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One Print, Many Moves: Monolithic Origami-inspired Folding Actuator for Composable Soft Multi-DoF Systems

Jaehyung Jang, Zhenish Zhakypov, Jasmin Elena Palmer, Melissa Klein, Jee-Hwan Ryu, Allison Mariko Okamura

arXiv:2609.00751v1cs.RO

TL;DR

Soft actuators offer compliance but uncontrolled deformation limits accurate, scalable multi-DoF robotics. MONORIGAMI addresses this gap with thickness-programmed origami stiffness in monolithic modules, demonstrating composable, directional motion across soft robotic systems. Its scope is bounded by post-processing demands and the limited stiffness contrast of single-material fabrication.

  • Problem

    Conventional soft actuators cannot sufficiently restrict undesired deformation, limiting accurate motion and scalability to multi-DoF systems.

  • Method

    MONORIGAMI uses spatially programmed stiffness anisotropy, with thickness-defined facets and creases integrated into single-material, monolithically printed composable actuators.

  • Results

    MONORIGAMI demonstrates directional, composable soft multi-DoF actuation, including a 4-DoF wearable haptic device with rotational DoFs retaining over 50% actuation magnitude above 4 Hz.

  • Takeaways & Limitations

    The module provides a general, reliable, and scalable platform for constructing accurate soft multi-DoF robotic systems.

  • Takeaways & Limitations

    The current process still requires post-processing, and single-material fabrication limits stiffness contrast between facets and creases.

Abstract

from arXiv · show

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.

Main Text: INTRODUCTION

MONORIGAMI addresses the accuracy and scalability limits of conventional soft actuators by programming stiffness anisotropy into origami-inspired, monolithically printed structures. Its modules preserve compliant folding where desired, suppress unwanted deformation, and compose into mechanically programmed multi-DoF systems.

  • Conventional soft actuators provide compliance but cannot sufficiently restrict undesired deformation, causing unintended motion, instability, and limited scalability for accurate tasks.
  • MONORIGAMI uses thickness-defined facets and creases to preserve compliance along prescribed folding directions while suppressing off-axis deformation under negative pressure.
  • Each MONORIGAMI actuator functions as a composable motion primitive whose serial or parallel arrangement mechanically encodes multi-DoF trajectories.
  • Locally varied wall thickness creates discrete stiffness tiers within a single material, integrating folding geometries, fluidic channels, and structural constraints without separate reinforcements or post-fabrication assembly.
  • MONORIGAMI establishes thickness-programmed origami stiffness as a general strategy for directional and composable soft actuation, supporting reliable and scalable multi-DoF robotic systems.

RESULTS

The actuator architecture combines origami stiffness tiers, modified crease topologies, and modular skeletons to produce sealed, directional motion and scalable multi-DoF devices. A single-print fabrication strategy integrates actuators, chambers, joints, and fluidic routing.

  • Design principle and composable architecture of MONORIGAMI actuators: Alternating stiff facets and compliant creases localize deformation at hinge-like regions, guiding pneumatic motion along predefined kinematic pathways.
  • Design principle and composable architecture of MONORIGAMI actuators: Thickened facet panels and compliant creases create spatial stiffness anisotropy that favors crease-direction folding and resists facet-crossing or off-axis deformation.
  • Design principle and composable architecture of MONORIGAMI actuators: For the closed crease network, N = 20 and M = 10 give DoF = N - 3M = -10, predicting an overconstrained configuration with no unconstrained rigid-folding mode.
  • Design principle and composable architecture of MONORIGAMI actuators: Removing the center Miura facet and replacing it with a flexible sealing panel converts the topology to one kinematic DoF while preserving enclosure.
  • Design principle and composable architecture of MONORIGAMI actuators: A modified waterbomb skeleton extends single-DoF modules to multi-DoF motion by aligning actuators with corresponding folding lines.
  • Design principle and composable architecture of MONORIGAMI actuators: Four paired unit structures form a fully functional 4-DoF device with independently controlled joints, while actuators, chambers, and fluidic routing are fabricated in one printing step.

Programming actuator performance through crease-facet geometry

MONORIGAMI programs actuator performance through crease thickness and designed folding angle, using geometry and an energy-based model to tune force, motion range, and dynamic response. Experiments across nine variants reveal complementary trade-offs between these geometric parameters.

  • Design model: The design model estimates effective folding energy by subtracting elastic crease energy from pressure work associated with chamber-volume change.Geometry defines the initial and folded volumes, crease stiffnesses, and folding angles; lateral parameters are optimized to minimize elastic-energy accumulation.
  • Experimental design: Nine variants combined crease thicknesses of 0.2, 0.3, and 0.4 mm with designed angles of 70°, 80°, and 90°.Each variant was evaluated for blocking torque, range of motion, bandwidth, and hysteresis using single-material SLA-printed actuators.
  • Blocking torque: 15.72 N·mm was the highest reported blocking torque, while 9.11 N·mm was the lowest across the tested crease-thickness and designed-angle combinations.The highest value occurred at 0.2 mm and 70°, whereas the lowest occurred at 0.4 mm and 90°; thicker creases and larger designed angles could increase elastic-energy loss.
  • Range of motion: 70.53° was the largest measured range of motion, while 43.35° was the smallest.The largest RoM occurred at 0.2 mm and 90°, and the smallest at 0.4 mm and 70°; increasing designed angle increased RoM but decreased measured blocking torque.
  • Design trade-offs: Crease thickness and designed angle provide complementary controls over force, motion, and dynamic response in each MONORIGAMI motion primitive.Thinner creases favor blocking torque and RoM, whereas thicker creases favor elastic recovery and bandwidth.

Load-bearing capacity and actuation speed

Load-bearing tests show that MONORIGAMI preserves accurate directional motion and repeatability under external loads, while actuation reaches full folding rapidly across loading conditions.

  • 56° to 26°: range of motion decreased as suspended load increased from 0 g to 100 g.The reduction is attributed to reduced internal volume at larger folding angles and lower generated torque.
  • 0° to −10°: material deformation increased as load rose from no load to 100 g.The x' reference frame defines negative positions as material deformation.
  • ±5%: endpoint displacement error remained within this bound across ten trials when normalized by unloaded full-scale displacement.The actuator maintained accurate rotational motion despite increasing material deformation under load.
  • Ten repeated trials showed high repeatability in actuation speed and range of motion under constant-load conditions.The consistency indicates stable torque generation across trials.
  • Approximately 50 ms: full folding was achieved under all tested load conditions.The reported sub-1 Hz bandwidth was attributed primarily to release time rather than response time.

4-DoF wearable haptics enabled by lightweight, compliant, and high-accuracy MONORIGAMI actuation

FingerPrint uses serially paired MONORIGAMI actuators in a compact monolithic structure to deliver four-DoF wearable cutaneous feedback in VR. It combines multi-axis workspace, compliant z translation, and high-frequency rotational actuation.

  • IMU-based fingertip pose and contact forces were mapped to actuator commands for real-time VR cutaneous feedback.Roll, pitch, and yaw were mapped one-to-one, while dorsal hand motion controlled z-axis translation.
  • Two-thirds: the updated FingerPrint reduced overall size to this fraction of an earlier prototype while providing a larger end-effector workspace.The device is described as lightweight, compliant, and accurate for VR skin-deformation feedback.
  • Four DoF: FingerPrint provides roll, pitch, yaw, and z-axis translation through four independently controlled actuator channels.Selective pair activation generates rotational motion, while simultaneous activation enables z-axis translation through compliant deformation.
  • ±17° roll and pitch, ±20° yaw, and 4.7 mm z-axis translation define the measured workspace.These motions correspond to typical fingertip orientation changes during manipulation and surface exploration.
  • >50% actuation magnitude above 4 Hz was retained across rotational DoFs.This response rate supports fast tactile interactions such as tapping, sliding, and button pressing.

A Compact 3-DoF Kinesthetic-Feedback Joystick for Teleoperation Enabled by Accurate and Compliant MONORIGAMI Actuation

A three-actuator parallel MONORIGAMI joystick provides compact, compliant kinesthetic feedback for teleoperation. Tests show rapid virtual-wall cues and displacement that tracks environmental force profiles across three axes.

  • 0.2–0.55 N: repeated virtual-wall encounters produced immediate kinesthetic cues for the operator.The virtual-wall setup used predefined workspace boundaries to trigger feedback at contact.
  • 35 × 35 × 35 mm³ and about 3 g: the monolithic joystick integrates its frame, actuators, and pneumatic channels in a compact form.Single-print fabrication removes assembly steps.
  • Three DoF: a delta-inspired parallel configuration uses three MONORIGAMI actuators for directionally resolved kinesthetic feedback.Each actuator functions as both a structural element and an actuation element.
  • Joystick displacement closely matched applied environmental force profiles in both temporal and amplitude dimensions.A follower-side 6 DoF force/torque sensor transmitted contact forces to selected joystick actuators in real time.
  • Geometry and material thickness allow directional stiffness and task-specific feedback to be tuned.Compliant behavior also enables passive return to neutral without external springs.

Modular soft robotic gripper with mechanically programmed finger actuation

The MONORIGAMI gripper uses serially combined actuators with varied crease thicknesses and design angles to encode finger trajectories. Replaceable monolithic fingers support task-specific grasping, reconfiguration, and underwater operation.

  • Different crease thicknesses and design angles generate mechanically programmed finger trajectories when actuators are connected in series.The actuator geometry determines each module’s folding characteristics.
  • Four modular fingers can be freely replaced to configure task-specific grasping strategies.Each finger’s motion profile is determined by its actuator configuration.
  • Identical actuator designs produce circular grasping, whereas varied designs produce elliptical grasping under identical pressure.Different actuator characteristics create different joint angles and therefore different contact-point arrangements.
  • Two-finger and four-finger configurations were demonstrated for objects with different geometries.Reconfiguration supported efficient task execution across the tested object shapes.
  • Underwater operation required no waterproofing treatment because the gripper uses soft materials and pneumatic actuation.Its monolithic, electronics-free construction enabled submerged operation.

DISCUSSION

MONORIGAMI redistributes softness through thickness-defined stiffness contrasts, preserving prescribed folding paths while suppressing off-axis motion. Its modules compose into multi-DoF systems through orientation, connection topology, and geometry, but fabrication, stiffness contrast, and sensing remain limitations.

  • MONORIGAMI design and operation: Thickness-defined stiffness contrasts preserve prescribed folding directions while suppressing off-axis motion, redistributing rather than eliminating material compliance.Under increasing loads, the prescribed rotational paths remain, but achievable range decreases and material deformation increases.
  • Composable architecture: Module orientation, serial–parallel topology, crease thickness, and folding angle generate multi-axis motions and nonuniform trajectories from individual directionally constrained modules.Embedded module connections and relative-motion constraints support system-level composition.
  • Demonstrated systems: A shared actuation principle supports a compact 4-DoF wearable haptic device, a 3-DoF teleoperation joystick, and a modular gripper with geometry-dependent finger trajectories.The systems use serial–parallel arrangements and heterogeneous geometric configurations for distinct system-level behaviors.
  • Limitations: Current limitations include post-processing burdens during miniaturization, restricted stiffness contrast from single-material fabrication, and absent integrated sensing with mostly open-loop actuation.The paper identifies support-free geometries, multi-material printing, geometric stiffening, and embedded sensing as future directions.

MONORIGAMI design and fabrication

MONORIGAMI is fabricated as a monolithic SLA-printed actuator using flexible resin and a five-step post-processing workflow. The workflow removes residual resin, seals drainage ports, cures the device, and removes supports.

  • Design and printing: The actuator is designed in SolidWorks, converted to an STL file, and prepared for printing with PreForm-generated support structures.A Form 3 SLA printer and flexible 80A resin are used to produce air-tight structures without additional processing.
  • Fabrication workflow: The fabrication process consists of five main steps.These steps are monolithic fabrication, residual-resin removal, drainage-port sealing, complete curing, and support removal.
  • Fabrication workflow: The entire device is fabricated monolithically using an SLA 3D printer.This establishes the single-print actuator body before post-processing.
  • Post-processing: Residual resin trapped in internal chambers is removed through drainage ports using a vacuum compressor and syringe needle.The cleaning step targets enclosed internal volumes before sealing.
  • Post-processing: Drainage ports are filled with uncured resin and partially cured using UV light to seal the openings.Sealing follows internal-resin removal.
  • Post-processing: Support structures are manually removed from the partially post-processed device.This is the final listed fabrication step.

Actuator Characterization Test Setup

Actuator characterization uses force sensing, marker-based motion tracking, pressure-wave inputs, and load tests to measure torque, bandwidth, hysteresis, and load-bearing behavior.

  • Blocking torque: Blocking torque is estimated from x-axis force measured with an ATI Nano 17 F/T sensor while a DC motor controls blocking position.The motor uses an encoder with 1024 pulses per revolution.
  • Blocking torque: The torque measurements use joint center–contact point distance as r and sample folding angles at 3° intervals.Experiments begin at Δθ_f = 0° and use 10 repetitions under several pressures.
  • Bandwidth: Bandwidth is measured by tracking a color marker at the actuator tip with video recorded at 240 FPS and analyzed using OpenCV.The response magnitude is calculated from the tracked motion.
  • Hysteresis: Hysteresis is measured with the same color-marker tracking method while pressure changes in 5-kPa increments under a 1-Hz square-wave input.The protocol reuses the motion-tracking approach while varying pressure stepwise.
  • Load-bearing test: Load-bearing behavior is tested at θ_d = 80° and t = 0.3 mm under loads of 0, 20, 50, and 100 g.The actuator is driven with a 1-Hz square-wave pressure input during tracking.

Virtual Reality Test Environment

The virtual-reality test environment combines IMU-based user input, simulated finger interaction, and pressure-driven MONORIGAMI feedback. Two implementations support threshold-triggered or force-proportional haptic actuation, while teleoperation returns position, force, and torque data to a joystick.

  • Version 1: Version 1 maps finger IMU orientation directly to the simulated finger and scales dorsal-hand IMU motion so 1° corresponds to 10 mm of z-axis translation.Reaction forces and directions are computed in MATLAB and sent through an Arduino Teensy to actuate solenoids.
  • Version 1: Version 1 generates signals upon virtual contact and actuates designated MONORIGAMI unit pairs when predefined translation and rotation thresholds are exceeded.The thresholds include z-axis translation and roll, pitch, and yaw limits.
  • Version 2: Version 2 uses the CHAI3D framework with finger-shaped avatars representing the user’s index finger and thumb.The environment simulates virtual interaction forces during contact.
  • Version 2: Upon contact in Version 2, FingerPrints receive air-pressure commands proportional to calculated interaction-force magnitude.This implementation couples simulated force magnitude to pneumatic feedback.
  • Virtual environment: The virtual environment can specify object mass, friction, and effective stiffness, combining dynamic force-producing objects with visual task-guidance objects.The example includes an interactive cube and visual hoops and target area.
  • Teleoperation: The teleoperation system sends follower position, force, and torque data back to the operator so the joystick can provide kinesthetic feedback.Communication occurs through TCP/IP between the Panda follower robot and a PC.
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