machines: a simple algorithmic model for molecular robotics.

Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We provide a suite of tools for reasoning about Turning Machines by fully characterising their ability to execute line rotations: executing an almost-full line rotation of 5 π / 3 radians is possible, yet a full 2 π rotation is impossible. Furthermore, line rotations up to 5 π / 3 are executed efficiently, in O ( log n ) expected time in our continuous time Markov chain time model. We then show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold shapes. In particular, arbitrarily large zig-zag-rastered squares and zig-zag paths are foldable, as are y-monotone shapes albeit with error (bounded by perimeter length). Finally, we give shapes that despite having paths that traverse all their points, are in fact impossible to fold, as well as techniques for folding certain classes of (scaled) shapes without error. Our approach relies on careful geometric-based analyses of the feats possible and impossible by a very simple robotic system, and pushes conceptional hardness towards mathematical analysis and away from molecular implementation.

Ultralight, strong, and self-reprogrammable mechanical metamaterials.

Versatile programmable materials have long been envisioned that can reconfigure themselves to adapt to changing use cases in adaptive infrastructure, space exploration, disaster response, and more. We introduce a robotic structural system as an implementation of programmable matter, with mechanical performance and scale on par with conventional high-performance materials and truss systems. Fiber-reinforced composite truss-like building blocks form strong, stiff, and lightweight lattice structures as mechanical metamaterials. Two types of mobile robots operate over the exterior surface and through the interior of the system, performing transport, placement, and reversible fastening using the intrinsic lattice periodicity for indexing and metrology. Leveraging programmable matter algorithms to achieve scalability in size and complexity, this system design enables robust collective automated assembly and reconfiguration of large structures with simple robots. We describe the system design and experimental results from a 256-unit cell assembly demonstration and lattice mechanical testing, as well as a demonstration of disassembly and reconfiguration. The assembled structural lattice material exhibits ultralight mass density (0.0103 grams per cubic centimeter) with high strength and stiffness for its weight ( 11.38 kilopascals and 1.1129 megapascals, respectively), a material performance realm appropriate for applications like space structures. With simple robots and structure, high mass-specific structural performance, and competitive throughput, this system demonstrates the potential for self-reconfiguring autonomous metamaterials for diverse applications.