A Universal Crease Pattern for Folding Orthogonal Shapes

Benbernou, Nadia M.; Demaine, Erik D.; Demaine, Martin L.; Ovadya, Aviv

doi:10.21236/ada524705

Cited by 30 publications

(30 citation statements)

References 3 publications

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“…1), which has square subunits composed of eight isosceles triangles. Motivated by programmable matter, we recently proved that an n × n box-pleat tiling has as a folded state any polyhedral surface made up of OðnÞ unit cubes on the cubic lattice (18). Another theorem guarantees that any such folded state can be reached by a continuous folding motion without the material penetrating itself (19).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The planning process consists of four distinct algorithms: the input to the process is one or more folded states of a common box-pleat grid, which can be computed by the universality algorithm of ref. 18 or designed by human origamists. The output is a design of a programmable matter sheet and controllers for folding that sheet into any of the input shapes.…”

Section: Processmentioning

confidence: 99%

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Programmable matter by folding

Hawkes

Benbernou

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

577

474

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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...

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Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Processmentioning

confidence: 99%

Programmable matter by folding

Hawkes

Benbernou

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

577

474

View full text Add to dashboard Cite

show abstract

“…Moreover, some origami crease patterns have a property of universality [4], [5], [13]. This means that with a large enough sheet of paper, or small enough features, any 3-D structure can be sculpted.…”

Section: Origami-inspired Robotsmentioning

confidence: 99%

An Origami-Inspired Approach to Worm Robots

Önal

Wood

Rus

2013

IEEE/ASME Trans. Mechatron.

301

174

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Abstract-This paper presents an origami-inspired technique which allows the application of 2-D fabrication methods to build 3-D robotic systems. The ability to design robots as origami structures introduces a fast and low-cost fabrication method to modern, real-world robotic applications. We employ laser-machined origami patterns to build a new class of robotic systems for mobility and manipulation. Origami robots use only a flat sheet as the base structure for building complicated bodies. An arbitrarily complex folding pattern can be used to yield an array of functionalities, in the form of actuated hinges or active spring elements. For actuation, we use compact NiTi coil actuators placed on the body to move parts of the structure on-demand. We demonstrate, as a proof-of-concept case study, the end-to-end fabrication and assembly of a simple mobile robot that can undergo worm-like peristaltic locomotion. 1

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“…In mathematics, this grid is called the tetrakis tiling. The n×n box-pleat pattern was recently shown to be universal in that crease patterns formed by subsets of the hinges fold into all possible orthogonal shapes made out of O(n) cubes [BDDO09]. Therefore, exponentially many shapes can be made from different subsets of one common hinge pattern, forcing this collection of foldings to share many creases.…”

Section: Introductionmentioning

confidence: 99%

Planning to fold multiple objects from a single self-folding sheet

Benbernou

Demaine

et al. 2011

Robotica

Self Cite

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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.

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A Universal Crease Pattern for Folding Orthogonal Shapes

Cited by 30 publications

References 3 publications

Programmable matter by folding

Programmable matter by folding

An Origami-Inspired Approach to Worm Robots

Planning to fold multiple objects from a single self-folding sheet

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