Programmable Matter Research Articles

Adaptive collective responses to local stimuli in anonymous dynamic networks

We develop a framework for self-induced phase changes in programmable matter in which a collection of agents with limited computational and communication capabilities can collectively perform appropriate global tasks in response to local stimuli that dynamically appear and disappear. Agents are represented by vertices in a dynamic graph G whose edge set changes over time, and stimuli are placed adversarially on the vertices of G where each agent is only capable of recognizing a co-located stimulus. Agents communicate via token passing along edges to alert other agents to transition to an Aware state when stimuli are present and an Unaware state when the stimuli disappear. We present an Adaptive Stimuli Algorithm that can handle arbitrary adversarial stimulus dynamics, while an adversary (or the agents themselves) reconfigures the connections (edges) of G over time in a controlled way. This algorithm can be used to solve the foraging problem on reconfigurable graphs where, in addition to food sources (stimuli) being discovered, removed, or shifted arbitrarily, we would like the agents to consistently self-organize, using only local interactions, such that if the food remains in a position long enough, the agents transition to a gather phase in which many collectively form a single large component with small perimeter around the food. Alternatively, if no food source has existed recently, the agents should undergo a self-induced collective phase change and switch to a search phase in which they distribute themselves randomly throughout the graph to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable, withstanding competing broadcast waves of state transition that may interfere with each other. Like a physical phase change, such as the ferromagnetic models underlying the gather and search algorithms used for foraging, microscopic changes in the environment trigger these macroscopic, system-wide transitions as agents share information and respond locally to get the desired collective response.

Electrostatically Interacting Wannier Qubits in Curved Space

A derivation of a tight-binding model from Schrödinger formalism for various topologies of position-based semiconductor qubits is presented in the case of static and time-dependent electric fields. The simplistic tight-binding model enables the description of single-electron devices at a large integration scale. The case of two electrostatically Wannier qubits (also known as position-based qubits) in a Schrödinger model is presented with omission of spin degrees of freedom. The concept of programmable quantum matter can be implemented in the chain of coupled semiconductor quantum dots. Highly integrated and developed cryogenic CMOS nanostructures can be mapped to coupled quantum dots, the connectivity of which can be controlled by a voltage applied across the transistor gates as well as using an external magnetic field. Using the anti-correlation principle arising from the Coulomb repulsion interaction between electrons, one can implement classical and quantum inverters (Classical/Quantum Swap Gate) and many other logical gates. The anti-correlation will be weakened due to the fact that the quantumness of the physical process brings about the coexistence of correlation and anti-correlation at the same time. One of the central results presented in this work relies on the appearance of dissipation-like processes and effective potential renormalization building effective barriers in both semiconductors and in superconductors between not bended nanowire regions both in classical and in quantum regimes. The presence of non-straight wire regions is also expressed by the geometrical dissipative quantum Aharonov–Bohm effect in superconductors/semiconductors when one obtains a complex value vector potential-like field. The existence of a Coulomb interaction provides a base for the physical description of an electrostatic Q-Swap gate with any topology using open-loop nanowires, with programmable functionality. We observe strong localization of the wavepacket due to nanowire bending. Therefore, it is not always necessary to build a barrier between two nanowires to obtain two quantum dot systems. On the other hand, the results can be mapped to the problem of an electron in curved space, so they can be expressed with a programmable position-dependent metric embedded in Schrödinger’s equation. The semiconductor quantum dot system is capable of mimicking curved space, providing a bridge between fundamental and applied science in the implementation of single-electron devices.

Rubik’s cube as in-situ programmable matter and a reconfigurable mechanical metamaterial

Rubik’s cube as in-situ programmable matter and a reconfigurable mechanical metamaterial

From Conventional to Programmable Matter Systems: A Review of Design, Materials, and Technologies

Programmable matter represents a system of elements whose interactions can be programmed for a certain behavior to emerge (e.g., color, shape) upon suitable commands (e.g., instruction, stimuli) by altering its physical characteristics. Even though its appellation may refer to a morphable physical material, programmable matter has been represented through several approaches from different perspectives (e.g., robots, smart materials) that seek the same objective: controllable behavior such as smart shape alteration. Researchers, engineers, and artists have expressed interest in the development of smart modeling clay as a novel alternative to conventional matter and classical means of prototyping. Henceforth, users will be able to do/undo/redo forms based on computed data (CAD) or interactions (sensors), which will help them unlock more features and increase the usefulness of their products. However, with such a promising technology, many challenges need to be addressed, as programmable matter relies on energy consumption, data transmission, stimuli control, and shape formation mechanisms. Furthermore, numerous devices and technologies are created under the name of programmable matter, which may pose ambiguity to the control strategies. In this study, we determine the basic operations required to form a shape, then review different realizations using the shape shifting ability of programmable matter and their fitting classifications, and finally discuss potential challenges.

The structural power of reconfigurable circuits in the amoebot model

AbstractThe amoebot model (Derakhshandeh et al. in: SPAA ACM, pp 220–222. https://doi.org/10.1145/2612669.2612712, 2014) has been proposed as a model for programmable matter consisting of tiny, robotic elements called amoebots. We consider the reconfigurable circuit extension (Feldmann et al. in J Comput Biol 29(4):317–343. https://doi.org/10.1089/cmb.2021.0363, 2022) of the geometric amoebot model that allows the amoebot structure to interconnect amoebots by so-called circuits. A circuit permits the instantaneous transmission of signals between the connected amoebots. In this paper, we examine the structural power of the reconfigurable circuits. We start with fundamental problems like the stripe computation problem where, given any connected amoebot structure S, an amoebot u in S, and some axis X, all amoebots belonging to axis X through u have to be identified. Second, we consider the global maximum problem, which identifies an amoebot at the highest possible position with respect to some direction in some given amoebot (sub)structure. A solution to this problem can be used to solve the skeleton problem, where a cycle of amoebots has to be found in the given amoebot structure which contains all boundary amoebots. A canonical solution to that problem can be used to come up with a canonical path, which provides a unique characterization of the shape of the given amoebot structure. Constructing canonical paths for different directions allows the amoebots to set up a spanning tree and to check symmetry properties of the given amoebot structure. The problems are important for a number of applications like rapid shape transformation, energy dissemination, and structural monitoring. Interestingly, the reconfigurable circuit extension allows polylogarithmic-time solutions to all of these problems.

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.

Multi-population dissolution in confined active fluids.

Autonomous out-of-equilibrium agents or cells in suspension are ubiquitous in biology and engineering. Turning chemical energy into mechanical stress, they generate activity in their environment, which may trigger spontaneous large-scale dynamics. Often, these systems are composed of multiple populations that may reflect the coexistence of multiple species, differing phenotypes, or chemically varying agents in engineered settings. Here, we present a new method for modeling such multi-population active fluids subject to confinement. We use a continuum multi-scale mean-field approach to represent each phase by its first three orientational moments and couple their evolution with those of the suspending fluid. The resulting coupled system is solved using a parallel adaptive level-set-based solver for high computational efficiency and maximal flexibility in the confinement geometry. Motivated by recent experimental work, we employ our method to study the spatiotemporal dynamics of confined bacterial suspensions and swarms dominated by fluid hydrodynamic effects. Our in silico explorations reproduce observed emergent collective patterns, including features of active dissolution in two-population active-passive swarms, with results clearly suggesting that hydrodynamic effects dominate dissolution dynamics. Our work lays the foundation for a systematic characterization and study of collective phenomena in natural or synthetic multi-population systems such as bacteria colonies, bird flocks, fish schools, colloid swimmers, or programmable active matter.

Programmable Matter with Free and High‐Resolution Transfiguration and Locomotion

Abstract“hot flow in the cold changes shape in a dead world comes matter to life”Programmable matter that allows free shape transfiguration and locomotion on command promises ubiquitous access to objects or functions of interest. Current approaches for the autonomous reshaping of solid objects (smart materials, soft actuators, modular robotics) are limited in spatial resolution and shape. Solid‐liquid phase change pumping as a mechanism for the contactless transfiguring and locomotion of solid objects is introduced. Thin objects are deformed into any intended shape with sub‐millimeter resolution and the ability to freely change their topology is demonstrated, including adding or removing holes, splitting and merging. The unique locomotion of objects through millimeter‐sized constrictions narrower than their body size is demonstrated, followed by restoring the original shape. This approach opens up avenues for developing autonomous programmable matter with free shape transfiguration.

Thermodynamics in Stochastic Conway’s Game of Life

Cellular automata can simulate many complex physical phenomena using the power of simple rules. The presented methodological platform expresses the concept of programmable matter, of which Newton’s laws of motion are an example. Energy is introduced as the equivalent of the “Game of Life” mass, which can be treated as the first level of approximation. The temperature presence and propagation was calculated for various lattice topologies and boundary conditions, using the Shannon entropy measure. This study provides strong evidence that, despite the principle of mass and energy conservation not being fulfilled, the entropy, mass distribution, and temperature approach thermodynamic equilibrium. In addition, the described cellular automaton system transitions from a positive to a negative temperature, which stabilizes and can be treated as a signature of a system in equilibrium. The system dynamics is presented for a few species of cellular automata competing for maximum presence on a given lattice with different boundary conditions.

Multimaterial Printing of Liquid Crystal Elastomers with Integrated Stretchable Electronics.

Liquid crystal elastomers (LCEs) have grown in popularity in recent years as a stimuli-responsive material for soft actuators and shape reconfigurable structures. To make these material systems electrically responsive, they must be integrated with soft conductive materials that match the compliance and deformability of the LCE. This study introduces a design and manufacturing methodology for combining direct ink write (DIW) 3D printing of soft, stretchable conductive inks with DIW-based "4D printing" of LCE to create fully integrated, electrically responsive, shape programmable matter. The conductive ink is composed of a soft thermoplastic elastomer, a liquid metal alloy (eutectic gallium indium, EGaIn), and silver flakes, exhibiting both high stretchability and conductivity (order of 105 S m-1). Empirical tuning of the LCE printing parameters gives rise to a smooth surface (<10 μm) for patterning the conductive ink with controlled trace dimensions. This multimaterial printing method is used to create shape reconfigurable LCE devices with on-demand circuit patterning that could otherwise not be easily fabricated through traditional means, such as an LCE bending actuator able to blink a Morse code signal and an LCE crawler with an on/off photoresistor controller. In contrast to existing fabrication methodologies, the inclusion of the conductive ink allows for stable power delivery to surface mount devices and Joule heating traces in a highly dynamic LCE system. This digital fabrication approach can be leveraged to push LCE actuators closer to becoming functional devices, such as shape programmable antennas and actuators with integrated sensing.

Exploiting compositional disorder in collectives of light-driven circle walkers.

Emergent behavior in collectives of "robotic" units with limited capabilities that is robust and programmable is a promising route to perform tasks on the micro and nanoscale that are otherwise difficult to realize. However, a comprehensive theoretical understanding of the physical principles, in particular steric interactions in crowded environments, is still largely missing. Here, we study simple light-driven walkers propelled through internal vibrations. We demonstrate that their dynamics is well captured by the model of active Brownian particles, albeit with an angular speed that differs between individual units. Transferring to a numerical model, we show that this polydispersity of angular speeds gives rise to specific collective behavior: self-sorting under confinement and enhancement of translational diffusion. Our results show that, while naively perceived as imperfection, disorder of individual properties can provide another route to realize programmable active matter.

DNA‐Encoded Synthetic Systems: Coding More than Life

DNA‐Encoded Synthetic Systems: Coding More than Life

The canonical amoebot model: algorithms and concurrency control

The amoebot model abstracts active programmable matter as a collection of simple computational elements called amoebots that interact locally to collectively achieve tasks of coordination and movement. Since its introduction at SPAA 2014, a growing body of literature has adapted its assumptions for a variety of problems; however, without a standardized hierarchy of assumptions, precise systematic comparison of results under the amoebot model is difficult. We propose the canonical amoebot model, an updated formalization that distinguishes between core model features and families of assumption variants. A key improvement addressed by the canonical amoebot model is concurrency. Much of the existing literature implicitly assumes amoebot actions are isolated and reliable, reducing analysis to the sequential setting where at most one amoebot is active at a time. However, real programmable matter systems are concurrent. The canonical amoebot model formalizes all amoebot communication as message passing, leveraging adversarial activation models of concurrent executions. Under this granular treatment of time, we take two complementary approaches to concurrent algorithm design. We first establish a set of sufficient conditions for algorithm correctness under any concurrent execution, embedding concurrency control directly in algorithm design. We then present a concurrency control framework that uses locks to convert amoebot algorithms that terminate in the sequential setting and satisfy certain conventions into algorithms that exhibit equivalent behavior in the concurrent setting. As a case study, we demonstrate both approaches using a simple algorithm for hexagon formation. Together, the canonical amoebot model and these complementary approaches to concurrent algorithm design open new directions for distributed computing research on programmable matter.

In materia implementation strategies of physical reservoir computing with memristive nanonetworks

Physical reservoir computing (RC) represents a computational framework that exploits information-processing capabilities of programmable matter, allowing the realization of energy-efficient neuromorphic hardware with fast learning and low training cost. Despite self-organized memristive networks have been demonstrated as physical reservoir able to extract relevant features from spatiotemporal input signals, multiterminal nanonetworks open the possibility for novel strategies of computing implementation. In this work, we report on implementation strategies of in materia RC with self-assembled memristive networks. Besides showing the spatiotemporal information processing capabilities of self-organized nanowire networks, we show through simulations that the emergent collective dynamics allows unconventional implementations of RC where the same electrodes can be used as both reservoir inputs and outputs. By comparing different implementation strategies on a digit recognition task, simulations show that the unconventional implementation allows a reduction of the hardware complexity without limiting computing capabilities, thus providing new insights for taking full advantage of in materia computing toward a rational design of neuromorphic systems.

Complex selective manipulations of thermomagnetic programmable matter

Programmable matter can change its shape, stiffness or other physical properties upon command. Previous work has shown contactless optically controlled matter or magnetic actuation, but the former is limited in strength and the latter in spatial resolution. Here, we show an unprecedented level of control combining light patterns and magnetic fields. A mixture of thermoplastic and ferromagnetic powder is heated up at specific locations that become malleable and are attracted by magnetic fields. These heated areas solidify on cool down, and the process can be repeated. We show complex control of 3D slabs, 2D sheets, and 1D filaments with applications in tactile displays and object manipulation. Due to the low transition temperature and the possibility of using microwave heating, the compound can be manipulated in air, water, or inside biological tissue having the potential to revolutionize biomedical devices, robotics or display technologies.

Machine Learning with Quantum Matter: An Example Using Lead Zirconate Titanate

Stephen Wolfram (2002) proposed the concept of computational equivalence, which implies that almost any dynamical system can be considered as a computation, including programmable matter and nonlinear materials such as, so called, quantum matter. Memristors are often used in building and evaluating hardware neural networks. Ukil (2011) demonstrated a theoretical relationship between piezoelectrical materials and memristors. We review that work as a necessary background prior to our work on exploring a piezoelectric material for neural network computation. Our method consisted of using a cubic block of unpoled lead zirconate titanate (PZT) ceramic, to which we have attached wires for programming the PZT as a programmable substrate. We then, by means of pulse trains, constructed on-the-fly internal patterns of regions of aligned polarization and unaligned, or disordered regions. These dynamic patterns come about through constructive and destructive interference and may be exploited as a type of reservoir network. Using MNIST data we demonstrate a learning machine.

Centralised connectivity-preserving transformations for programmable matter: A minimal seed approach

We study a model of programmable matter systems consisting of n devices lying on a 2-dimensional square grid which are able to perform the minimal mechanical operation of rotating around each other. The goal is to transform an initial shape A into a target shape B. We investigate the class of shapes which can be constructed in such a scenario under the additional constraint of maintaining global connectivity at all times. We focus on the scenario of transforming nice shapes, a class of shapes consisting of a central line L where for all nodes u in S either u∈L or u is connected to L by a line of nodes perpendicular to L. We prove that by introducing a minimal 3-node seed it is possible for the canonical shape of a line of n nodes to be transformed into a nice shape of n−1 nodes. We use this to show that a 4-node seed enables the transformation of nice shapes of size n into any other nice shape of size n in O(n2) time. We leave as an open problem the expansion of the class of shapes which can be constructed using such a seed to include those derived from nice shapes.

Rotation Control, Interlocking, and Self‐Positioning of Active Cogwheels

Gears and cogwheels are elemental components of machines. They restrain degrees of freedom and channel power into a specified motion. Building and powering small‐scale cogwheels are key steps toward feasible micro and nanomachinery. Assembly, energy injection, and control are, however, a challenge at the microscale. In contrast with passive gears, whose function is to transmit torques from one to another, interlocking and untethered active gears have the potential to unveil dynamics and functions untapped by externally driven mechanisms. Here, it is shown the assembly and control of a family of self‐spinning cogwheels with varying teeth numbers and study the interlocking of multiple cogwheels. The teeth are formed by colloidal microswimmers that power the structure. The cogwheels are autonomous and active, showing persistent rotation. Leveraging the angular momentum of optical vortices, we control the direction of rotation of the cogwheels. The pairs of interlocking and active cogwheels that roll over each other in a random walk and have curvature‐dependent mobility are studied. This behavior is leveraged to self‐position parts and program microbots, demonstrating the ability to pick up, direct, and release a load. The work constitutes a step toward autonomous machinery with external control as well as (re)programmable microbots and matter.

Creating three-dimensional magnetic functional microdevices via molding-integrated direct laser writing

Magnetically driven wireless miniature devices have become promising recently in healthcare, information technology, and many other fields. However, they lack advanced fabrication methods to go down to micrometer length scales with heterogeneous functional materials, complex three-dimensional (3D) geometries, and 3D programmable magnetization profiles. To fill this gap, we propose a molding-integrated direct laser writing-based microfabrication approach in this study and showcase its advanced enabling capabilities with various proof-of-concept functional microdevice prototypes. Unique motions and functionalities, such as metachronal coordinated motion, fluid mixing, function reprogramming, geometrical reconfiguring, multiple degrees-of-freedom rotation, and wireless stiffness tuning are exemplary demonstrations of the versatility of this fabrication method. Such facile fabrication strategy can be applied toward building next-generation smart microsystems in healthcare, robotics, metamaterials, microfluidics, and programmable matter.

A Bi-State Shape Memory Material Composite Soft Actuator

Shape memory materials have been widely used as programmable soft matter for developing multifunctional hybrid actuators. Several challenges of fabrication and effective modelling of these soft actuating systems can be addressed by implementing novel 3D printing techniques and simulations to aid the designer. In this study, the temperature-dependent recovery of an embedded U-shaped Shape Memory Alloy (SMA) and the shape fixity of a 3D-printed Shape Memory Polymer (SMP) matrix were exploited to create a bi-state Shape Memory Composite (SMC) soft actuator. Electrical heating allowed the SMA to achieve the bi-state condition, undergoing phase transformation to a U shape in the rubbery phase and a flat shape in the glassy phase of the SMP. A COMSOL Multiphysics model was developed to predict the deformation and recovery of the SMC by leveraging the in-built SMA constitutive relations and user-defined material subroutine for the SMP. The bi-state actuation model was validated by capturing the mid-point displacement of the 80 mm length × 10 mm width × 2 mm-thick 3D-printed SMC. The viability of the SMC as a periodic actuator in terms of shape recovery was addressed through modelling and simulation. Results indicated that the proposed COMSOL model was in good agreement with the experiment. In addition, the effect of varying the volume ratio of the SMA wire in the SMC on the maximum and recovered deflection was also obtained. Our model can be used to design SMC actuators with various performance profiles to facilitate future designs in soft robotics and wearable technology applications.