From Folding Mechanics to Robotic Function: A Unified Modeling Framework for Compliant Origami

2026-03-16

AI Summary

This work addresses the lack of a unified mechanical framework for compliant origami robots, which has hindered the integrated description of rigid folding, elastic deformation, and stability transitions. By leveraging discrete differential geometry, the authors develop a geometrically consistent variational model that couples panel bending with crease rotation, enabling a unified characterization of rigid-foldable limits, distributed bending, multistability, and nonlinear dynamic snapping behaviors. The formulation further supports implicit dynamic simulations incorporating gravity, contact, friction, and magnetic actuation. For the first time, discrete differential geometry is established as a foundational design language for intelligent origami robotics, facilitating programmable control over stability and deformation—from static structures to active modules. Validation through applications such as single-crease bifurcations, Miura sheets, Waterbomb bistable units, and Kresling crawling robots demonstrates the direct functional relevance of geometry-driven dynamics in robotic design.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• compliant origami
• unified mechanics framework
• rigid folding
• elastic deformation
• multistability

Innovation

• discrete differential geometry
• compliant origami
• multistability
• unified modeling framework
• robotic actuation