Programmable matter is a material whose properties can be programmed to achieve specific shapes or stiffnesses upon command. This concept requires constituent elements to interact and rearrange intelligently in order to meet the goal. This paper considers achieving programmable sheets that can form themselves in different shapes autonomously by folding. Past approaches to creating transforming machines have been limited by the small feature sizes, the large number of components, and the associated complexity of communication among the units. We seek to mitigate these difficulties through the unique concept of self-folding origami with universal crease patterns. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation. To implement this self-folding origami concept, we have developed a scalable end-to-end planning and fabrication process. Given a set of desired objects, the system computes an optimized design for a single sheet and multiple controllers to achieve each of the desired objects. The material, called programmable matter by folding, is an example of a system capable of achieving multiple shapes for multiple functions.reconfigurable robotics | self-assembly | multifunctional materials | computational origami E very day, scientists and engineers design new devices to solve a current problem. Each device has a unique function and thus has a unique form. The geometry of a cup is designed to hold liquid and is therefore different from that of a knife which is meant to cut. Even if both are made of the same material (e.g., metal, ceramic, or plastic), neither can perform both tasks. Is this redundancy in material, yet limitation in tasks entirely necessary? Is it possible to create a programmable material that can reshape for multiple tasks?Programmable matter is a material whose properties can be programmed to achieve specific shapes or stiffnesses upon command. In this paper we consider the theory and design of programmable matter material that can assume multiple desired shapes on demand.We have developed a unique concept of self-folding origami with universal crease patterns that decreases the complexity in individual elements and is scalable in the number and size of elements. Instead of relying on many individual subunits, which may be complex and difficult to orient correctly, we utilize a single sheet with repeated triangular tiles connected by flexible creases. This sheet can fold with a certain crease pattern to create multiple three-dimensional shapes, depending on which creases fold, in which direction, and in which order. We build on a large body of prior work in self-reconfiguring robotics to realize machines with changing shapes. Self-reconfiguring robots are modular systems whose bodies consist of multiple modules that can communicate and move relative to each other to form different shapes. These shapes support the different locomotive, manipulative, or sensing needs of the robo...

We introduce the problem of shape replication in the Wang tile self-assembly model. Given an input shape, we consider the problem of designing a self-assembly system which will replicate that shape into either a specific number of copies, or an unbounded number of copies. Motivated by practical DNA implementations of Wang tiles, we consider a model in which tiles consisting of DNA or RNA can be dynamically added in a sequence of stages. We further permit the addition of RNase enzymes capable of disintegrating RNA tiles. Under this model, we show that arbitrary genus-0 shapes can be replicated infinitely many times using only O(1) distinct tile types and O(1) stages. Further, we show how to replicate precisely n copies of a shape using O(log n) stages and O(1) tile types.

This paper considers planning and control algorithms that enable a programmable sheet to realize different shapes by autonomous folding. Prior work on self-reconfiguring machines has considered modular systems in which independent units coordinate with their neighbors to realize a desired shape. A key limitation in these prior systems is the typically many operations to make and break connections with neighbors, which lead to brittle performance. We seek to mitigate these difficulties through the unique concept of self-folding origami with a universal fixed set of hinges. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation.We describe the planning algorithms underlying these self-folding sheets, forming a new family of reconfigurable robots that fold themselves into origami by actuating edges to fold by desired angles at desired times. Given a flat sheet, the set of hinges, and a desired folded state for the sheet, the algorithms (1) plan a continuous folding motion into the desired state, (2) discretize this motion into a practicable sequence of phases, (3) overlay these patterns and factor the steps into a minimum set of groups, and (4) automatically plan the location of actuators and threads on the sheet for implementing the shape-formation control.

We present a universal crease pattern-known in geometry as the tetrakis tiling and in origami as box pleating-that can fold into any object made up of unit cubes joined face-to-face (polycubes). More precisely, there is one universal finite crease pattern for each number n of unit cubes that need to be folded. This result contrasts previous universality results for origami, which require a different crease pattern for each target object, and confirms intuition in the origami community that box pleating is a powerful design technique.

Abstract-Modular robots consist of many small units that attach together and can perform local motions. By combining these motions, we can achieve a reconfiguration of the global shape. The term modular comes from the idea of grouping together a fixed number of units into a module, which behaves as a larger individual component.Recently, a fair amount of research has focused on Crystalline robots, whose units (and modules) fit on a cubic lattice. When the proper module size is formed, these robots can reconfigure in linear time within a rather physically restrictive model, or in O(log n) time in a more unrestricted theoretical model.In this paper, we show that the results for Crystalline robots also apply to two other modular robots: M-TRAN and Molecube. The common requirement, for each robot type, is that a fixed number of units combine to create modules of specified shapes. In this way, we are able to simulate the actions of Crystalline modules. Previous reconfiguration bounds thus transfer automatically, as long as the robots are composed of the module shapes that we specify.