arXiv subjects

Robert J. Lang

Publications and source records attributed to Robert J. Lang.

5 recordsLinked to original sources

arXiv2026

COrigami: An AI Pipeline for Co-Designing Flat-Foldable Visually Recognisable Origami

While generative AI has achieved remarkable success in solving problems with verifiable solutions, generating physical art that satisfies both strict geometric constraints and subjective visual aesthetics remains a challenge. This paper presents an approach to tackle these difficulties in the domain of computational origami, a mathematically rigid environment that grounds artistic design within the equations of flat foldability. We present COrigami, an end-to-end AI-driven pipeline that assists the design cycle by generating crease patterns from natural language. Our pipeline involves generating a semantic stick figure, computing a base packing, solving for a flat-foldable crease pattern, shaping the flat-folded crease pattern, and refining the generated model using reinforcement learning driven by an autonomous aesthetic evaluation loop. Our system acts as a highly effective collaborative assistant, generating structural starting points that human artists can further expand and shape. By integrating algorithmic optimisation with autonomous aesthetic critique, this work demonstrates how AI systems can satisfy multi-objective physical constraints to enable reliable, mathematically grounded co-creativity.

cs.AI↗

arXiv2020

Bidirectional Self-Folding with Atomic Layer Deposition Nanofilms for Microscale Origami

Origami design principles are scale invariant and enable direct miniaturization of origami structures provided the sheets used for folding have equal thickness to length ratios. Recently, seminal steps have been taken to fabricate microscale origami using unidirectionally actuated sheets with nanoscale thickness. Here, we extend the full power of origami-inspired fabrication to nanoscale sheets by engineering bidirectional folding with 4 nm thick atomic layer deposition (ALD) SiNx-SiO2 bilayer films. Strain differentials within these bilayers result in bending, producing microscopic radii of curvature. We lithographically pattern these bilayers and localize the bending using rigid panels to fabricate a variety of complex micro-origami devices. Upon release, these devices self-fold according to prescribed patterns. Our approach combines planar semiconductor microfabrication methods with computerized origami design, making it easy to fabricate and deploy such microstructures en masse. These devices represent an important step forward in the fabrication and assembly of deployable micromechanical systems that can interact with and manipulate micro- and nanoscale environments.

physics.app-ph↗

arXiv2017

Sculpting the Vertex: Manipulating the Configuration Space Topography and Topology of Origami Vertices to Design Mechanical Robustness

The geometric, aesthetic, and mathematical elegance of origami is being recognized as a powerful pathway to self-assembly of micro and nano-scale machines with programmable mechanical properties. The typical approach to designing the mechanical response of an ideal origami machine is to include mechanisms where mechanical constraints transform applied forces into a desired motion along a narrow set of degrees of freedom. In fact, to date, most design approaches focus on building up complex mechanisms from simple ones in ways that preserve each individual mechanism's degree of freedom (DOF), with examples ranging from simple robotic arms to homogenous arrays of identical vertices, such as the well-known Miura-ori. However, such approaches typically require tight fabrication tolerances, and often suffer from parasitic compliance. In this work, we demonstrate a technique in which high-degree-of-freedom mechanisms associated with single vertices are heterogeneously combined so that the coupled phase spaces of neighboring vertices are pared down to a controlled range of motions. This approach has the advantage that it produces mechanisms that retain the DOF at each vertex, are robust against fabrication tolerances and parasitic compliance, but nevertheless effectively constrain the range of motion of the entire machine. We demonstrate the utility of this approach by mapping out the configuration space for the modified Miura-ori vertex of degree 6, and show that when strung together, their combined configuration spaces create mechanisms that isolate deformations, constrain the configuration topology of neighboring vertices, or lead to sequential bistable folding throughout the entire origami sheet.

cond-mat.soft↗

arXiv2015

Rigid Origami Vertices: Conditions and Forcing Sets

We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.

math.MG↗

arXiv2010

Circle Packing for Origami Design Is Hard

We show that deciding whether a given set of circles can be packed into a rectangle, an equilateral triangle, or a unit square are NP-hard problems, settling the complexity of these natural packing problems. On the positive side, we show that any set of circles of total area 1 can be packed into a square of size 4/\sqrt{pi}=2.2567... These results are motivated by problems arising in the context of origami design.

cs.CG↗