DOI: 10.5061/dryad.kd51c5bm7
title: Data from: Fluidic torque-enabled object manipulation by microrobot collectives

description: Micro-scale systems experience strong viscous interactions because of the
 low-Reynolds-number regime in which they exist. This means that fluidic
 manipulation and actuation of passive objects can be enabled and
 influenced by the individual spin rate of micro-scale agents, the number
 of agents, and their positions relative to the objects. We explore these
 parameter spaces and find that the fluidic torque generated by a magnetic
 microrobot collective can be exploited to apply bidirectional torque to
 concentric ring structures and demonstrate this through physical
 experiments and numerical simulations. Additionally, we demonstrate how
 the fluidic torque of the microrobots can be exploited to actuate gear
 trains, rotate comparatively large 3D objects, dynamically self-assemble
 internally driven ring structures, and absorb and expel large numbers of
 circular objects. Finally, we show emergent behaviors where the microrobot
 collective’s morphology and method of locomotion change as a function of
 the spin rate of the microrobots and the size and shape of the surrounding
 objects.
description: # Data from: Fluidic torque-enabled object manipulation by microrobot
 collectives Access this dataset on Dryad; DOI:
 [10.5061/dryad.kd51c5bm7](https://doi.org/10.5061/dryad.kd51c5bm7) This
 dataset corresponds to the results shown in the manuscript: “Fluidic
 Torque-Enabled Object Manipulation by Microrobot Collectives”, Science
 Advances ### Data_for_Fig_1.zip Figure 1 characterizes the azimuthal flow
 fields generated by a single 300 μm diameter magnetic microrobot spinning
 at the air–water interface under a rotating magnetic field. ####
 Description of the data and file structure OVERVIEW This dataset contains
 the experimental measurements used to generate: * Fig. 1C: Flow velocity
 (u, mm/s) as a function of magnetic field frequency (Omega, Hz) at various
 normalized distances from the microrobot center. * Fig. 1D: Normalized
 flow velocity (u / (omega*R)) as a function of normalized distance (d/R),
 demonstrating inverse-square scaling consistent with low-Reynolds-number
 hydrodynamics. The raw data were extracted from video microscopy
 experiments in which 3 micrometer tracer particles were used to visualize
 local fluid velocities around a spinning microrobot. FILES INCLUDED 1\. u
 vs omega at 5R.xlsx Description: Flow velocity as a function of magnetic
 field frequency measured at d/R = 5. Columns include: Magnetic field
 frequency (Hz), measured flow velocity u (mm/s) This file was used to
 generate the d/R = 5 curve in Fig. 1C. 2\. u vs omega at 7.5R.xlsx
 Description: Flow velocity as a function of magnetic field frequency
 measured at d/R = 7.5. Columns include: Magnetic field frequency (Hz),
 measured flow velocity u (mm/s) This file was used to generate the d/R =
 7.5 curve in Fig. 1C. 3\. u vs omega at 10R.xlsx Description: Flow
 velocity as a function of magnetic field frequency measured at d/R = 10.
 Columns include: Magnetic field frequency (Hz), measured flow velocity u
 (mm/s) This file was used to generate the d/R = 10 curve in Fig. 1C. 4\. u
 vs distance normalised.xlsx Description: Normalized velocity data used to
 generate Fig. 1D. Columns include: Normalized distance d/R, Magnetic field
 frequency (Hz), Measured flow velocity u (mm/s), Normalized velocity u /
 (omega*R) This file demonstrates the scaling: u is proportional to (omega
 * R) / (d/R)^2^, which is expected for low-Reynolds-number flow generated
 by a rotating micro-disk. EXPERIMENTAL CONTEXT Microrobot properties:
 (Diameter: 300 micrometers), (Radius R = 150 micrometers), Located at the
 air–water interface, Actuated by a rotating magnetic field Key variables:
 Omega = magnetic field frequency (Hz) omega = microrobot angular velocity
 (rad/s) d = distance from microrobot center R = microrobot radius u =
 local flow velocity (mm/s) Measurements were extracted from 30
 frames-per-second recordings using particle tracking techniques. Flow
 immediately adjacent to the microrobot boundary was not included because
 it exceeded imaging resolution limits. --- ### Data_for_Fig_2.zip Figure 2
 quantifies the programmable co- and counter-rotation of concentric ring
 structures driven by a rotating magnetic microrobot collective. ####
 Description of the data and file structure OVERVIEW This dataset contains
 the experimental and simulation measurements used to generate: * Fig. 2A:
 Inner ring angular velocity (omega_ring) as a function of the number of
 microrobots in the annulus region (N_annulus) for various field
 frequencies (Omega). * Fig. 2E: Heat map of experimental inner ring
 angular velocity across the (N_annulus, Omega) parameter space when
 N_center = 20. * Fig. 2F: Heat map of simulated inner ring angular
 velocity across the same parameter space. * Fig. 2G: Experimental and
 simulation comparison of omega_ring versus N_annulus at fixed Omega. *
 Fig. 2H: Experimental and simulation comparison of omega_ring versus Omega
 at fixed N_annulus. These data quantify how hydrodynamic torque generated
 by rotating microrobot collectives transfers to passive concentric ring
 structures. EXPERIMENTAL PARAMETERS Key variables: Omega = magnetic field
 frequency (Hz) omega_ring = angular velocity of passive ring (rad/s)
 N_annulus = number of microrobots in the annulus region N_center = number
 of microrobots in the center region Unless otherwise stated: N_center = 20
 for heat map experiments Field frequencies range from 5 Hz to 70 Hz Each
 experiment recorded 10 seconds at 30 frames per second Ring orientation
 was manually tracked every 10 frames Angular velocity was calculated from
 the slope of angular position versus time. Fluidic torque (tau) was
 estimated using the low-Reynolds-number drag torque approximation: tau = 8
 * pi * eta * R_ring^3^ * omega_ring where: eta = dynamic viscosity of
 water R_ring = ring radius omega_ring = measured angular velocity FILES
 INCLUDED (TYPICAL CONTENTS) The ZIP archive contains processed numerical
 datasets corresponding to: 1\. Experimental angular velocity vs N_annulus
 for multiple Omega values used to generate Fig. 2A. Columns include:
 N_annulus, Omega (Hz), omega_ring (rad/s) Experimental heat map data
 (N_center = 20) Used to generate Fig. 2E. Columns include: N_annulus,
 Omega (Hz), omega_ring (rad/s) 2\. Simulation heat map data (N_center =
 20) used to generate Fig. 2F. Columns include: N_annulus, Omega (Hz),
 omega_ring (rad/s) 3\. Comparison datasets for fixed Omega (e.g., Omega =
 70 Hz) used to generate Fig. 2G. Columns include: N_annulus,
 omega_ring_experiment (rad/s), omega_ring_simulation (rad/s) 4\.
 Comparison datasets for fixed N_annulus (e.g., N_annulus = 30) used to
 generate Fig. 2H. Columns include: Omega (Hz), omega_ring_experiment
 (rad/s), omega_ring_simulation (rad/s) All reported values are
 steady-state angular velocities measured after the system reached dynamic
 equilibrium. DATA PROCESSING Experimental data were obtained using: *
 Video recordings at 30 frames per second * Manual tracking of ring angular
 position using a circular marker * Linear regression of angular position
 versus time to compute angular velocity * MATLAB used for interpolation
 and heat map generation Heat maps were generated by interpolating discrete
 measurements over the (N_annulus, Omega) parameter space using MATLAB
 interpolation functions. Simulations were performed using a
 low-Reynolds-number hydrodynamic interaction model of microrobots and
 passive rings. --- ### Data_for_Fig_3.zip Figure 3 demonstrates functional
 exploitation of fluidic torque generated by microrobot collectives,
 including gear actuation, 3D object rotation, dynamic self-assembly of
 ring structures, and absorption/expulsion of passive particles by a dense
 collective. OVERVIEW This dataset contains experimental measurements used
 to generate: * Fig. 3A: Angular velocities of mechanically coupled gears
 driven by a microrobot collective. * Fig. 3B: Angular position and angular
 velocity of a 3D floating object actuated by microrobots. * Fig. 3C:
 Collective radius of dynamically self-assembling ring structures as a
 function of magnetic field frequency. * Fig. 3D: Distribution of passive
 particle distances to arena boundaries under different field frequencies
 (absorption vs. expulsion behavior). These data quantify how fluidic
 torque can be harnessed for multi-body actuation and collective
 manipulation. EXPERIMENTAL PARAMETERS Key variables: Omega = magnetic
 field frequency (Hz) omega = angular velocity (rad/s or deg/s depending on
 dataset) theta = angular orientation (degrees or radians) N_microrobots =
 number of microrobots in the collective N_objects = number of passive
 objects General conditions: Experiments recorded at 30 frames per second,
 Steady-state behavior measured after approximately 20 seconds of driving
 at the frequency of interest, Microrobots operate below step-out threshold
 (&lt; 120 Hz) FILES INCLUDED The ZIP archive contains processed numerical
 datasets corresponding to: 1\. Gear Actuation Data (Fig. 3A) Description:
 Angular velocities of two mechanically coupled gears. Columns include:
 Time (s), Angular velocity of left gear (rad/s), Angular velocity of right
 gear (rad/s) The left gear is directly driven by a microrobot collective.
 The right gear is actuated through mechanical contact. Instantaneous
 angular velocities were computed from frame-to-frame angular displacement.
 2\. 3D Object Actuation Data (Fig. 3B) Description: Angular orientation
 and angular velocity of a floating 3D object driven by microrobots located
 in a thin liquid film on top of the object. Columns include: Time (s),
 Angular orientation (degrees), Angular velocity (deg/s) The object mass is
 approximately 45,000 times greater than a single microrobot. 3\. Dynamic
 Self-Assembly Data (Fig. 3C) Description: Collective radius of ring
 structures driven by embedded microrobots. Columns include: Magnetic field
 frequency Omega (Hz), Collective radius (mm), Number of rings or
 microrobots These measurements quantify how collective morphology changes
 as a function of driving frequency. At low frequencies, rings cluster. At
 higher frequencies, rings form a rotating circular structure with
 increasing collective radius. 4\. 1000-Microrobot Collective
 Absorption/Expulsion Data (Fig. 3D) Description: Nearest distance of
 passive particles to arena boundary under different frequencies. Columns
 include: Frequency Omega (Hz), Particle index, Distance to nearest arena
 edge (mm) At low frequency (e.g., 5 Hz): Particles are expelled toward the
 arena boundary. At high frequency (e.g., 70 Hz): Particles are distributed
 throughout the arena. Histograms in Fig. 3D were generated from these
 distance measurements. DATA PROCESSING Gear and 3D object angular
 positions were manually tracked frame-by-frame. Angular velocities were
 computed using: omega = d(theta)/dt Dynamic self-assembly collective
 radius was computed by measuring: Centroid of ring structures, Average
 radial distance of rings from centroid Particle-boundary distances were
 calculated using geometric distance measurements from particle centroid to
 nearest arena edge. MATLAB was used for: Histogram generation, Statistical
 analysis, Plot generation --- ### Data_for_Fig_4.zip Figure 4 examines how
 fluidic torque generated by microrobot collectives couples back to
 collective morphology and object geometry, leading to transitions between
 dispersed encapsulation and aggregated crawling behaviors. ####
 Description of the data and file structure OVERVIEW This dataset contains
 experimental measurements used to generate: * Fig. 4F: Angular velocity of
 circular, gear-shaped, and rod-shaped objects across a range of field
 frequencies. * Fig. 4G–I: Rotation of aggregating circular objects driven
 by a 100-microrobot collective. * Fig. 4J: Heat map of angular velocity
 across the (N_obj, Omega) parameter space. * Fig. 4K: Angular velocity
 comparison between single circular objects and aggregates of comparable
 area. These data quantify how object shape, size, and aggregation
 influence rotation rate and collective state (crawling vs encapsulation).
 EXPERIMENTAL PARAMETERS Key variables: Omega = magnetic field frequency
 (Hz) omega_obj = angular velocity of passive object (deg/s) theta =
 angular orientation (degrees) N_obj = number of aggregated circular
 objects Object diameter or length (mm) General conditions: * Experiments
 recorded at 30 frames per second * Objects have characteristic length ~4
 mm unless otherwise stated * Microrobot collective size ~100 microrobots
 for these experiments Collective behavior classified as: * Crawling state
 (aggregated clusters along object boundary) * Encapsulation state
 (dispersed rotation surrounding object) * Angular velocity was computed
 from linear regression of angular position vs time during steady-state
 motion. FILES INCLUDED The ZIP archive contains processed numerical
 datasets corresponding to: 1\. Object Angular Velocity vs Frequency (Fig.
 4F) Description: Angular velocity of circular, gear, and rod-shaped
 objects across multiple frequencies. Columns include: Frequency Omega
 (Hz), Angular velocity of circular object (deg/s), Angular velocity of
 gear-shaped object (deg/s), Angular velocity of rod-shaped object (deg/s)
 Hollow markers in Fig. 4F correspond to crawling state. Filled markers
 correspond to encapsulation state. 2\. Aggregated Object Rotation Data
 (Fig. 4G–I) Description: Angular velocity of aggregates formed by circular
 objects. Columns include: N_obj (number of objects in aggregate),
 Frequency Omega (Hz), Angular velocity (deg/s) Each dataset corresponds to
 steady-state measurements over a 10-second interval. 3\. Heat Map Data
 Across N_obj – Omega Parameter Space (Fig. 4J) Description: Angular
 velocity values measured across combinations of N_obj (number of
 aggregated circular objects) and Omega (Hz) Columns include: N_obj, Omega
 (Hz), Angular velocity (deg/s) Heat map was generated in MATLAB using
 interpolation across discrete measured points. 4\. Area-Matched Object
 Comparisons (Fig. 4K) Description: Angular velocity comparison between: *
 Single circular object (diameter 4 mm) * Single circular object (diameter
 7.5 mm) * Aggregate with N_obj = 20 * Aggregate with N_obj = 60 Columns
 include: Frequency Omega (Hz), Angular velocity (deg/s) These datasets
 demonstrate how concave aggregate boundaries shift the frequency threshold
 for crawling-to-encapsulation transition. DATA PROCESSING Object angular
 position was tracked manually or via image processing. Angular velocity
 was calculated as: omega_obj = d(theta)/dt Collective state (crawling vs
 encapsulation) was determined visually based on microrobot spatial
 distribution: Crawling: clustered microrobots moving along one side of
 object Encapsulation: dispersed microrobots surrounding object perimeter
 Heat maps were generated using MATLAB interpolation functions applied to
 discrete measurements.