From Fold to Function: Dynamic Modeling and Simulation-Driven Design of Origami Mechanisms

TL;DR

A design framework for origami mechanism simulation that utilizes MuJoCo's deformable-body capabilities and allows users to generate physically consistent simulations that capture both the geometric structure of origami mechanisms and their interactions with external objects and surfaces is presented.

Abstract

Origami-inspired mechanisms can transform flat sheets into functional three-dimensional dynamic structures that are lightweight, compact, and capable of complex motion. These properties make origami increasingly valuable in robotic and deployable systems. However, accurately simulating their folding behavior and interactions with the environment remains challenging. To address this, we present a design framework for origami mechanism simulation that utilizes MuJoCo's deformable-body capabilities. In our approach, origami sheets are represented as graphs of interconnected deformable elements with user-specified constraints such as creases and actuation, defined through an intuitive graphical user interface (GUI). This framework allows users to generate physically consistent simulations that capture both the geometric structure of origami mechanisms and their interactions with external objects and surfaces. We demonstrate our method's utility through a case study on an origami catapult, where design parameters are optimized in simulation using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and validated experimentally on physical prototypes. The optimized structure achieves improved throwing performance, illustrating how our system enables rapid, simulation-driven origami design, optimization, and analysis.

Figures (9)

• Figure 1: An overview of the proposed framework: users define their origami designs through a graphical user interface (GUI), which automatically converts the specifications into a MuJoCo compatible simulation model. The simulation environment then generates data through dynamically interacting with the modeled mechanism which can be used as feedback for design optimization. We validate the final optimized configuration by fabricating the design in hardware and demonstrating improved performance compared to non-optimized variants.
• Figure 2: (Left) purple circles show the key points, yellow highlights key points with defined actuation, black lines are boundary edges, and red lines are creases. Our algorithm converts input from the GUI (left) into MuJoCo XML format to simulate the specified components (upper right), and by using the actuated key points at the very tip of each arm, we can raise and move the mechanism (lower right), dynamically interacting with a rigid sphere placed on the top panel of the mechanism.
• Figure 3: Examples of standard origami fold patterns processed through our framework. The left column shows user-defined specifications in the graphical interface, where key points (purple) and crease lines (red) define the geometric relationships between panels (actuations omitted for clarity). The middle column shows the corresponding 2D renderings of the generated MuJoCo flex sheets, and the right column shows the resulting 3D closed and actuated mechanisms. From top to bottom: (1) parallel strip folds forming an accordion-like structure; (2) a corrugation pattern with V-shaped valley folds supporting a central mountain ridge; (3) a modular origami actuator block achieving rotational motion through coordinated folding; and (4) a modular origami actuator block achieving horizontal contraction.
• Figure 4: Examples of origami mechanisms interacting with their environment. (A) An origami gripper that can push, grasp, and release an object. (B) An origami catapult where the top panel rotates upward under lateral actuation. (C) A walker that propels itself forward on the ground plane through cyclic contraction and release. (D) A triangular, legged origami mechanism capable of balancing a rolling sphere by modulating actuation across its legs. The purple arrows indicate the direction of motion of each structure.
• Figure 5: Optimization of the origami catapult mechanism over two design parameters: (1) the sector angle of the mountain folds ($\theta$) and (2) the length of the throwing arm ($l$). The top row shows the initial and optimized configurations of the mechanism. The bottom row illustrates the CMA-ES optimization process, where the population of candidate designs progressively converges toward the region corresponding to maximal throwing distance.