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IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 7, NO. 3, JULY 2022

Soft Lattice Modules That Behave Independently
and Collectively
Luyang Zhao , Yijia Wu, Julien Blanchet, Maxine Perroni-Scharf , Xiaonan Huang , Joran Booth ,Rebecca Kramer-Bottiglio , and Devin Balkcom

Abstract—Natural systems integrate the work of many sub-units(cells) toward a large-scale unified goal (morphological and behavioral), which can counteract the effects of unexpected experiences,damage, or simply changes in tasks demands. In this letter, we
exploit the opportunities presented by soft, modular, and tensegrity
robots to introduce soft lattice modules that parallel the sub-units
seen in biological systems. The soft lattice modules are comprisedof 3D printed plastic “skeletons,” linear contracting shape memory alloy spring actuators, and permanent magnets that enable
adhesion between modules. The soft lattice modules are capableof independent locomotion, and can also join with other modules
to achieve collective, self-assembled, larger scale tasks such ascollective locomotion and moving an object across the surfaceof the lattice assembly. This work represents a preliminary step
toward soft modular systems capable of independent and collective
behaviors, and provide a platform for future studies on distributed
control.
Index Terms—Cellular and modular robots, soft robot materials
and design, biologically-inspired robots.

I. INTRODUCTIONHIS letter presents soft modules that can attach to one
another to form larger, more capable lattices. Different
shapes of lattice assemblies support different tasks, and we
demonstrate configurations performing locomotion, peristaltic
surface manipulation and prehensile gripping.
We are particularly interested in exploring the intersectionof work on soft and modular robots. While modular robot systems collectively reconfigure themselves to allow manipulation
or locomotion, flexible lattices allow deformation as well asreconfiguration, motivating the exploration of new behaviors; inthis letter, we explore whole-body manipulation of a ball along

T

Manuscript received October 11, 2021; accepted March 3, 2022. Date of
publication March 18, 2022; date of current version April 12, 2022. This work
was supported by National Science Foundation (NSF) : Robust Assembly ofCompliant Modular Robots. This letter was recommended for publication by
Associate Editor R. MacCurdy and Editor K.-J. Cho upon evaluation of thereviewers’ comments. (Corresponding author: Luyang Zhao.)Luyang Zhao, Yijia Wu, Julien Blanchet, and Devin Balkcom are with
the Department of Computer Science, Dartmouth College, Hanover, NH
03755 USA (e-mail: luyang.zhao.gr@dartmouth.edu; yijia.wu@dartmouth.edu;
julien.b.blanchet.gr@dartmouth.edu; devin.balkcom@dartmouth.edu).
Maxine Perroni-Scharf is with the Department of Computer Science, Princeton University, Princeton, NJ 08544 USA (e-mail: mp4215@princeton.edu).
Xiaonan Huang, Joran Booth, and Rebecca Kramer-Bottiglio are with the
Department of Mechanical Engineering and Materials Science, School ofEngineering and Applied Science, Yale University, New Haven, CT 06520
USA (e-mail: xiaonanh@andrew.cmu.edu; joranbooth@gmail.com; rebecca.
kramer@yale.edu).
Digital Object Identifier 10.1109/LRA.2022.3160611

the surface of the lattice. Eventually, we imagine that such asystem could be used as a rapidly deployable, flexible structurewith applications in disaster relief and construction, capable ofserving as a 2D conveyance for materials or as active scaffolding
for construction in hostile environments.
Soft robots constructed of flexible materials offer the possibility of simple mechanical designs, safe operation in the presenceof humans and delicate objects, excellent resistance to mechanical impact, and compliance to adapt to uneven terrain [1]. Owing
to high force-to-mass ratio, high work density, and the capabilityof being actuated by light on-board electronics [2], many soft
robots are actuated using spring-memory alloy (SMA) variable
length tendons [1], which can be combined with a flexible bodyto enable limb-like bending.
Collective behavior to perform complex tasks has garneredinterest in recent years [3]. One thrust of prior research has been
on rigid-bodied units capable of rearranging into various chainsor circular configurations in order to achieve novel locomotive
capabilities [4]–[6]. Another thrust has been self-assembly andreconfiguration of lattice-based systems, in which robot modules
are connected in a grid-like pattern [6].
The modules in this letter are composed of 3D printed skeleton
using a flexible Thermoplastic Polyurethane (TPU) material,
shaped like a pair of stacked tetrahedrons (Fig. 1(a)), and SMA
coils which are tethered to an Arduino located externally. SMAs
are selected as actuators of this modular system due to their highforce-to-mass ratio and high work density. The modules attach
together via specially arranged magnets located at the end of themodule arms.
We designed two methods of locomotion for the individual
module based off the principle of shifting the center of mass
to change the relative friction of the bottom three feet as theyslide along a surface. Once individual modules approach eachother, they engage in an attachment protocol that helps ensure all
four contact points are connected (Fig. 1(b)). We also developed
a walking gait for locomotion of three-module units that isused to assemble a larger lattice (Fig. 1(c)). Once the lattice
is assembled, a peristaltic control algorithm is used to roll one
or more balls along the lattice surface. (Fig. 1(d)).
Peristaltic motion has been used in the robotics field as amethod of locomotion [7], [8], but little information is available
about the use of peristalsis (whole-body flexing) by robots
for object manipulation. We explore such manipulation using
the flexible surface in a way that resembles contact juggling
performed by humans. To further explore the capabilities of2377-3766 © 2022 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.

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structure is held intact through a combination of compressive
and tensional elements. Although our modules and system do
not rely on tensional forces when static, they behave much liketensegrities when an SMA spring is activated.
A. Modular Soft Robots

Fig. 1.

System overview

these lattice modules we also tested prehensile module-based
gripper capable of grasping various objects. (Fig. 1(e)).
Ourprimary contribution is the instantiation of semi-soft lattice modules capable of attachment and detachment on-demand,
enabling a rich application space including self-assembled structures and multi-functional robots. Taking inspiration and benefits from soft robotics, modular robotics, and tensegrity robotics,
our proposed soft lattice modules locomote independently andcollectively. Collections of modules achieve faster locomotion,and permit various manipulation strategies.
This letter is organized as follows. First, we discuss related
work, andthe design of our system, starting with a description of
the single module locomotion, followed by attachment into 3module, followed by multi-module locomotion and attachment
into a lattice, and then by peristaltic manipulation and modulebase gripper.We also discuss limitations of the current system,and propose future work.
II. RELATED WORK
Our work lies at the intersection of soft robots and modular
robots and relates to much other work in these fields. Anotherfield of related work is tensegrity robots, in which the robot

Lee et al. [1] provide a review of soft robot research, including
an overview of fabrication methods (ours is 3D printed), actuation methods (ours uses SMA wire), and control techniques.
Several modular soft robots are composed of repeating sections,
often arranged in caterpillar-inspired shapes and commandedwith traveling peristaltic waves. For example, the Zou catepillar
robot [9] used modular segments with pneumatic feet connected
in series and the Wormbot [10] featured custom audio speakerassemblies embedded in sections. Both locomoted using peristaltic control strategies.
The use of magnetic attachment is also fairly common among
modular rigidand soft robots. Tosun et al. designed a connector embedded in planar face for rigid modular robots using
electro-permanent magnets where power is needed for changing
magnets state [11].The Kwok self-assembling finger robot [12]demonstrated magnetic self assembly of robotic fingers to form
hexapods and grippers manually and remotely. The CBalls
modules [13] are soft robots composed of pairs or trios ofinflatable spherical bodies magnetically attached together anddriven through a rolling motion between bodies.
There are other soft robots described as modular, but which
use the word differently than we are using in this work. The“Click-e-bricks” components [14] and The Limpet II [15] areboth described as modular, but this term is used to describeinterchangeable components, such as sensors or actuators, andnot that the individual robots work together as a collective.
The Omniskins Prior “robotic skins” (or omniskins) [16] arereconfigurable components that afford new shapes rather thancollective robot swarms that can link together.
Another major distinction between this work and prior is that,exceptKwok finger robots, none of these robots demonstrated
self-assembly, including self-locomotion and attachment. Jellocube is a soft robot that can jump individually [17]. Usevitch et al. [18] designed a modular shape soft robot allowing forshape-changing, punctuated rolling and manipulation, but noneof them show attachment functionality.
Although rolling or jumping locomotion might be faster [13],[17], [18], in this letter, we focus on walking and sliding motions
as they provide the needed precision for docking, as well as
multi-module locomotion.
B. Self-Reconfiguring Robots
Yim et al. [3] and more recently Parker et al. [6] provide reviews of re-configurable and self-assembling robots,and points out important challenges of self-configuring robot
systems [19].These robots often assemble into a chain or latticearrangement. Yim et al. first presented locomotion gaits table ofrigid modular re-configurable robots [20].
SMORES [21] andSambot [22] modules are un-tethered andfully autonomous reconfigurable robot (our system is tethered), but are rigid-bodied and requires additional part for

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IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 7, NO. 3, JULY 2022

manipulation capability. ShapeBots [23] are shape-changing
robots capable of working together to perform object manipulation, but cannot fully deform because the robots are rigid.
Motion planning is a significant challenge for a large amountof modular robot and reconfigurable robot.Kilobots [24] collectively make up a 1024-robot system capable of self-assembly.
Liu and Yim proposed a motion planning algorithm for selfreconfiguration ability of variable topology truss [25].
C. Tensegrity Robots
The module design draws some inspiration from tensegrity
structures [26]. There is much prior research surrounding tensegrity robots and their applications, following on seminal workat NASA on the lightweight SUPERball, which is especiallywell-adapted to maneuvering over hazardous terrain [27]–[29].
Soft tensegrity robots have also been explored for different
purposes. Rieffel and Mourel accomplished fast locomotion
using soft tensegrity robot actuated with 3 motors [30]. Lee et al.
fabricated soft tensegrity robots with 3D printing materials to
avoid additional pose-assembly process for single robot [31].
Zappetti et al. proposed a soft modular robot inspired by cytoskeleton of living cell based on tensegrity [32].
Soft biologically-inspired tensegrity robots, built with rods,
tension springs and motorized cables, lend themselves to manydifferent modes of motion [33]–[35]. These tensegrity structures
are known as “bio-tensegrity robots,” and take inspiration froma variety of animals. Mirletz1 et al. used NASA Tensegrity
Robotics Toolkit (NTRT) to simulate morphology and control
of modular spine-like tensegrity robots [36], where they tested
on Octahedral and Tetrahedal complexes, which looks similar
to our module, but their module cannot locomote individuallyor do self-assembly. Moreover, the connection between theirmodules are strings, and ours are magnets, which means oursingle module is more flexible and separable.
There is also much prior work on the coordination of nontensegrity multi-robot systems and usingthese systems for object manipulation. There are many advantages to multi-robot
systems [37], and they are particularly well suited for the transportation of large objects in hazardous environments. There area variety of approaches to coordinate the motions of robots inthese systems. For example, cluster space control [38] relies ona pilot to use a joystick and manually coordinate four robots.
These robots can be used together for object transportation.
Decentralized control methods have also been studied that allow
robots to identify and approach a target object and move aroundto transport it together [39]. The majority of such approaches relyon the robots themselves to travel distances and move aroundthe surface, but there is less existing work on static robots topass objects between them.
III. MODULE DESIGN
A. Hardware Design and Assembly
An individual module is composed of a skeleton, SMAs
and spherical magnets. The shape of the skeleton is a pair ofsymmetric stacked tetrahedrons, inspired by the geometry of a

Fig. 2.

Top view of 2 pairs and 1 pair magnetic connectors

tetrahedral molecule (Fig. 1(a)). Each tetrahedron is composedof four equal-length bars. The angle between each two neighboring bars is cos−1 (−1/3) ≈ 109.5◦ , which is the same as thebond angle of the tetrahedron molecule. The diameter of eachbar is smaller near the connection point for better flexibility,with grooves for mounting SMAs. The skeleton is printed withflexible TPU material with an infill density of 90% to achieve astronger adversarial bending force that helps restore a module’s
original shape after SMA contraction.
Given the small size of each module and the need for nine
actuators in order to achieve our target locomotive gaits and manipulation capabilities, we used one-way SMA (shape memory
alloy) coils (coil diameter, 3.45 mm; wire diameter, 0.51 mm,
Dynalloy) to actuate the robots. The end of each spring SMAs
is crimped with fishing wire and electric wire in a ferrule andmounted to the grooves in the skeleton with the fishing wire.
The detwinned Martensite rest length of each SMA is longer
than the distance between two grooves to make sure that they
can be extended when the skeleton deforms because of SMA
actuation.The Austenitic (actuated) rest length of the actuators is
1.52 cm/1.42 cm/0.91 cm (vertical/diagonal/horizontal). Wheninstalled, the detwinned Martensite rest length is set to be
8.0 cm/7.6 cm/4.4 cm, though this exact length changes withactuation cycles due to variance in antagonistic forces appliedby other SMA actuators and the elastic energy stored in the
deformed soft skeleton.
Spherical magnets are affixed at the end of each tetrahedrallimb to enable the modules to connect together. We oriented thepolarity of the magnets in a circle as described in [40], where
each magnet in the loop is aligned head-to-tail and the magnetic
field inside the loop is either clockwise or counterclockwise.
Therefore, once all the magnetic balls are glued on the modules
with the same magnetic field direction, any modules can then be
attached together from all directions.
B. Choice of Spherical Magnets
The pull force of the spherical magnet has a strongly influences on the attachment property. We tested four sizes ofspherical magnets: 3/16,” 1/4,” 5/16,” and 3/8”. Six experiments
were done to evaluate their attachment properties including
the maximum distance that two modules can be attached bymagnetic force only and the minimum length that SMAs areallowed to be contracted to avoid detachment of magnetic
connectors. The maximum distances were tested in two cases:
four feet facing each other (8 magnets) and two feet facing
each other (4 magnets). The minimum contraction length were
tested in four cases: two feet connected (Fig. 2(a)) and four
feet connected (Fig. 2(b)) while only SMAs in one module

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TABLE IATTACHMENT AND DETACHMENT EVALUATION

Fig. 3.

Physical analysis of Shuffling pattern locomotion (top-down view of bottom legs).

contracted and SMAs in two modules contracted. Experimental
results are shown in Table. I, where 1.52 cm is the Austenitic rest
length of the vertical SMA. Results indicate that the magnetic
connection does not break even with maximum SMA actuation.
Based on the results, we chose the 1/4” diameter for locomotion
and peristaltic manipulation because of its low cost, and chosethe 5/16” magnets for gripper experiments that required larger
deformation while keeping modules connected.
IV. SINGLE MODULE LOCOMOTION & ATTACHMENT

Fig. 4. Physical analysis of Grab-and-pull pattern locomotion (top-down viewof bottom legs).

A. Analysis of Locomotive Gaits
We have chosen two gaits (and a combination of them) for
single-module locomotion. The purpose of locomotion for single
module is to move towards other modules to assemble into a 3module unit for locomotion, where 3-module units are utilized toassemble into a larger structure for manipulation. While there aregaits that roll modules end-over-end to achieve fast locomotion,
the need for precise control during attachment motivated us toinstead explore gaits that cause the robot to slide along the floor
in an upright configuration.
Both gaits operate on the same principle: the module iscontrolled in order to move the center of mass to reduce thefriction at contacts that are sliding forwards, while increasing
friction at contacts that are planted.
1) Single-Module Gait #1: Grab-and-Pull: In this grab-andpull gait (akin to breaststroke), the first step shifts the center ofmass backwards to plant the back leg while contracting the front
SMA to slide the front legs forward ( Fig. 4 a). Similarly, during
release of the front SMA, the robot rocks so that the center ofmass lies over the front two feet (Fig. 4 b). Therefore, afterswitching the center of mass from back to front, the distancemoving forward h3 (Fig. 4 b) is equal to h1 − h2 , where h1 andh2 are the same when the center of mass is not switched andkept in the center.
2) Single-Module Gait #2: Shuffling: In this pattern,the robot
walks by dragging left and right feet alternately without lifting
the feet from the ground. The physical analysis behind it issimilar to the grab-and-pull pattern. Fig. 3 shows the wholeFig. 5.

Control signal for single module locomotion.

process, where the center of mass is switched to front duringcontraction of left SMA and switched backward during recovery
process to intensify the impact of forward friction and weaken
the impact of backward friction. Then the right SMA works inthe same way symmetrically.
Importantly, if the contraction time of left and right SMAs
are different, the robot can rotate to the direction that is lesscontracted, which means with this pattern, the upright robot canmove to arbitrary locations and orientations in the plane.
3) Single-Module Gait #3: Combined: We used the property
that motion of the center of mass is opposite in the two patters tocreate a combined pattern with faster locomotion. Specifically,
the combined gait is “left → front → right → front”. Fig. 6 shows

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IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 7, NO. 3, JULY 2022

TABLE IIRUNNING TIME COMPARISON BETWEEN DIFFERENT PATTERNS (MOVING 2 CM)

Fig. 6.

Combining Grab-and-pull and shuffling patterns

an example where the center of mass switches from front to backwhen left foot is contracted & released and then the front bottom
SMA is contracted – the corresponding control signal is shownin Fig. 5 (SMAs are labeled in Fig. 1(a); The labels Vx, Dx, Hxxrepresent vertical, diagonal and horizontal SMAs respectively,
where x/xx is determined by the limb label). We ultimately
selected combined gait for the single-module locomotion andattachment task.
B. Experiments
1) Locomotion Performance: To control the SMAs, we used
Arduino and 12 V DC power supply. 120 grit sandpaper supplies
a coarse locomotionsurface . To reduce drag, we used light,
flexible silicone insulated stranded wires for the tether.
We conducted some experiments to validate the effectiveness of the two locomotion patterns. The grab-and-pull gait
took 8.3 min to travel 2 cm, or 0.00095body lengths per second (BL/s), where 1.38 min was used to actuate and the rest
was used to cool the SMA actuators. The shuffling pattern
took 5.02 min to travel 2 cm, or 0.00157 BL/s,where 0.84 min
was used to actuate. For the combined gait, the time cost of
moving forward 2 cm is 3.15 min (median of 10 trials), or
0.00252 BL/s,where the actuation time is 0.75 min.
2) Strategies to Increase the Speed: Given the slow speeds
observed with the gaits mentioned above, we experimented withseveral methods of expediting the locomotion (Table II).
Vibration: Since legs are unable to be lifted off the ground,backward friction between the sliding legs and the ground inhibits movement speed. To reduce this friction, we alternately
actuate and relax the back vertical SMAs on a 50 ms : 1000 ms(actuation : cooling) interval.
Cooling Fan: We tested putting a fan opposite to the directionof motion to simulate locomotion in outdoor conditions.
Multiple Thinner SMAs: We tested replacing single SMAs
with multiple thinner SMAs to increase the surface area andspeed cooling, similar to the “stacked-ribbon” design [41].

Fig. 7.

Attachment between single modules(Fig. 7). During this protocol, one module actively moves towards the other one while the other module waits and cooperates
with the active module. Once two modules are close enough, thehead of the passive module leans outward to prevent the upper
magnets from attaching together, since an initial attachment of
the top magnetic balls can prevent successful attachment of thebottom two balls because the modules are unable to shift theircenter of gravity sufficiently to slide the bottom feet. When atleast one pair of bottom feet has been attached (Fig. 7(b)), all the
SMA actuators on the two modules are commanded to release
until returning to initial states. During this process, other pairsof magnetic balls will be attached automatically as shown in
Fig. 7(c). For those exceptional cases where not allthe remaining
magnetic balls are attached automatically, the strategy we used is
to contract the four neighboring vertical SMAs simultaneously
and then contract the two front horizontal SMAs at the sametime.
D. Attachment Test
To test this attachment strategy we conducted an experiment
where we attached one of the bottom magnets and varied thealignment angle between the modules. Fig. 7(b) is an example
with an approximately 10◦ alignment angle. We tested 5 trials
for each angle (0◦ , 30◦ , 60◦ , 90◦ , 120◦ ). The success rate was
100% for angles less than or equal to 90 degrees, while 4 out of 5
trials with 120◦ succeeded. Furthermore, for trials with angle 0◦ ,30◦ , and 60◦ , the remaining pair of magnetic balls automaticallyattached during recovery process. For trials with angle 90◦ , 2
trials out of 5 required an additional approach after recovery tohelp with attachment.
V. 3-MODULE LOCOMOTION & ATTACHMENT
The locomotion pattern of 3-module is like a three-legged
race, where the feet in between are strapped by magnetic balls
and only the left most and right most feet can move freely.

C. Attachment Between Single Modules

A. Physical Analysis of “three-Legged Race” Pattern

Once two modules are in close proximity they enter an attachment protocol to ensure a fully connected four-magnet bond

The principle of moving forward for 3-module unit is similar
to the combined Shuffling and Grab-and-pull pattern of single

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Fig. 10.

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A sequence of actions the 3-module takes to move the left feet forward

B. Experiments

Fig. 8. Physical analysis of three-module locomotion (left-leg step, top-downview of bottom legs)

To move forward for 2 cm, the running time of 3-module unit
was 2.35 min (median of 5 trials) and the cooling time for eachcycle was 12 s out of 22.6 s, or 0.0335 BL/s. This motion is fasterthan a single module as each foot can be lifted and then moved
forward in air, allowing more forward displacement during eachcycle. A sequence of actions to move the left feet forward shownin Fig. 10,
C. Attachment Between 3-Module Units

Fig. 9.

Control signal of three-module locomotion.

module locomotion, where left foot and right foot are alternately
moving forward, and the front SMA is actuated to speed up
the forward movements. The main difference and advantage ofthree-module locomotion is that given the greater number ofground contact points, feet can be lifted and advanced in the air
while maintaining stability, thereby eliminating sliding frictionand enabling significantly faster locomotion as compared to asingle module.
Take the left foot as an example. The first step is to raise the leftfoot and move it forward in the air (Fig. 8(b)).The second step
(Fig. 8(c)) plants the outside back feet (nodes 3 & 5) by switching
the center of gravity backward while lifting and advancing thecenter-back leg (node 4). The last step is to raise the front leftfoot (node 1) and actuate the front horizontal SMA to reduce
the friction that influences the movement. As shown in Fig. 8(d)only three feet remain on the ground. Finally, the three-module
can move the left side of the body forward (Fig. 8(e)). The
sequence will then be mirrored for the right side. Photos of the
gait sequence shownin Fig. 10 and Fig. 9 shows the control
signal for moving the left foot forward (Lx, Mx, Rx represent
the SMAs on the left, middle and right modules separately, withx labelled in the same way as in Fig. 1(a), with limb labels (A,B, C) for each module shown in Fig. 10(a)).

Fig. 1(c) shows an example of attaching four three-module
groups together. Unlike single-module attachment, the passive
module unit waits motionlessly instead of leaning backward
to cooperate, due to the complexity that would be required
for the leaning motion. Moreover, since the unit will not lean
forward as the single module does during locomotion, either thebottom magnetic balls will be attached first when unit is leaning
backward or all balls (top and bottom) will attach simultaneously
when the unit is upright.
When a 3-module unit approaches the lattice it is common for
all magnetic connection points to snap together nearly simultaneously, but this is not always the case. Fig. 1 c3 shows a casewhere only a partial connection is made between the orange unit
and the lattice. In this case, we used a rotation motion to pivot
the unit around the connected points until a full connection wasreached. Closing the loop with sensing and fully automating thisprocess is a next step in future work.
VI. NON-PREHENSILE MANIPULATIONIn this section, we describe strategies to roll a single ball or
multiple balls along the surface of the structure. Ultimately, we
imagine transporting other objects or even modules themselves
along the surface, using lattice deformation as a whole-bodymanipulation strategy.
A. Bi-Directional Linear Manipulation With SMAs in 3D
Vertical SMAs are actuated to change the shape of the top
surface to make the ball roll. Fig. 14(b) shows an example ofbi-direction linear manipulation.
An example of moving a ball from the left node to the rightnode is shown in Fig. 12. The first step is to drag the left
node down vertically by actuating six connected vertical SMAs
(shown in Fig. 12(b)). During release of these SMAs, the heightof left node increases gradually. When the left node rises, theball might drop either left and right; to avoid this, before theleft node becomes flat, the first node connector SMAs (marked
in red in Fig. 12(c)) is actuated to give the ball velocity in the

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TABLE IIIGRIPPING CONFIGURATION SUCCESS RATES

Fig. 11.

Top and front view of lattice with 10 modules.

manipulation, we alsotested parallelogram manipulation on thissurface (Fig. 14(c)) andmanipulating two balls on the top surface, where as Fig. 1(d) shows, two balls move in opposite
directions without touching each other.
VII. GRIPPER FORMED FROM MODULES

Fig. 12.

Manipulation process

We have also tested using a module-based gripper to grasp
various objects, as shown in Fig. 1(e). Top horizontal SMAs areadded for each module such that the object can be grasped whenboth top and bottom horizontal SMAs on the inside boundary
are actuated. To grasp larger objects, top and bottom horizontal
SMAs on the outside boundary are actuated to open the gripper
at first. To avoid detachments between modules easily whengrasping heavy objects, we used larger ball magnets with 5/16”
diameter and 2.52 lbs pull force.
Objects with different weight/shape/size/surface as shown in
Fig. 1(e) were tested, and the results are shown in Table III.
The gripper appears capable of gripping a variety of objects
with a success rate that varies depending on the roughness ofthe gripper and the weight/shape/size/surface of the object. To
increase the success rate, future work could test increasing theroughness of the gripper, using magnets with higher pulling
force, using softer skeletons to allow more deformation, or trying
new arrangements of modules to grasp different objects.
VIII. CONCLUSION AND FUTURE WORK

Fig. 13.

Control signal of manipulation (1st node → 2nd node).

Fig. 14. (a) Path control of a ball (b) Bi-direction manipulation (c) Parallelogram manipulation

desired direction. After 5 seconds, the second node connector
SMAs (marked in blue in Fig. 12(d)) is actuated to give the balla rightwards velocity towards a stable position on top of the
middle module. The corresponding control signal is shown in
Fig. 13 (vertical actuated SMAs are labeled in Fig. 11(a)).
B. Path Control of a Ball
Using the same principle, adding additional modules to thelattice allows us to do path control of a ball along the top surface.
Fig. 14(a) shows an example of a 3x3 grid, where white edges
are the allowed paths to move through. Except bi-directional

In this letter, we instantiated soft lattice modules that behave both independently and collectively. Using these lattice
modules, we demonstrated preliminary steps toward the selfassembly of robotic lattice structures and employed several
behaviors to perform collective and coordinated tasks.
Our system has several limitations and opportunities for further development. At present, all the modules are tethered to an
Arduino which controls the lattice as a whole. To allow modules
be self-contained and autonomous, on-board computing, power,
and sensing would be required. The modules would need communication through a contact-based mesh scheme or a wirelessscheme. Methods of realizing distributed control of the latticewould need to be implemented.
Our single module locomotion strategy relies on friction, so
the speed is limited even on rough surfaces. However, for 3module locomotion, since the feet can be lifted, the speed ismuch faster. We plan to explore moving more modules together
for centipede-type locomotion, and improve module design tomake it walk individually instead of sliding.
Our system is capable of self-assembly, but the magnetspresent a challenge for self-disassembly. One potential approachis to use the principle of “tug of war” to generate sufficient
detachment force, but detaching multiple connection points
simultaneously may be difficult and a hardware modificationis perhaps necessary for this purpose.

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ZHAO et al.: SOFT LATTICE MODULES THAT BEHAVE INDEPENDENTLY AND COLLECTIVELY

Yet another direction for further development lies in simulation. We have built a simple simulation using an energy-based
quasi-static model that estimates the configuration with theminimal potential energy using Lagrange multipliers. Our model
assumes a pseudo-rigid bodied skeleton and requires further
development to better reflect the system dynamics.
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