Research ArticleSOFT ROBOTS

Millimeter-scale flexible robots with programmable three-dimensional magnetization and motions

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Science Robotics  24 Apr 2019:
Vol. 4, Issue 29, eaav4494
DOI: 10.1126/scirobotics.aav4494
  • Fig. 1 Schematic representation of the system for patterning discrete 3D magnetization.

    (A) Physical apparatus for patterning permanent magnetic particles in a UV-curable elastomeric matrix composite. DOF, degree of freedom. (B) Experimentally measured maximum cross-link thickness with respect to magnetic particle concentration. Error bars indicate SD. (C) Schematic representation of a dual-layer structure that has both horizontal and vertical magnetization components. Yellow arrows show the direction of magnetization patterned in each block. (D) Top view image of the dual-layer structure fabricated. Scale bar, 2 mm. (E) Out-of-plane magnetic flux distribution measured at the near surface of each layer separately using a magneto-optical sensor. The magneto-optical images are taken with the two layers fabricated independently to better visualize the magnetization profile.

  • Fig. 2 Flexible magnetic planar structures that have distributed 3D magnetization profiles.

    Yellow arrows represent the direction of local magnetization, and green arrows represent the direction of the actuating magnetic field. The materials are about 80 μm thick. The actuating magnetic field was 200 mT for “accordion” and less than 20 mT for all the others. All the items presented reversible and rapid transformation between the original shape and the folding shape. Scale bars, 2 mm.

  • Fig. 3 Models for predicting the shape changes and capabilities to tune the patterning angle in 3D.

    (A) Side view images showing large-angle deflection under 20 mT. Scale bars, 2 mm. (B) Numerical model of the large-angle deflection. (C) Side view images showing undulatory bending of a ring under 20 mT. Scale bars, 2 mm. (D) Simulation of the ring using the finite element method. (E) Geometry, dimension, and the magnetization profile of the tri-arm structure. Unit, mm. (F) Top view images of the tri-arm structures that bear different magnetization profiles. They were actuated under a 20-mT magnetic field out of the plane. Scale bars, 2 mm.

  • Fig. 4 Millimeter-scale segmented magnetic swimmer.

    (A) Magnetization profiles of three types of swimmers. The body length L is 4.5 mm. (B) Simulated TWC analysis of the swimmers. Blue markers represent the deformation at each phase, and the yellow dashed lines represent the equivalent deformation circle in one period. (C) Experimental swimming speed of the swimmers under different conditions. Solid triangles represent the average of six samples, and error bars represent their SDs. (D) Segmented swimmers fabricated from the same precursor in one process. Scale bar, 1 mm. (E) Path following of a magnetic swimmer. (F) Path following error of a magnetic swimmer, corresponding to the path shown in (E).

  • Fig. 5 Untethered multi-arm magnetic microgripper.

    (A) Geometry, magnetization profile, and working mechanism of a magnetic microgripper. Black arrows represent the direction of local magnetization in each part, and blue arrows represent the actuating magnetic field. (B) Illustration of the cargo transportation task. (C) Top view and side view images of the cargo transportation task in silicone oil (20 cSt; Sigma-Aldrich). Silicone oil is used to lift the body weight and to slow down the shape changes of the gripper to make open-loop control easier. Scale bar, 5 mm. (D) Close-up images of different microgrippers at various field strengths. Scale bars, 2 mm.

  • Fig. 6 Multi-legged paddle-crawling robot.

    (A) Image and magnetization profile of a paddle-crawling robot. Local magnetization is denoted by black arrows. When the legs labeled G1 perform power strokes, the legs labeled G2 perform recovery strokes, and vice versa. Scale bar, 2 mm. (B) Schematic representation of the gait from the side. (C) Top view images of the robot at different phases. (D) Illustration of the microchannel. The cross section of the channel is 4.7 mm by 1.0 mm. (E) Top view images showing the locomotion of the robot in a microchannel filled with silicone oil (20 cSt; Sigma-Aldrich). Silicone oil was used to lift the body weight and to slow down the stroke motions of the robot so that the camera could capture the motion clearly. The stroke motions and the velocity of the robot were faster in water. Scale bar, 4 mm.

  • Fig. 7 Untethered magnetic mirror mount for laser steering.

    (A) Close-up image of the mirror mount with a tiny mirror mounted at the center. The magnetization profile of the structure is shown in Fig. 2L. Scale bar, 2 mm. (B) Schematic representation of the laser steering experiment. (C) Coil system used in the experiment (43). (D) Target trajectories (orange) and experimental trajectories (blue) of the laser. The T-shaped and star-shaped trajectories are tracked at 0.5 and 0.2 Hz, respectively.

  • Fig. 8 Distribution of magnetic flux at the near surface of different samples.

    Modeled magnetic flux distribution, measured magnetic flux distribution, and the fitting results along the black dashed line of (A) a six-arm magnetic microgripper (front), (B) a six-arm magnetic microgripper (back), (C) an accordion, and (D) a multi-legged paddle-crawling robot. The data were collected 60 μm away from the sample surfaces. The magnitude of magnetization in the model was fitted to that in the measured data using least squares fitting. (E) Thin polymer sheet that carried a magnetically encoded QR code “UofT”. Scale bar, 2 mm. (F) Magnetic flux measured at the surface of the QR code sample corresponding to (E).

  • Table 1 Capabilities of major existing methods to pattern magnetic particles. 1D: Only binary magnetization can be patterned, e.g., longitudinal or perpendicular recording in a hard disk drive. 2D: Direction of magnetization in each layer is restricted to a single plane. 3D: Magnetization in each layer can be patterned in arbitrary direction. Discrete: Magnetization in each area is independent of adjacent areas. Continuum: Magnetization in each area cannot have sudden changes with respect to adjacent areas. N/A, not applicable.
    MethodMagnet typeShape of media*Template or mold requiredStates of magnetization
    Electrodeposition of
    magnetic particles on
    lithographically printed
    microstructures (18, 21, 22)
    Soft3DNoN/A
    Lithographic patterning of
    magnetic nanoparticles
    (2628)
    Soft2DNoDiscrete, 3D
    Magnetic particles linked by
    DNA (44)
    SoftN/ANoDiscrete, 1D
    Microassembly of magnetic
    components (33, 34, 45)
    Hard3DYesDiscrete, 3D
    Magnetic recording
    technology (46)
    Hard2DNoDiscrete, 1D
    Template-aided magnetizing
    (2931)
    Hard2DYesContinuum, 3D
    3D printing of ferromagnetic
    domains (35)
    Hard3DNoDiscrete, 2D
    This workHard2DNoDiscrete, 3D

    *Shape of media refers to the structure of the composite materials in which the magnetic particles are dispersed. 2D refers to planar structures, whereas 3D refers to solid 3D structures.

    †States of magnetization is defined as degrees of freedom related to the orientation of hard magnetic particles or preferred magnetic axes of soft magnetic particles in each area.

    • Table 2 Trajectory after results.

      Data were recorded with a 30-frames per s CMOS camera; each has no less than 10 cycles.

      TrajectoryFrequency
      (Hz)
      Path
      length
      (mm)
      RMS
      accuracy
      (mm)
      RMS
      precision
      (mm)
      T0.05611.78 ± 2.460.10 ± 0.14
      T0.5611.76 ± 2.420.10 ± 0.13
      Star0.05721.72 ± 2.600.08 ± 0.11
      Star0.2721.73 ± 2.490.62 ± 0.79

    Supplementary Materials

    • robotics.sciencemag.org/cgi/content/full/4/29/eaav4494/DC1

      Text S1. Manual material feeding for multilayer structures.

      Text S2. TWC analysis for magnetic swimmers.

      Text S3. Time required for fabricating a four-arm magnetic gripper.

      Text S4. Velocity of multi-legged paddle-crawling robot.

      Text S5. Turning motion of multi-legged paddle-crawling robot.

      Text S6. Magnetic dipole array model for calculating the distribution of magnetic flux.

      Text S7. Connection of hardware and flow of control signals.

      Text S8. Geometrical resolution of the custom UV lithography system.

      Text S9. Measurement of Young’s modulus of the material.

      Text S10. Magnitude of the magnetization developed by reorienting premagnetized particles.

      Fig. S1. Sequence diagram for patterning magnetization in a dual-layer structure.

      Fig. S2. Magnetization and dimensions of the devices fabricated.

      Fig. S3. TWC analysis of the deformation of type 1 swimmer at different magnetic field angles.

      Fig. S4. TWC analysis of the deformation of type 2 swimmer at different magnetic field angles.

      Fig. S5. TWC analysis of the deformation of type 3 swimmer at different magnetic field angles.

      Fig. S6. Velocity of the multi-legged robot crawling in silicone oil under a 1-Hz rotating magnetic field.

      Fig. S7. Velocity of the multi-legged robot swimming (drag-based paddling) at the interface of water and silicone oil under a 2-Hz rotating magnetic field.

      Fig. S8. Schematic representation of steering motion of the multi-legged paddle-crawling robot.

      Fig. S9. Schematic representation of the magnetic dipole array model.

      Fig. S10. Image of the physical apparatus.

      Fig. S11. Schematic representation of signal flow and hardware control.

      Fig. S12. Intensity profile of squares generated at the object plane.

      Fig. S13. Intensity profile of other shapes generated at the object plane.

      Fig. S14. Measurement of the stiffness of the material using a microforce sensor.

      Fig. S15. Electromagnetic coil system used for actuation.

      Fig. S16. Distribution of magnetic flux observed at the near surface of the samples cured in different field strength.

      Table S1. Dimension, magnetization, and parameters obtained from TWC analysis.

      Table S2. Coefficient of first-order terms of the Fourier series in TWC analysis.

      Table S3. Dimensions of the sample used in Young’s modulus measurement.

      Movie S1 (.mp4 format). Fabrication procedure and demonstration of the microrobots.

    • Supplementary Materials

      The PDF file includes:

      • Text S1. Manual material feeding for multilayer structures.
      • Text S2. TWC analysis for magnetic swimmers.
      • Text S3. Time required for fabricating a four-arm magnetic gripper.
      • Text S4. Velocity of multi-legged paddle-crawling robot.
      • Text S5. Turning motion of multi-legged paddle-crawling robot.
      • Text S6. Magnetic dipole array model for calculating the distribution of magnetic flux.
      • Text S7. Connection of hardware and flow of control signals.
      • Text S8. Geometrical resolution of the custom UV lithography system.
      • Text S9. Measurement of Young’s modulus of the material.
      • Text S10. Magnitude of the magnetization developed by reorienting premagnetized particles.
      • Fig. S1. Sequence diagram for patterning magnetization in a dual-layer structure.
      • Fig. S2. Magnetization and dimensions of the devices fabricated.
      • Fig. S3. TWC analysis of the deformation of type 1 swimmer at different magnetic field angles.
      • Fig. S4. TWC analysis of the deformation of type 2 swimmer at different magnetic field angles.
      • Fig. S5. TWC analysis of the deformation of type 3 swimmer at different magnetic field angles.
      • Fig. S6. Velocity of the multi-legged robot crawling in silicone oil under a 1-Hz rotating magnetic field.
      • Fig. S7. Velocity of the multi-legged robot swimming (drag-based paddling) at the interface of water and silicone oil under a 2-Hz rotating magnetic field.
      • Fig. S8. Schematic representation of steering motion of the multi-legged paddle-crawling robot.
      • Fig. S9. Schematic representation of the magnetic dipole array model.
      • Fig. S10. Image of the physical apparatus.
      • Fig. S11. Schematic representation of signal flow and hardware control.
      • Fig. S12. Intensity profile of squares generated at the object plane.
      • Fig. S13. Intensity profile of other shapes generated at the object plane.
      • Fig. S14. Measurement of the stiffness of the material using a microforce sensor.
      • Fig. S15. Electromagnetic coil system used for actuation.
      • Fig. S16. Distribution of magnetic flux observed at the near surface of the samples cured in different field strength.
      • Table S1. Dimension, magnetization, and parameters obtained from TWC analysis.
      • Table S2. Coefficient of first-order terms of the Fourier series in TWC analysis.
      • Table S3. Dimensions of the sample used in Young’s modulus measurement.
      • Legend for movie S1

      Download PDF

      Other Supplementary Material for this manuscript includes the following:

      • Movie S1 (.mp4 format). Fabrication procedure and demonstration of the microrobots.

      Files in this Data Supplement:

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