2024 7th International Conference on Soft Robotics (RoboSoft)San Diego, CA, USA. April 14-17, 2024

Compliant Electropermanent Magnets

2024 IEEE 7th International Conference on Soft Robotics (RoboSoft) | 979-8-3503-8181-8/24/$31.00 ©2024 IEEE | DOI: 10.1109/ROBOSOFT60065.2024.10521977

William R. Johnson III1 and Rebecca Kramer-Bottiglio1

Abstract— Modular and climbing robots have employed electropermanent magnets as a power-efficient alternative to electromagnets for tasks that involve attaching modules or exerting
forces on ferromagnetic surfaces. In this paper, we present
compliant electropermanent magnets that extend the benefitsof electropermanent magnets to the field of soft robotics. We
describe a process for designing compliant electropermanent
magnets with different materials and mixing ratios to achieve
desired properties without sacrificing the mechanical compliance necessary for integration into soft robots. Finally, wecharacterize the performance of the compliant electropermanent magnets and demonstrate their ability to repeatably andreversibly switch their magnetization ON and OFF.

I. I NTRODUCTION
The growing field of soft robotics aims to create robots
whose mechanical compliance makes them more robust,more versatile, and safer for interacting with humans [1].
Toward this goal, researchers have developed compliant
analogues to traditional robot components for sensing [2],[3], actuation [4], and computation [5].
A subset of soft robots leverage electromagnetism fortheir actuation strategies [6]–[8]. Many researchers embedmagnetic particles into silicone elastomers to make soft
magnetic composites that can be actuated with external
magnetic fields [9]–[12] or local magnetic fields [13], [14].
Kohls et al. designed a soft electromagnet with a coil ofliquid metal and a soft magnetic composite [15] and thenextended this work to produce an all-soft electric motor [16].
Li et al. introduced magnetic putty as a reprogrammable,
self-healing building material for soft robots [17].
As an alternative to power-hungry electromagnets, roboticists have made use of electropermanent magnets [18].
Electropermanent magnets consist of two permanent magnets
with the same magnetization but different coercivities [19].
A conductive coil is wrapped around the magnet suchthat a brief pulse of current can generate a magnetic fieldstrong enough to reverse the magnetization of the lowcoercivity magnet but not strong enough to affect the highcoercivity magnet. Thus, by selectively reversing the polarityof the low-coercivity magnet, the system can be turned ON(nonzero net magnetization) or OFF (neutral net magnetization). In contrast to electromagnets, which continuously draw
current, the electropermanent magnet only consumes energy
briefly when the state is switched; the permanent magnets
do not consume power, even in the ON state [20].

Fig. 1. Magnetic hysteresis curves for AlNiCo and NdFeB samples (oneeach) at a temperature of 300 K. With a far wider hysteresis loop, NdFeB has
a much higher coercivity. The vertical axis intercepts show that NdFeB also
has a greater remanent magnetization. Here, the magnetization is normalized
by the volume of the magnetic material, not the total volume of the sample.

Electropermanent magnets save energy for applications
where the switching frequency between ON and OFF islow [21]. Researchers have chosen electropermanent magnets
for modular robots that attach together to complete a task andlater detach [22]. Hong et al. employed electropermanent
magnets for a legged robot that climbs ferromagnetic surfaces [23]. In soft robotics, electropermanent magnets havebeen used in valves [24], [25] and as actuators [26], butthere is still no soft analogue to these rigid electropermanent
magnets. Modular soft robots need modular connectors thatare strong, energy-efficient, and congruent with their compliant bodies [27]; however, many modular soft robots use
rigid magnets [28]–[33], compromising on body compliance,or melting adhesives [34], which consume a large amountof energy. Park et al. introduced a soft robot that climbs
ferromagnetic surfaces [35], reminiscent of [23], but the
robot had to have a partially rigid body to accommodate
rigid permanent magnets.
In this paper, we present a compliant electropermanent
magnet, a soft analogue to electropermanent magnets previously introduced in the literature. Our experimental characterization provides soft roboticists the data they need todesign compliant electropermanent magnets to fit a varietyof specifications (e.g., modulus, pull-off force, coercivity,*This work was supported by NASA CT Space Grant under PTE Federal
Award No: 80NSSC20M0129. WRJ was supported by the National Science
Foundation (NSF) under grant no. IIS-1955225.
1 Dept. of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, USA will.johnson@yale.edu

979-8-3503-8181-8/24/$31.00 ©2024 IEEE

347

Authorized licensed use limited to: Yale University. Downloaded on May 24,2024 at 15:32:38 UTC from IEEE Xplore. Restrictions apply.

Fig. 2. Coercivity and remanent magnetization for AlNiCo composites
at different loading weight percents. Greater weight percents of magnetic
powder can lead to greater residual flux densities without changing thecoercivity. Here, the composite magnetization is the remanence normalized
by the volume of the composite, hence why greater weight percents show
greater magnetization (if we normalize by the volume of magnetic material,
all three magnetizations are similar). Each data point represents one sample
measured on the SQUID-VSM at a temperature of 300 K.

Fig. 3. Magnetic hysteresis curve for the 80% (by weight) EP sample at atemperature of 300 K compared to the curves from Figure 1. The sample wasmagnetized in a saturating field (2,400 kA/m), and the field was removed
immediately before this hysteresis was measured between −800 kA/m and800 kA/m. The hysteresis loop is no longer symmetric with respect to
M = 0 but rather shifted up such that the remanent magnetization (atH = 0) is larger on the upper part of the curve and smaller on the lower
part, meaning the material can be used as an electropermanent magnet. The
shaded regions visualize the asymmetry with respect to the horizontal axis.
The magnetization is normalized by the volume of the magnetic material.

remanent magnetization) for a diversity of applications, including modular connections, climbing robots, and pick andplace tasks. After a brief note on nomenclature (Section IA) and a description of our design process (Section II),we characterize the magnetic and mechanical properties ofour compliant magnets in Sections III and IV, respectively.
Finally, we demonstrate the compliant electropermanent
magnet in Section V.

reversed without affecting the high-coercivity magnet, andwhen the magnets are oppositely magnetized (the OFF state)
there will be no net magnetization.
While previous electropermanent magnets have been assemblies of rigid components, here we present the design ofa composite material using AlNiCo powder (AL-NICO-01P.200M; American Elements) and NdFeB powder (FE-NDB02R-P.10UM; American Elements) mixed into a silicone
elastomer (Eco-Flex 50; Smooth-On). An advantage of thisapproach, in addition to mechanical compliance, is the ability
to tune the properties of the electropermanent magnets bychanging the mixing ratios.
Our design process involves first characterizing the magnetic properties of the two magnetic materials, especially
coercivity and remanent magnetization (Section III). Fromthese properties, we calculate the electropermanent (EP)mixing ratio (by weight) where the AlNiCo and NdFeB parts
will have the same remanence. In Section IV, we investigate
the trade-offs between mechanical compliance and pull-off
force as a function of magnetic powder weight percent. The
compositions of the two magnetic powders, which can beused to calculate the weight of an electropermanent magnet,
are given in Table I. The average particle size is ≤ 10 µm
for the NdFeB powder and ≤ 74 µm for the AlNiCo powder.

A. Nomenclature
In soft robotics, the word “soft” commonly refers tomaterials and structures with low elastic moduli, affording
them bulk mechanical compliance [1]. Physicists who study
magnetism use the word “soft” to refer to magnetic materials
with low coercivity, meaning their polarity can be easily
reversed in the presence of weak applied magnetic fields [17].
To eschew confusion, we avoid the word “soft” when possible in the remaining sections of this paper; instead we use“compliant” to refer to a material’s mechanical properties(i.e., low elastic modulus) and “low-coercivity” to refer to amaterial’s magnetic properties.
II. D ESIGN AND FABRICATION
Researchers have built electropermanent magnets using aluminum-nickel-cobalt (AlNiCo) as the low-coercivity
magnet and neodymium-iron-boron (NdFeB) as the highcoercivity magnet [18]–[26]. The critical design parameters
in selecting these materials are coercivity and remanent
magnetization: the two magnets should have similar magnetization but significantly different coercivities. With theseparameters, the polarity of the low-coercivity magnet can beIII. V IBRATING S AMPLE M AGNETOMETRY
The magnetic properties of the composite materials were
tested with a superconducting quantum interference device(SQUID) magnetometer (MPMS 3; Quantum Design) using
348

Authorized licensed use limited to: Yale University. Downloaded on May 24,2024 at 15:32:38 UTC from IEEE Xplore. Restrictions apply.

AlNiCo
Al
10%
Ni
19%
Co
13%
Fe
58%

NdFeB
Nd
19.1%
Fe
73.7%
B
0.9%
Pr
6.3%

TABLE IC OMPOSITION OF M AGNETIC P OWDERS BY W EIGHT

vibrating-sample magnetometry (VSM). Samples were prepared by mixing magnetic powder (AlNiCo or NdFeB) withpre-cure silicone (Eco-Flex 50) at a given weight percent
and curing the composite in an acrylic mold for four hours atroom temperature. This process produced cylindrical samples
that were 1.6 mm thick and 1.4 mm in diameter.
The magnetic hysteresis loops for the 80% (by weight)
AlNiCo and NdFeB samples, as measured by SQUID-VSM,
are shown in Figure 1. The magnetic hysteresis is measured
by applying a varying magnetic field H and measuring
the magnetic moment of the sample. The vertical axis is
the magnetization of the sample, defined as the magnetic
moment normalized by volume. Here, we normalize by thevolume of the magnetic material, ignoring the volume of thesilicone in the composite. The remanent magnetization, themagnetization of the sample in the absence of an appliedfield, is the vertical axis intercept of the hysteresis curve,
and the coercivity, the external field required to reverse thepolarity of the sample, is the horizontal intercept. The widthof the NdFeB hysteresis loop confirms that its coercivity(676 kA/m) is an order of magnitude greater than thecoercivity of AlNiCo (42 kA/m). Moreover, the remanent
magnetization of NdFeB (456 kA/m) is greater than that of
AlNiCo (100 kA/m) by a factor of 4.55. Therefore, to design
electropermanent magnets where the AlNiCo and NdFeB
components have the same residual flux density, we needa volume mixing ratio of 4.55:1, which means a mixture of
82.2% AlNiCo and 17.8% NdFeB by weight. We call thismixture EP for electropermanent.
Figure 2 confirms that modifying the weight percent of
AlNiCo in the AlNiCo-silicone composite indeed changes
the residual flux density without affecting the coercivity. So,
an EP sample was prepared that is also 1.6 mm thick and1.4 mm in diameter, and it is 80% EP by weight (where
EP is a mixture that is 82.2% AlNiCo and 17.8% NdFeB
by weight). A hysteresis curve for the EP sample is shownin Figure 3 and compared to the curves from Figure 1.
The EP sample was first magnetized in a saturating field(2,400 kA/m), and then the field was removed before thehysteresis loop was measured between −800 kA/m and800 kA/m. The discontinuity on the upper part of the curveat H = 0 indicates that the remanent magnetization is lower
after one hysteresis cycle (i.e., turning the EP magnet OFF
and ON again) since we only apply a field of 800 kA/minstead of returning to the saturating field of 2,400 kA/m.
Compared to Figure 1, the hysteresis curve in Figure 3 isshifted up such that the remanent magnetization (when theapplied magnetic field is zero) on the lower part of the curveis closer to zero than the remanent magnetization on theupper part of the curve. This feature of the hysteresis curve

Fig. 4.
Compression modulus measurements for samples of varying
material and weight percent. (Top) Stress vs. strain curves for magnetic
composites compared to neat Eco-Flex 00-50. Solid lines represent themean of five samples, and shaded areas represent one standard deviation.
(Bottom) Compressive modulus for the same samples, calculated for theregion ≤ 20% strain. Colored bars represent the mean of five samples whileerror bars represent one standard deviation. Higher weight percents lead tostiffer materials, and the EP material has a similar stiffness to AlNiCo since
it is mostly AlNiCo by weight.

indicates that the material, once magnetized in a saturating
field, can easily be switched between a high-remanence ON
state and low-remanence OFF state, a desired property for
applications like module attachment and climbing robots.
Since we were motivated by these applications, we designed
the EP mixture to have a remanence close to zero on thelower part of the hysteresis curve, but we note that othermixing ratios could be used for tunable magnetic properties.
For example, in applications where a nonzero remanence in
the OFF state can be tolerated, a ratio with more NdFeB
could be used, shifting the hysteresis loop further upward349

Authorized licensed use limited to: Yale University. Downloaded on May 24,2024 at 15:32:38 UTC from IEEE Xplore. Restrictions apply.

Fig. 5. Magnetic pull-off force of magnetized samples of varying materials
and weight percents. Samples were magnetized with a self-contained magnetizer. Then, the maximum pull-off force was measured after compressing
samples with a steel plate. The mean of five samples is plotted where error
bars indicate the standard deviation. Higher weight percents lead to greatermagnetic forces. Congruent with Figure 3, NdFeB is the strongest magnet.
The EP mixture compromises on strength in favor of its electropermanence.

Fig. 6. Magnetic pull-off force of EP samples of varying weight percent
after toggling states. The leftmost ON state is immediately after the sample
was magnetized. Samples were subsequently switched OFF and ON andmeasured as in Figure 5. Markers represent the mean of five samples whileerror bars represent the standard deviation. The EP magnets lose some of
their strength, compared to their initial magnetization, when they are firstswitched OFF and back ON, but thereafter state switching is repeatable.

and leading to stronger forces in the ON state. For the restof this paper, the EP samples are prepared with the ratio
calculated in this section.

B. Pull-off Force
Next, we investigated the pull-off forces of the compliant magnets, including the pull-off forces of the EP
magnets in both ON and OFF states. The same samples
from Section IV-A were magnetized with a self-contained
magnetizer (MAG24C; Master Magnetics) and then adhered
to 6.35 mm-thick acrylic plates with a silicone adhesive (SilPoxy; Smooth-On). Samples were then brought in contact
with a 76.2 mm x 76.2 mm A36 low-carbon steel plate(1388K102; McMaster-Carr) with a thickness of 6.35 mm.
The sample was compressed by the steel plate at a rateof 3 mm/min until a compressive force of 50 mN was
measured by the load cell. We note that the 50 mN threshold
represents a coupled measurement between the compression
force and the force of magnetic attraction, and samples withdifferent stiffnesses will experience different compressive
strains at 50 mN, yet some normalizing threshold must
be chosen. After the initial normalizing compression, theplate was pulled off the sample at a rate of 3 mm/min,and the peak magnetic pull-off force was measured. The
results for five samples of each weight percent and material
are shown in Figure 5. Congruent with the results from
Figure 3, the NdFeB samples exert higher forces than the
AlNiCo samples due to NdFeB’s greater remanence. Samples
with higher weight percents exert stronger forces due to thegreater magnetic moments that come from higher magnetic
volumes. The results also demonstrate that, to achieve thedesired properties of electropermanence in our EP samples,
we compromise on the strength of our magnets compared to
NdFeB composites.
The same pull-off experiments were repeated on the EP

IV. M ECHANICAL C HARACTERIZATION
Next, we characterize the mechanical properties of thecompliant electropermanent magnets. Similar to Section III,
samples were prepared by mixing magnetic powder into precure Eco-Flex 50 at specific weight percents, filling acrylic
molds with the composite, and curing for four hours at room
temperature. Samples in this section are cylinders with adiameter of 6.35 mm and a height of 6.35 mm. Experiments
were conducted on a materials testing system (Instron 3345)
with a 50-N load cell (Instron 2519-102; 0.1 mN resolution).
A. Elastic Modulus
Compression tests were conducted to characterize themechanical compliance of our electropermanent magnets asa function of magnetic powder material and weight percent.
Figure 4 shows the results of five samples of each material
and weight percent compressed between two acrylic plates,
each 6.35 mm thick, at a rate of 3 mm/min. At 80% magnetic
powder by weight, samples are stiffer, but on the same orderof magnitude as neat Eco-Flex. At lower weight percents, thecomposites approach the compliance of neat Eco-Flex, but
lower weight percents also come with the trade-off of weakermagnetic moments (see Section IV-B). The plots in Figure 4
show data from the same experiments; the compression
modulus in the bottom plot is calculated in the region from
0% to 20% strain. The EP and AlNiCo moduli match closely
because the EP mixture is mostly AlNiCo by weight; NdFeB
composites are stiffer.
350

Authorized licensed use limited to: Yale University. Downloaded on May 24,2024 at 15:32:38 UTC from IEEE Xplore. Restrictions apply.

samples after toggling the state from ON to OFF and viceversa. The state of the EP magnet can be switched by subjecting it to a magnetic field antiparallel to its magnetization ifthat field is sufficiently above the coercivity of AlNiCo but
well below the coercivity of NdFeB. In practice, we used
a 10 mm coil made from 400 turns of 24 AWG enameledcopper wire (7588K77; McMaster-Carr) energized with 10 Aof current. The coil has an inner radius of 15 mm, and whenenergized, it produces a magnetic field with a maximum
magnitude of 400 kA/m (0.5 T) along its central axis per
Equation 1:NI(1)lwhere H is the applied field, N is the number of turns, I
is the current, and l is the overall length of the coil. To
switch the state from ON to OFF, the EP sample is placedin the center of the coil and held in place such that the field
produced by the coil will be antiparallel to its magnetization.
Then, the coil is energized with a brief (>1 ms) pulse ofcurrent. We know from previous literature [19], [25] thatelectropermanent magnets saturate if the pulse duration isat least 1 ms, so any pulse >1 ms should yield the same
result. To switch the state from OFF to ON, this procedure
is repeated with the sample flipped relative to the coil.
Figure 6 shows the results of the pull-off force experimentfor five EP samples of each weight percent. There is a large
decrease in pull-off force compared to the initial magnetization after switching the EP magnets OFF and then ON again
because we do not use a saturating field (2,400 kA/m) toswitch states, but rather a much weaker field (≤400 kA/m).
After the first cycle, the ON and OFF states demonstrate
stable switching, with the difference between states more
pronounced at higher weight percents. Even in the OFF state,
the samples still have some remanent magnetization, so thepull-off forces are nonzero; however, they are weaker than
the forces in the ON state, and in practice that discrepancy
makes the difference in the 80% sample’s ability to hold its
own weight (see Section V).
H=

Fig. 7. Operating principle of the compliant electropermanent magnet. The
material is compliant, so it can be easily compressed. The scale bar is 6 mm.
When in the ON state, it can support its own weight magnetically, as shown,as it is lifted by a pair of pliers. In the OFF state, it cannot. The state can beswitched by placing the compliant electropermanent magnet in a magnetic
field of about 400 kA/m, for example, in the hand-made electromagnetic
coil shown. The reader is directed to the supplementary video to see thestate switching demonstrated.

magnetic field is strong enough to reverse the polarity of
the AlNiCo in the EP magnet but not strong enough toaffect the NdFeB, resulting in a net magnetization close
to zero (the OFF state). Once turned OFF, the compliant
electropermanent magnet is unable to lift its own weight
when in contact with the same pair of pliers, and it struggles
to lift the same paper clip. By flipping the coil and placing thecompliant electropermanent magnet in its center once more,
the magnet is turned back ON, and it again can easily lift the
paper clip and support its own weight, sticking to the pliers
via magnetism. Note that the magnetic force is dependent on
the object the magnet attaches to, and the paper clip used inthis demonstration has a much smaller ferromagnetic volume
than the steel plate from Section IV.
The process of turning the compliant electropermanent
magnet ON and OFF is reversible and repeatable. These
compliant magnets can be used in soft robots that would
benefit from the ability to selectively magnetize parts of theircompliant bodies.

V. D EMONSTRATION OF THE C OMPLIANT
E LECTROPERMANENT M AGNET

VI. C ONCLUSION

Figure 7 and the supplementary video illustrate the operational principle of compliant electropermanent magnets.
Compliant electropermanent magnets exhibit the mechanicalcompliance necessary to be integrated into the bodies of soft
robots. Furthermore, their magnetism can be turned ON and
OFF with a brief pulse of a magnetic field of 400 kA/m.
In the supplementary video, a newly magnetized compliant
electropermanent magnet (80% EP, identical to the samples
from Section IV) is shown lifting a paper clip with a mass of
0.5 g and supporting its own weight with its magnetism in thepresence of a ferromagnetic surface, in this case, needle-nose
pliers. Then, the compliant electropermanent magnet is heldin place by a piece of tape in the center of an electromagnetic
coil (400 turns of 24 AWG wire as in Section IV) that isbriefly (>1 ms) energized with 10 A of current. The inducedThis paper introduced the compliant electropermanent
magnet, a mechanically compliant material whose permanent
magnetism can be switched ON and OFF by subjecting it toa magnetic field. We illustrated the process for designingcompliant electropermanent magnets by measuring the remanent magnetization and coercivity of magnetic powders
and selecting mixing ratios to achieve desired properties.
Experiments characterized the mechanical compliance of
this material and the forces it can generate. Lastly, wedemonstrated the repeatable, reversible switching between
ON and OFF states.
Future work can incorporate different magnetic materials
and mixing ratios to expand the design space and enablefurther tunability in magnetic soft robots. A limitation of351

Authorized licensed use limited to: Yale University. Downloaded on May 24,2024 at 15:32:38 UTC from IEEE Xplore. Restrictions apply.

this work is the necessity of a rigid, external coil in contrast
to the co-located coils in rigid electropermanent magnets;
further advances in compliant electromagnetic coils that canachieve high field strengths would complement this work.
Finally, future research can focus on integrating compliant
electropermanent magnets into the bodies of soft robots toevaluate their efficacy in robotics applications.

[17] M. Li, A. Pal, J. Byun, G. Gardi, and M. Sitti, “Magnetic putty
as a reconfigurable, recyclable, and accessible soft robotic material,”
Advanced Materials, p. 2304825, 2023.
[18] K. Gilpin, A. Knaian, and D. Rus, “Robot pebbles: One centimeter
modules for programmable matter through self-disassembly,” in 2010
IEEE International Conference on Robotics and Automation. IEEE,
2010, pp. 2485–2492.
[19] A. N. Knaian, “Electropermanent magnetic connectors and actuators:
devices and their application in programmable matter,” Ph.D. dissertation, Massachusetts Institute of Technology, 2010.
[20] J. Daudelin, G. Jing, T. Tosun, M. Yim, H. Kress-Gazit, and M. Campbell, “An integrated system for perception-driven autonomy withmodular robots,” Science Robotics, vol. 3, no. 23, p. eaat4983, 2018.
[21] T. Tosun, J. Davey, C. Liu, and M. Yim, “Design and characterizationof the ep-face connector,” in 2016 IEEE/RSJ International Conferenceon Intelligent Robots and Systems (IROS). IEEE, 2016, pp. 45–51.
[22] G. Jing, T. Tosun, M. Yim, and H. Kress-Gazit, “An end-to-end system
for accomplishing tasks with modular robots.” in Robotics: Scienceand systems, vol. 2, 2016, p. 7.
[23] S. Hong, Y. Um, J. Park, and H.-W. Park, “Agile and versatile climbing
on ferromagnetic surfaces with a quadrupedal robot,” Science Robotics,
vol. 7, no. 73, p. eadd1017, 2022.
[24] A. D. Marchese, C. D. Onal, and D. Rus, “Soft robot actuators
using energy-efficient valves controlled by electropermanent magnets,”
in 2011 ieee/rsj international conference on intelligent robots andsystems. IEEE, 2011, pp. 756–761.
[25] K. J. McDonald, L. Kinnicutt, A. M. Moran, and T. Ranzani,“Modulation of magnetorheological fluid flow in soft robots using
electropermanent magnets,” IEEE Robotics and Automation Letters,
vol. 7, no. 2, pp. 3914–3921, 2022.
[26] P. Zhang, M. Kamezaki, Z. He, H. Sakamoto, and S. Sugano,“Epm–mre: electropermanent magnet–magnetorheological elastomer
for soft actuation system and its application to robotic grasping,” IEEE
Robotics and Automation Letters, vol. 6, no. 4, pp. 8181–8188, 2021.
[27] C. Zhang, P. Zhu, Y. Lin, Z. Jiao, and J. Zou, “Modular soft robotics:
Modular units, connection mechanisms, and applications,” AdvancedIntelligent Systems, vol. 2, no. 6, p. 1900166, 2020.
[28] J.-Y. Lee and K.-J. Cho, “Development of magnet connection ofmodular units for soft robotics,” in 2017 14th International Conference
on Ubiquitous Robots and Ambient Intelligence (URAI). IEEE, 2017,
pp. 65–67.
[29] A. Vergara, Y.-s. Lau, R.-F. Mendoza-Garcia, and J. C. Zagal, “Softmodular robotic cubes: toward replicating morphogenetic movementsof the embryo,” PloS one, vol. 12, no. 1, p. e0169179, 2017.
[30] W. Wang, N.-G. Kim, H. Rodrigue, and S.-H. Ahn, “Modular assemblyof soft deployable structures and robots,” Materials horizons, vol. 4,
no. 3, pp. 367–376, 2017.
[31] J. Zou, Y. Lin, C. Ji, and H. Yang, “A reconfigurable omnidirectional
soft robot based on caterpillar locomotion,” Soft robotics, vol. 5, no. 2,
pp. 164–174, 2018.
[32] L. Zhao, Y. Wu, J. Blanchet, M. Perroni-Scharf, X. Huang, J. Booth,
R. Kramer-Bottiglio, and D. Balkcom, “Soft lattice modules that behave independently and collectively,” IEEE Robotics and Automation
Letters, vol. 7, no. 3, pp. 5942–5949, 2022.
[33] L. Zhao, Y. Wu, W. Yan, W. Zhan, X. Huang, J. Booth, A. Mehta,
K. Bekris, R. Kramer-Bottiglio, and D. Balkcom, “Starblocks: Softactuated self-connecting blocks for building deformable lattice structures,” IEEE Robotics and Automation Letters, 2023.
[34] L. Wang and F. Iida, “Towards “soft” self-reconfigurable robots,” in2012 4th IEEE RAS & EMBS International Conference on Biomedical
Robotics and Biomechatronics (BioRob). IEEE, 2012, pp. 593–598.
[35] G. Park and H. Rodrigue, “Soft climbing robot with magnetic feet for
multimodal locomotion,” Scientific Reports, vol. 13, no. 1, p. 8377,
2023.

ACKNOWLEDGMENT
The authors thank Peter Schiffer for providing accessto the SQUID MPMS 3 and Ioan-Augustin Chioar for
conducting the VSM experiments in Section III.
R EFERENCES[1] D. Rus and M. T. Tolley, “Design, fabrication and control of soft
robots,” Nature, vol. 521, no. 7553, pp. 467–475, 2015.
[2] W. R. Johnson, A. Agrawala, X. Huang, J. Booth, and R. KramerBottiglio, “Sensor tendons for soft robot shape estimation,” in 2022
IEEE Sensors. IEEE, 2022, pp. 1–4.
[3] J. Shintake, E. Piskarev, S. H. Jeong, and D. Floreano, “Ultrastretchable strain sensors using carbon black-filled elastomer composites andcomparison of capacitive versus resistive sensors,” Advanced Materials
Technologies, vol. 3, no. 3, p. 1700284, 2018.
[4] X. Huang, K. Kumar, M. K. Jawed, A. Mohammadi Nasab, Z. Ye,
W. Shan, and C. Majidi, “Highly dynamic shape memory alloy actuator
for fast moving soft robots,” Advanced Materials Technologies, vol. 4,
no. 4, p. 1800540, 2019.
[5] D. J. Preston, P. Rothemund, H. J. Jiang, M. P. Nemitz, J. Rawson,
Z. Suo, and G. M. Whitesides, “Digital logic for soft devices,”
Proceedings of the National Academy of Sciences, vol. 116, no. 16,
pp. 7750–7759, 2019.
[6] M. Mohammadi, M. Berggren, and K. Tybrandt, “Versatile ultrasoft electromagnetic actuators with integrated strain-sensing cellulose
nanofibril foams,” Advanced Intelligent Systems, p. 2200449, 2023.
[7] W. R. Johnson, S. J. Woodman, and R. Kramer-Bottiglio, “An electromagnetic soft robot that carries its own magnet,” in 2022 IEEE 5thInternational Conference on Soft Robotics (RoboSoft). IEEE, 2022,
pp. 761–766.
[8] G. Mao, M. Drack, M. Karami-Mosammam, D. Wirthl, T. Stockinger,
R. Schwödiauer, and M. Kaltenbrunner, “Soft electromagnetic actuators,” Science advances, vol. 6, no. 26, p. eabc0251, 2020.
[9] W. Hu, G. Z. Lum, M. Mastrangeli, and M. Sitti, “Small-scale softbodied robot with multimodal locomotion,” Nature, vol. 554, no. 7690,
pp. 81–85, 2018.
[10] L. S. Novelino, Q. Ze, S. Wu, G. H. Paulino, and R. Zhao, “Untethered
control of functional origami microrobots with distributed actuation,”
Proceedings of the National Academy of Sciences, vol. 117, no. 39,
pp. 24 096–24 101, 2020.
[11] P. Lloyd, T. L. Thomas, V. K. Venkiteswaran, G. Pittiglio, J. H.
Chandler, P. Valdastri, and S. Misra, “A magnetically-actuated coiling
soft robot with variable stiffness,” IEEE Robotics and Automation
Letters, vol. 8, no. 6, pp. 3262–3269, 2023.
[12] M. Richter, M. Kaya, J. Sikorski, L. Abelmann, V. Kalpathy Venkiteswaran, and S. Misra, “Magnetic soft helical manipulatorswith local dipole interactions for flexibility and forces,” Soft Robotics,
vol. 10, no. 3, pp. 647–659, 2023.
[13] N. Kohls, B. Dias, Y. Mensah, B. P. Ruddy, and Y. C. Mazumdar,“Compliant electromagnetic actuator architecture for soft robotics,”
in 2020 IEEE International Conference on Robotics and Automation(ICRA). IEEE, 2020, pp. 9042–9049.
[14] M. Richter, J. Sikorski, P. Makushko, Y. Zabila, V. K. Venkiteswaran,
D. Makarov, and S. Misra, “Locally addressable energy efficientactuation of magnetic soft actuator array systems,” Advanced Science,
p. 2302077, 2023.
[15] N. Kohls, I. Abdeally, B. P. Ruddy, and Y. C. Mazumdar, “Design of a
xenia coral robot using a high-stroke compliant linear electromagnetic
actuator,” ASME Letters in Dynamic Systems and Control, vol. 1, no. 3,
p. 031011, 2021.
[16] N. D. Kohls, R. Balak, B. P. Ruddy, and Y. C. Mazumdar, “Softelectromagnetic motor and soft magnetic sensors for synchronous
rotary motion,” Soft Robotics, 2023.

352
Authorized licensed use limited to: Yale University. Downloaded on May 24,2024 at 15:32:38 UTC from IEEE Xplore. Restrictions apply.