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The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials.…

Origami designs and structures have been widely used in many fields, such as morphing structures, robotics, and metamaterials. However, the design and fabrication of origami structures rely on human experiences and skills, which are both…

Origami, where two-dimensional sheets are folded into complex structures, is proving to be rich with combinatorial and geometric structure, most of which remains to be fully understood. In this paper we consider \emph{flat origami}, where…

Origami offers a versatile framework for designing morphable structures and soft robots by exploiting the geometry of folds. Tubular origami structures can act as continuum manipulators that balance flexibility and strength. However,…

We propose a novel computational framework for modeling and simulating origami structures. In this framework, bilinear solid-shell elements are employed to model the origami panels while crease folding is considered through the angle…

Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of…

While the grasping capability of robotic grippers has shown significant development, the ability to manipulate objects within the hand is still limited. One explanation for this limitation is the lack of controlled contact variation between…

We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to…

Origami and crumpling are two extreme tools to shrink a 3-D shell. In the shrink/expand process, the former is reversible due to its topological mechanism, while the latter is irreversible because of its random-generated creases. We observe…

Origami-inspired robots offer rapid, accessible design and manufacture with diverse functionalities. In particular, origami robots without conventional electronics have the unique advantage of functioning in extreme environments such as…

This paper presents the design of a new soft-rigid robotic platform, "GeoGami". We leverage origami surface capabilities to achieve shape contraction and to support locomotion with underactuated forms. A key challenge is that origami…

We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…

In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative…

We prove several hardness results on folding origami crease patterns. Flat-folding finite crease patterns is fixed-parameter tractable in the ply of the folded pattern (how many layers overlap at any point) and the treewidth of an…

Adaptation to various scene configurations and object properties, stability and dexterity in robotic grasping manipulation is far from explored. This work presents an origami-based shape morphing fingertip design to actively tackle the…

We study the three-dimensional equilibrium shape of a shell formed by a deployed accordion-like origami, made from an elastic sheet decorated by a series of parallel creases crossed by a central longitudinal crease. Surprisingly, while the…

Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled…

We explore the surprisingly rich energy landscape of origami-like folding planar structures. We show that the configuration space of rigid-paneled degree-4 vertices, the simplest building blocks of such systems, consists of at least two…

This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…

Origami structures have been proposed as a means of creating three-dimensional structures from the micro- to the macroscale, and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding…