Organizations: Department of Engineering Mechanics,Northwestern Polytechnical University, Xi’an, 710072, China · Shenzhen Research Institute of Northwestern Polytechnical University, Shenzhen, 518063, China · School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 610031, China · School of Engineering, University of Liverpool, Liverpool, L69 3GH, U.K. · School of Aeronautics and Astronautics, Sun Yat-sen University, No.66 Gongchang Road, Guangming District, Shenzhen, 518107, Guangdong, China · School of Science, Qingdao University of Technology, Qingdao, 266520, China · Department of Mechanical Engineering, University of Birmingham, Birmingham, B15 2TT, UK · School of Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
Origami inspired architectures offer a powerful route toward lightweight, reconfigurable, and programmable robotic systems. Yet, a unified mechanics framework capable of seamlessly bridging rigid folding, elastic deformation, and stability driven transitions in compliant origami remains lacking. Here, we introduce a geometry consistent modeling framework based on discrete differential geometry (DDG) that unifies panel elasticity and crease rotation within a single variational formulation. By embedding crease panel coupling directly into a mid edge geometric discretization, the framework naturally captures rigid folding limits, distributed bending, multistability, and nonlinear dynamic snap through within one mechanically consistent structure. This unified description enables programmable control of stability and deformation across rigid and compliant regimes, allowing origami structures to transition from static folding mechanisms to active robotic modules. An implicit dynamic formulation incorporating gravity, contact, friction, and magnetic actuation further supports strongly coupled multiphysics simulations. Through representative examples spanning single fold bifurcation, deployable Miura membranes, bistable Waterbomb modules, and Kresling based crawling robots, we demonstrate how geometry driven mechanics directly informs robotic functionality. This work establishes discrete differential geometry as a foundational design language for intelligent origami robotics, enabling predictive modeling, stability programming, and mechanics guided robotic actuation within a unified computational platform.
Figures & tables
Figure 1: Schematic illustration of a flexible origami structure and its discrete modeling framework. (a) Minimal structural composition of a flexible origami unit, consisting of a single crease (highlighted in orange) connecting two shell panels (highlighted in blue). (b) Discretization of the shell module: the smooth panel surface is approximated by a triangular mesh, within which the discrete first and second fundamental forms are defined to characterize in-plane stretching and bending. (c) Discretization of the crease module: the crease is modeled as a combination of rotational elements and additional bending elements.
Figure 2: Mechanical response of the single-fold structure. (a) Deformation configuration under tensile displacement loading. (b,c) Boundary profile evolution for varying applied displacement d1 and different crease stiffness values. (d) Variation of the folding angle as a function of crease stiffness. (e) Two distinct deformation modes under shear displacement loading: mirror-symmetric and centrally-symmetric configurations. (f,g) Deformed boundary profiles corresponding to the two modes. (h,i) Evolution of nodal displacement and total energy in the two modes.
Figure 3: Mechanical behavior of rigid and flexible Miura origami structures. (a) Compressive deformation of the rigid Miura configuration, and (b) corresponding load–displacement response. (c) Evolution of the effective in-plane Poisson’s ratio. (d) Four-point bending configuration applied to the flexible Miura structure. The theoretical model is derived from Ref. [ 41 , 30 ] . (e) Evolution of the folding angle. (f) Comparison between the simulated curvature ratio and the analytical prediction. (g,h) Two deformed configurations under bending, exhibiting saddle-shaped and cylindrical surface morphologies.
Figure 4: Deployment simulation of Miura origami membranes. (a) Evolution of the deployed configuration at representative time instants. The deployable membrane configuration is derived from Ref. [ 39 ] . (b,c) Load–response curves under displacement-controlled and force-controlled actuation, respectively. (d) Influence of crease stiffness on the surface flatness of the deployed membrane.
Figure 5: Bistable mechanical behavior of the Waterbomb origami. (a) Two stable states of the flexible Waterbomb configuration and the associated flip. (b) Deformation profiles at representative instants during the state-switching process. (c,d) Load–displacement response and corresponding energy evolution. (e) Two stable states of the rigid Waterbomb configuration [ 33 ] and its snap-through behavior. (f,g) Time–displacement histories under free fall from heights z=5 and z=10 , leading to recovery and flip, respectively. (h,i) Quasi-static load–displacement response and energy distribution .
Figure 6: Multistable behavior of the rigid Kresling origami. (a–c) Load–displacement response and corresponding energy landscape of a single rigid Kresling unit under axial displacement loading. (d–f) Load–displacement response and energy distribution under circumferential rotational displacement loading. (g) Dynamic switching simulation of a four-unit rigid Kresling assembly exhibiting multistable transitions. (h) Time histories associated with the dynamic switching process. (i) Deformed configurations at representative time instants during multistable transition.
Figure 7: Dynamic locomotion of a compliant crawling robot actuated by Kresling-based units. (a–d) Mechanical characteristics of a compliant Kresling actuator, including its load–displacement response and multistable behavior. (e) One complete locomotion cycle of the crawling robot [ 47 ] . (f) Schematic of the external magnetic field and orientation of the net magnetization vector in the actuator. (g) Robot configurations under varying magnetic field strengths. (h) Definition of the friction coefficient governing foot–ground interaction. (i) Time histories of the foot displacement during robot locomotion.
Conventional soft robot actuators excel in compliance, but their uncontrolled deformations compromise accuracy and hinder scaling to multi-degree-of-freedom (DoF) systems. We introduce a MONOlithic ORIGAMI-inspired soft folding actuator design (MONORIGAMI) that establishes a design strategy based on spatially programmed stiffness anisotropy to preserve material compliance along desired folding directions while selectively restricting deformation in unwanted directions. The actuator leverages stiffness tiers based on material thickness, patterned in an origami-inspired geometry with facets and creases, converting unconstrained soft deformation into accurate, repeatable, and composable folding motions without additional reinforcements. The design is fully 3D-printable through a single-material, single-print process that requires no assembly. Each actuator serves as a scalable motion primitive, and linking and orienting multiple actuators mechanically programs multi-DoF trajectories. Using the same fundamental module, we demonstrate three 3D-printed soft multi-DoF robotic systems spanning distinct application domains: (1) a compact 4-DoF wearable haptic device for high-fidelity cutaneous feedback in virtual reality (VR), (2) a 3-DoF joystick for kinesthetic feedback in teleoperation, and (3) a modular robotic gripper capable of underwater operation with geometry-encoded grasp trajectories. These systems demonstrate the module's capabilities for compact multi-axis integration, controlled physical interaction, and geometry-programmed operation across different environments. Together, these results show that MONORIGAMI provides a general, composable, accessible, reliable, and scalable platform for high-precision soft multi-DoF robotics, addressing long-standing limitations in both soft actuator design and fabrication.
Jaehyung Jang, Zhenish Zhakypov, Jasmin Elena Palmer +3
IRiS Lab, Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea. · CHARM Lab, Department of Mechanical Engineering, Stanford University, Stanford, CA, USA.
Deployable structures inspired by origami have provided lightweight, compact, and reconfigurable solutions for various robotic and architectural applications. However, creating an integrated structural system that can effectively balance the competing requirements of high packing efficiency, simple deployment, and precise morphing into multiple load-bearing configurations remains a significant challenge. This study introduces a new class of hyper-Yoshimura origami, which exhibits a wide range of kinematically admissible and locally metastable states, including newly discovered symmetric "self-packing" and asymmetric "pop-out" states. This metastability is achieved by breaking a design rule of Yoshimura origami that has been in place for many decades. To this end, this study derives a new set of mathematically rigorous design rules and geometric formulations. Based on this, forward and inverse kinematic strategies are developed to stack hyper-Yoshimura modules into deployable booms that can approximate complex 3D shapes. Finally, this study showcases the potential of hyper-Yoshimura with a meter-scale pop-up cellphone charging station deployed at our university's bus transit station, along with a 3D-printed, scaled prototype of a space crane that can function as an object manipulator, solar tracking device, or high-load-bearing structure. These results establish hyper-Yoshimura as a promising platform for deployable and adaptable robotic systems in both terrestrial and space environments.
Ziyang Zhou, Yogesh Phalak, Vishrut Deshpande +3
Department of Mechanical Engineering, Virginia Tech,, Blacksburg & 24060, USA. · Department of Electrical Engineering and Computer Science, University of Wyoming, Laramie & 82071, USA.
We present FoldingAgent, an agentic framework for inferring explicit parametric folding programs directly from origami demonstration videos. Our framework leverages the reasoning power of a pre-trained Vision-Language Model (VLM) equipped with a suite of specialized tools that enable the agent to simulate geometric transitions, verify physical plausibility, retrieve and compare visual content, and evaluate its own predictions. To translate visual content into folding programs, we define a parametric space that consists of the paper's geometry and a set of parametric folding actions. Unlike models that predict static crease patterns, our agent operates sequentially and possesses the ability to re-plan its actions, effectively mitigating the compounding errors inherent in multi-step folding. Our approach takes a step toward closing the gap between human origami knowledge, which is primarily shared through unstructured visual demonstrations, and computational methods, which typically rely on structured, parametric representations such as a crease pattern or an executable parametric plan. We evaluate our approach on PurelandFold, a newly curated benchmark of diverse Pureland origami videos with ground-truth geometry and action labels. Our results demonstrate that by combining VLM reasoning with a set of specialized tools and physical simulation, we can successfully transform unstructured visual demonstrations into executable, physically plausible folding procedures.
Maya Moriya, Sigal Raab, Yael Vinker +1
Weizmann Institute of Science, Rehovot, Israel · MIT, Boston, USA