IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 8, NO. 8, AUGUST 2023

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StarBlocks: Soft Actuated Self-Connecting Blocks
for Building Deformable Lattice Structures
Luyang Zhao , Yijia Wu, Wenzhong Yan , Weishu Zhan, Xiaonan Huang , Joran Booth ,Ankur Mehta, Member, IEEE, Kostas Bekris , Senior Member, IEEE, Rebecca Kramer-Bottiglio ,and Devin Balkcom

Abstract—In this paper, we present a soft modular block inspiredby tensegrity structures that can form load-bearing structures
through self-assembly. The block comprises a stellated compliant
skeleton, shape memory alloy muscles, and permanent magnet
connectors. We classify five deformation primitives for individual
blocks: bend, compress, stretch, stand, and shrink, which can be
combined across modules to reason about full-lattice deformation.
Hierarchical function is abundant in nature and in human-designed
systems. Using multiple self-assembled lattices, we demonstrate
the formation and actuation of 3-dimensional shapes, including aload-bearing pop-up tent, a self-assembled wheel, a quadruped,a block-based robotic arm with gripper, and non-prehensile manipulation. To our knowledge, this is the first example of active
deformable modules (blocks) that can reconfigure into different
load-bearing structures on-demand.
Index Terms—Cellular and modular robots, robotics andautomation in construction, soft robot materials and design,
biologically-inspired robots.

I. INTRODUCTION
N NATURE, many creatures are capable of working collectively by joining together to form large-scale assemblies
to achieve a unified goal, e.g., navigating through unstructured
terrain, transporting heavy goods, and surviving in severe environments [1], [2]. For example, the army ants of the Eciton genus
can use their own bodies to collectively build bridges to span
gaps in the colony’s foraging trail [3]. The fire ants Solenopsis

I

Manuscript received 19 January 2023; accepted 12 May 2023. Date of
publication 8 June 2023; date of current version 19 June 2023. This letter wasrecommended for publication by Associate Editor Kirstin Hagelskjaer Petersen
and Editor M. Ani Hsieh upon evaluation of the reviewers’ comments. This work
was supported by the National Science Foundation (NSF) : Robust Assemblyof Compliant Modular Robots. (Corresponding author: Luyang Zhao.)Luyang Zhao, Yijia Wu, Weishu Zhan, 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; weishu.
zhan.th@dartmouth.edu; devin.balkcom@dartmouth.edu).
Wenzhong Yan and Ankur Mehta are with the Department of MechanicalEngineering, University of California, Los Angeles, Los Angeles, CA 90095
USA (e-mail: wzyan24@g.ucla.edu; mehtank@ucla.edu).
Xiaonan Huang, Joran Booth, and Rebecca Kramer-Bottiglio are with the Department of Mechanical Engineering and Materials Science, School of Engineering and Applied Science, Yale University, New Haven, CT 06520 USA (e-mail:xiaonan.huang@yale.edu; joran.booth@yale.edu; rebecca.kramer@yale.edu).
Kostas Bekris is with the Department of Computer Science, Rutgers, The
State University of New Jersey, New Brunswick, NJ 08901 USA (e-mail: kostas.
bekris@cs.rutgers.edu).
This letter has supplementary downloadable material available athttps://doi.org/10.1109/LRA.2023.3284361, provided by the authors.
Digital Object Identifier 10.1109/LRA.2023.3284361

Fig. 1. Starbots: (a) Locomotion of a single module; (b) Five deformation primitives of a single module; (c) Attachment of a pair of modules;(d) Detachment of a pair of modules; (e) Formation and weight-carrying ofa 3D dome-shaped tent; (f) Locomotion of a modular rolling robot; (g) Object
manipulation of a module-based robotic arm and gripper.

invicta can form a raft, and can contract their muscles to squeeze
the raft into a tight mass to survive a flood [2]. Such collective biological structures are built from individually capable,
flexible individuals.
In robotic construction, robotic manipulators often build
structures from rigid load-bearing blocks [4], [5], [5], [6], [6],[7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. On
the other hand, soft robots can adapt their shapes to suit particulartasks [19], [20], [21]. To bridge the gap between rigid blocks
and soft robotics, we design a smart soft modular lattice-based
block that can be used for building structures that can deform
for locomotion or manipulation, or lock into a shape to bearloads. Individual blocks can locomote, allowing self-assembly
into structures without external helpers.
We have previously explored soft modules for locomotion
and manipulation [21], but the prior design does not perform asa smart block, as it does not allow 3D lattice stacking or disassembly. The current design also has a much larger deformation
space than the previous design; the current design has 12 degreesof actuation compared to 9 for the prior.
There is existing work using rigid smart blocks, assembled
using a robotic helper [15], [16], [17], [18]. There are also soft
modular robot designs [22], [23], [24], [25], [26], [27]. However,these soft modular robots do not allow either weight bearing or
3D lattice stacking.
A single module is composed of a stellated skeleton, twelve
spring-memory alloy (SMA) actuators, and eight endcaps. SMA
variable length tendons [22] are frequently used to actuate soft
robots, allowing for limb-like bending when combined with aflexible body. The drawback of SMA is that the current design

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does not allow for fast locomotion. Replacing SMA with otheractuators like motors would increase the actuation speed.SMA
was chosen for its high power density, lightweight, and uniform
weight distribution allowing easy attachment to the flexible
skeleton.
The core functions of a single block are locomotion, deformation, and connection. To achieve locomotion and deformation
primitives, a single module is composed of a soft stellated skeleton printed from Thermoplastic Polyurethane (TPU) material as
shown in Fig. 2. At rest, the convex hull of each block is acube. Twelve SMA actuators connect the vertices of the cube
along each of the edges; contraction shortens selected edges,
which expand passively when the SMA is relaxed. To enable
connection to other blocks, there are eight endcaps at the verticesof the cube, where the same polarity disk magnet is placed in
the same position on each endcap. These connections allow
blocks to assemble into 3D structures and allows lattices to lockand bear loads. Attachment and detachment between blocks areachieved by the combinations of these core functions, which
permits structure self-assembly as well as self-reconfiguration.
We use these capabilities to explore several applications andshapes, with strategies for transformation, locomotion, and manipulation. Specifically, we explored the assembly of a weightsustaining self-locking tent (Fig. 1(e)), locomotion using botha rolling wheel (Fig. 1(f)) and a quadruped design (Fig. 5(c)),
and manipulation using two different strategies: an arm made ofmodules (Fig. 1(g)), and deformable surface-based peristaltic
manipulation (Fig. 5(e)). Further details of these structuresappear below in figures 3 and 5. These assemblies are adaptive
and compliant, which may make them suitable for unstructured
and hazardous environments [28].
Our contribution in this work is to provide a design of a
block that can self-assemble with other blocks to create flexible,
actuated, load-bearing structures. Self-locomotion, docking, andun-docking properties enable the formation of different structures to achieve various tasks.

functionalities, such as locomotion (e.g. crawling, rolling [19],swimming [36], and cluster-based locomotion [37]), manipulation [24], [38], shape morphology [39], reconfiguration [40],or combinations of these tasks [25], [41]. Nevertheless, most ofthese soft modular robots rely on manual assembly entirely [19],[25], [34], [36], [38], [39], [40], [41] or initially [20], [23], [37]as their individual modules do not have locomotion capability.
None of these soft modular robots are designed for architectureassembly, which means they cannot provide weight-bearing or
3D lattice stacking properties.
III. DESIGN OF A SINGLE BLOCK
Each symmetric block consists of three parts: a soft skeleton,
twelve SMA actuators, and eight rigid connectors.
A. Soft Stellated Skeleton and Actuators
The skeleton is rotationally symmetric about different axes
in 3D, provides sufficient compliance for various deformation
modes, and possesses sufficient space for installing connectors
and actuators. Each skeleton resembles a stellated octahedron,with a convex hull that is a cube at rest.
The edge length of each block is ∼ 7.2 cm, and the detwinned
Martensite rest length of each SMA (coil diameter, 3.45 mm;
wire diameter, 0.51 mm, Dynalloy) is ∼ 3.7 cm. The austenitic(actuated) rest length is ∼ 1.2 mm. When the SMAs are actuated, they are capable of deforming the skeleton, and when
the SMAs cool, the skeleton has sufficient restoring force tostretch the SMA back to its detwinned Martensite rest length.
We control the SMA open-loop by actuating it for a certain
duration under 5 V. We performed physical experiments for eachapplication to determine a suitable actuation duration.The 20%
printing fill density and 4 mm skeleton bar diameter were chosen
informed by experiments described in Section V-A. Each SMA
coil requires 15 − 20 s to cool down and recover from a rigid
austenite phase to a relatively compliant martensite phase.

II. RELATED WORK
Ground and underwater robotics construction has explored various assembly methods. These methods can be broadlyclassified into three categories: 1) using an external manipulator
to assemble passive blocks [5], [6], [7], [8], [9], [10]; 2) using
swarm robots to transport and assemble passive blocks [11],[12], [13], [14]; 3) using programmable blocks with simple
robots for structure assembly [15], [16], [17], [18].Each of these
construction methods utilizes rigid blocks with load-bearing
capabilities. However, they rely on external assistance for assembly and lack the inherent self-reconfigurability of modular
robots.
Modular self-reconfigurable robots (MSRRs) offer a
promising alternative approach to traditional construction methods. MSRRs are typically composed of a group of modules, eachwith the ability to locomote and mechanically join together [29],[30], allowing them to rearrange their connectivity and better
adapt to new tasks [31]. Frequently, the individual modules arearticulated rigid structures.
Adding compliance and flexibility to modules has been explored as a way to expand the capabilities of soft modular
robots [32], [33], including the potential for new modes of actuation and mobility [34], safer interaction with humans [27], andgreater adaptation to the physical environment [35]. These soft
modular robots can achieve a wide range of morphologies andB. Rigid Magnetic Endcap
To limit size, weight, and energy requirements, we chose touse a passive connector with magnets attached.The magnets
introduce a trade-off between connection strength and easeof separation. We carefully selected the magnets to provide
connection strength while still allowing separation under nearmaximum force applied by the SMAs. Experimentally, we foundthat the magnets with force = 3.566 lbs; diameter = 0.25 inch;
thickness = 0.0625 inch matched the selection criteria.The
magnetic endcaps consist of two parts: inner endcap (Fig. 2(d)and outer endcap (Fig. 2(e)). The inner endcap is used to connect
the skeleton and the outer endcap. Six permanent magnets aremounted on each endcap; two of opposite polarity on each of thethree faces. The same polarity disk magnet is placed in the same
position on each endcap surface to enable attachment between
multiple modules (Fig. 2(e)) [29] to form a lattice structure.
Two additional geometric features are intended to increaseconnection strength between endcaps as the structure flexes
without affecting the separation. One feature is a groove along
the diagonal direction. For many flexing motions, this groove
prevents sliding motion between endcaps, since magnets provide
weak resistance to shear forces. The second feature is that facing
endcaps have complementary pegs/holes that further prevent
sliding motions.

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other researchers to compare our results to their own and to evaluate the potential real-world applications of our modular robot
design. For our system, the COT of single module locomotion is
53200 J · m−1 · kg−1 . COT values for multi-module structures
are provided below.
B. Deformation Primitives

Fig. 2. Module design. (a) A single module is composed of a stellated skeleton,
twelve SMA actuators, and eight endcaps. (b) Front/side view of the module.
(c) The skeleton is designed to sustain loading and also to hold SMA actuatorsand endcaps. (d) An endcap’s inner part (e) An endcap’s outer part.

C. Module Fabrication
The skeleton and endcaps are 3D printed (Voxel 3D Printer,
Monoprice) using TPU material (1.75 mm, Amazon Basics)
and PETG material (1.75 mm, Amazon Basics) separately. The
inner endcaps are glued to the endcap stoppers on the skeleton.
Each SMA is crimped with an electric wire and a fishing wire
inside a ferrule, and tied to the SMA slot in the skeleton passing
through the holes in the inner endcaps. For the outer endcaps,
magnets are glued according to the designed polarity as shown in
Fig. 2(e). After all the SMAs are assembled, the outer endcaps
are glued with the inner endcap. A single module’s weight is
47 − 50 g.
IV. CORE FUNCTIONS OF STARBLOCKSStarBlocks have three core functions (see Fig. 3), which are a)
locomotion (to enable self-assembly), b) assorted deformation
primitives (to enable lattice deformation) c) attachment anddetachment (to allow formation of shaped lattices).
A. Locomotion
We hand-designed a walking gait that shifts the center ofmass (CoM) by increasing the friction/normal force at a planted
foot while decreasing the force at the advancing feet by lifting
them,similar totensegrity robots [42]. This walking gait enables
faster locomotion speed than our previous soft modules could
achieve [21]. The detailed locomotion sequence is shown in
Fig. 3(a), with the corresponding SMA actuation sequence. The
current module design enables a maximum step size that is
89.58% of the body length, which is ∼ 26.15× improvementon our prior work. A module can walk 110 mm in 15 minuteswith an average locomotion speed of ∼ 7.33 mm/min (0.102
body length/ min), where more than 80% of the time is used forcooling the actuators.
Cost of Transport (COT) is a metric used to evaluate theefficiency of locomotion in robotic systems. COT provides ameasure of the energy required to move the robot over a given
distance and can be used to compare the efficiency of different
locomotion strategies [42]. We calculated the COT for each of
our locomotion experiments to provide a quantitative measure of
the relative energy efficiency of different assembled structures.
We also believe that reporting the COT is important as it allows

The shape of each module is determined by the lengths ofthe edges, which can be controlled by the actuation of thecorresponding SMAs. In principle, the module can achieve any
quadrilaterally-faced hexahedron shape, with some constraints
on maximum and minimum size. To simplify control of module shapes and allow reasoning about lattice deformations, wechoose five major deformation primitives for a single module:
bend, compress, stretch, stand and shrink. Each of these primitives falls into a symmetry class; for example, stretch involves
two parallel faces (out of six total), so there are three possible
stretch actions.
A. Bend allows rotation of one module with respect toanother, allowing formation of 3D curved surfaces (seeSection VI-A) or rotation actions for locomotion or manipulation (see Section VI-C1). Bend is achieved by actuating
two parallel SMAs on one side. The range of the bending
angle is from 0◦ to ∼ 30◦ .
B. Compress allows linear translation with axial length
reduction while increasing the cross-section area. This modecan be used to increase lateral stiffness, which is beneficial for the spatial operation of slender structures (seeSection VI-C1). Compress is implemented by contracting
four parallel SMAs at the same time to reduce the height ofthe module by ∼ 40%.
C. Stretch achieves axial extension while reducing thecross-section area (Fig. 3(b4)). It is obtained by actuating eight SMAs on two opposite surfaces. This mode canbe useful for tasks that require axial elongation (see Section VI-B1). The maximum stretching length is ∼ 122%.
D. Stand is realized by driving four SMAs on the same
surface (Fig. 3(b5)). The area of the corresponding surface
becomes smaller with a slight increase of the height Thismode can facilitate the generation of curved surfaces bybending four connected modules in different directions andit is useful for detachment of modules (see Section IV-C).
We also used this primitive for gripper function (see Section VI-C1).
E. Shrink is implemented by actuating all twelve SMAs
simultaneously, the volume is reduced by ∼ 30%.
C. Attachment and Detachment Between Modules
Attachment and detachment are needed to form lattices ofvarious shapes. We now describe one effective strategy; others
may be possible.
1) Attachment: To attach two modules, one module first remains motionless while the other module approaches. Then,
all actuators are turned off and magnetic discs on endcaps
form the connection. Due to alignment errors, some of theendcaps may not initially connect. To complete the process andreduce alignment error, both modules simultaneously performthe stand primitive to push the modules together. We characterizealignment performance and connection strength in experiments
described in Section V.

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Fig. 3. Core functions. (a) Locomotion of a single block. (a1) A simplified representative of the distribution of SMA actuators with labels; (a2) Snapshots of
the locomotion of a block with the corresponding actuated actuators labeled. (a3) top view, timeline, and center of mass location during gait. (b) Deformation
primitives of a single block. (c) Attachment and detachment of two blocks.

2) Detachment: To improve the strength of connections,
we designed groove and peg-in-a-hole mechanisms. Theseenhancements, however, make detachment more challenging.
Here, we describe one detachment strategy.
The first motion for detachment is a modified “stand” deformation; this deformation introduces large rotation and translation between connected endcaps (Fig. 3(c2)). To create thisdeformation, vertical SMAs are actuated on one module andhorizontal SMAs on the other, along the interface between themodules. After this operation, the coupled endcaps are staggered, but still close to each other.Four SMAs of each module
perpendicular to the interface are actuated to pull the endcaps
apart. To ensure full detachment,the two modules locomote awayfrom each other. We placed sandpaper on the ground to increase
the friction to provide enough force to separate any remaining
connections. Without sandpaper, help may be needed from othermodules in the lattice; see Fig. 5(b).

connector design; c) connection success rate between two blocks
at varying initial angles and positions.
A. Rod Diameter Choice
Using SMAs, the ideal rod diameter should enable a blocka) deform into desired shapes when SMAs are actuated and b)
return to the original shape when SMAs are released.
We did two experiments to find a rod diameter that satisfies
both requirements for our particular module geometry. We firsttested the relationship between force and displacement of blocks
with various diameters. As showed in Fig. 4(a), given the forceof four SMAs (the black line) and the displacement we needto achieve (27 mm), only diameters less than 4 mm satisfy therequirement. We then measured the SMA length on each block
after release, and found that 4 mm to be an effective rod diameter.
We tested the weight capacity of the actuated module and foundthat it sustained 29.5 N press force. Details are shown by thegreen line in Fig. 4(a).

V. CHARACTERIZATION EXPERIMENTS
We did experiments to characterize a) block stiffness withvarious rod diameters; b) connection force in shear/normal direction with two distinct endcap designs to motivate the peg-in-hole

B. Connection Force
We did two experiments to measure the normal and shear
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Fig. 4. Characterization experiments for core functions. (a) Relationship between force and displacement of single module with different diameters; SMAs
recovered length after cooling down for module with different diameters (b) Characterization experiments for normal force and shear force for blocks w/ andw/o peg-in-hole endcap design. Left: 
1 the force increased until endcaps detached partially (red) or completely (blue) 
2 force decreased until detaching (red)Right: 
1 Compression force increased until top endcaps detached partially (red & blue) 
2 force decreased until detached (blue) or the top endcaps touch thebottom endcaps (red) 
3 the force needed to compress top and bottom endcaps increased until the bottom endcaps detached partially (red) 
4 force decreased until
detached (red). (c) Alignment experiments for a pair of modules w/o and w/ peg-in-hole endcap design.

shows the results. The peg-in-hole mechanism is designed tocompensate for the weak magnetic strength in the lateral (shear)direction; the joint functions primarily as a mechanical stopper toprevent sliding between endcaps. The two plots show the significant increased force with peg-in-hole design in both directions,allowing larger lattice structures.
C. Alignment
Two blocks will automatically magnetically connect witheach other within a certain distance and angle. The relative
configuration space is 6D and hard to measure. To simplify,
we place both blocks on the ground and fix the position of
the left block (showed in Fig. 4(c)), where the right block canmove to any position and angles. We discretize the angle into
30◦ , 60◦ , 90◦ , and discretize y value by a step size = 0.5 tomeasure the x values that successfully attach two blocks. In theexperiment, we positioned the right module by hand to achieve a
specific initial position and angle. From the experiments, while
the peg-in-hole mechanism enlarged the connection force, italso increased the difficulty of alignment. We observe that for
30-degree attachment, only part of the peg-in-hole insertion wasachieved for the attached endcaps.
VI. EXAMPLES OF LATTICE STRUCTURES
We provideexamples using StarBlocks to build various lattice
structures for construction, manipulation and locomotion.
A. Example of Lattice Structure for Construction
1) Self-Assembly of a Dome-Shaped Tent: A dome-shaped
tent formed by StarBlocks demonstrates the capabilities ofbuilding load-bearing architecture via self-locking.

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Fig. 5. Applications using StarBlocks. (a) Self-assembly of a dome-shaped tent. (a1) 2D precursor; Snapshots of the formation are shown in (a2)–(a4).
(b) Formation and locomotion of a rolling robot. (top left) Self-assembly of the wheel from a chain-shaped precursor to standing wheel; (right) When assembled,
the robot can roll forward; the rolling is mainly induced by the shift of center of the mass as modules deform; (bottom left) The rolling robot can self-disassemble
back to the chain-shaped configuration by detaching the top-middle connection. (c) Arrangement of modules for a quadruped. (c1) Front view; (c2) Arrangement;(c3) Quadruped with a walking gait. (d) Ball manipulation with a soft robotic arm with a gripper. (d1) Initial state. The tip module functions as a soft gripper; (d2)
Lifting up; (d3) Orientating toward the ball; (d4) Stretching to reach; (d5) Grabbing; (d6) Placing the ball into the target box.(e) Non-prehensile manipulation of aball.

Fig 5(a) shows a 2D precursor shape that can be assembled
from loose modules. Modules are arranged into the pattern ofa “+” sign with two additional modules at the end of eachline segment. “Bend,” “stretch,” and “stand” modes are thenapplied by various modules to erect and lock the tent. During
tent construction, the central modules arch up to form two orthogonal main arcs of a dome as a supporting skeleton. To realize
passive locking and large loading-carry ability after assembly,
the additional outer modules passively attach to neighboring
modules to form a circle. To simplify the attachment and mediate
the alignment issue of neighboring endcaps, we used simplified
endcaps without the peg/hole joints for connecting modules.
To verify passive self-locking of the self-assembled tent,
we conducted weight load tests without supplied power. The
experiment shows that the tent can sustain at most ∼ 1.5× of its
own weight (see Fig. 1(e)).

Ultimately, we envision that larger-scale versions of modular deployable tents would be useful for rescue in disasters.
Specifically, soft modules can be stored and transported in acompact configuration, and due to their light weight and compliance, and might be dropped into position by helicopter.
B. Example of Lattice Structure for Locomotion
1) Self-Assembly of Rolling Wheel: Fig. 5(b) shows assembly of a chain of modules on plane into a wheel; the rolling process; and the process of disassembly. To assemble the wheel, twoends of a chain of modules attach once the lattice bends. To roll
the wheel, the center of mass of the wheel is shifted rightwards
continuously, by repeatedly stretching the module close to thebottom labeled in Fig. 6. Currently, the wheel can move forward
72 mm in 52 s, achieving an average speed of ∼ 82.8 mm/min

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Fig. 6. Locomotion mechanism of the rolling robot. (a) Initially, the center ofthe mass is in the middle; (b) The center of the mass shifts rightward when we
stretch the specific module; (c) The shift causes the robot to roll forward.
Fig. 7. Maximum reach of the arm in the x direction; black dots show a pointon the center of the end effector).

(1.15 body length/ min), which is 11× the maximum speed of thegaits we developed for a single module. The locomotion could be
sped up by reducing the cooling time needed for SMAs [21]. The
Cost of Transport (COT) is 4782 J · m−1 · kg−1 . To disassemble
the wheel, we use the detachment strategy to separate any two
modules on the top of the wheel. With the help of the gravity ofadjacent modules, the two modules on the top separate easily.
2) Quadruped Dog Locomotion: To explore multi-legged
gaits, we manually assembled 19 blocks together to form a
dog-inspired quadruped (Fig. 5(c)), since we do not yet havea strategy for vertical assembly. Each leg is composed of two
blocks, with an eight-block body and a three-block head.
There are different gaits that a real dog uses for locomotion,
where trot is the most efficient pattern [43]. For the “Trot”
pattern, two legs on the diagonal move forward together. For
our case, to simplify, we modified the normal “Trot” pattern andinstead of letting two diagonal feet move at the same time, wemove the rear foot first to permit a longer time for landing. In
particular, we loop over the pattern “left-rear → right-front →release-SMAs → right-rear → left-front → release-SMAs”. This
arrangement of blocks can locomote 730 mm in 10.4 minuteswith an average speed of ∼ 70.19 mm/min (0.975 body length/min), which is ∼ 9.58 times the speed of the single block and
77% of the time is used in releasing the SMA actuators; the COT
is 898 J · m−1 · kg−1 , which is the most energy-efficient locomotion method in this paper. For comparison, Huang et al. [44]designed a soft robot actuated by SMA, and the calculated COT
equal to 786 J · m−1 · kg−1 .
C. Examples of Lattice Structure for Manipulation
In this section, we explore two very different strategies forobject manipulation: an arm-based gripper, and non-prehensile
contact juggling along the surface of the lattice.
1) Module-Based Gripper and Robot Arm: We implemented
a block-based robot arm to grasp objects and deliver them to atarget box. We designed three control strategies for the arm.
a) “lift:” uses “compress” primitives vertically to decrease thevertical length of robot arm. b) “extend:” uses “stretch” primitives vertically to increase the length of the arm. c) “re-orient:”
individual modules use “bend” primitives.
To perform the experiments, we mounted a chain of modules
under a round table as Fig. 5(d)) shows. We used a single
module as a gripper to grasp an object with the “stand” primitive.
The payload capacity of the arm depends on the connection
force between the uppermost module and the second uppermost
module as it endures the load and the gravity of all the modules
below the uppermost module.
Our experiments in Section V-B demonstrate the endcaps
can sustain more than 20 N before detachment. Considering theestimated gravity of the eight modules attached below the top

module as 4 N, the arm’s maximum payload in fully extended
configuration is no greater than 16 N/1.6 kg.
We also did an experiment to measure some characteristics of
the workspace. We found the maximum reach in the x directionis around 26 cm, and the maximum height the effector can belifted is roughly 25.5 cm (shown in Fig. 7).
Similar to other soft arms, the benefits of the arm structure we
explored are that it is flexible, has high error tolerance and provides safe human-robot interaction. Furthermore, we imagine
that the module-based arm and gripper could reconfigure into
other shapes for objects with different shapes and weights. For
example, to grasp larger objects, modules might be re-arranged
into other shapes, such as using five modules to form the gripper
in the shape of an inverted letter U.
2) Non-Prehensile Manipulation: Fig. 5(e) shows linear manipulation using assembled blocks. The principal is to create awave-like surface deformation to transport the objects similar towhat we implemented in prior work [21].
VII. CONCLUSION AND FUTURE WORKIn this letter, we designed a soft robotic block that can build
passive weight-sustaining structures or actuated structures forlocomotion and manipulation. Self-locomotion and deformation primitives, as well as attachment/detachment capabilities,
permit behaviors including self-reconfiguration, self-assembly,
complex deformation, and robust locomotion.
The proposed system provides opportunities for additional
design and development. Un-tethered robots are needed for deployment outside of the lab, requiring on-board power, computing, sensors, and inter-block communications. To enable betterreconfiguration, we would like to close the loop by adding an
external sensor. Other actuators, such as electromagnetic motors,
dielectric elastomer actuators [45], or super-coiled polymer
actuators [46], would increase actuation speed, with mass orstrength trade-offs.
Our system is capable of self-assembly and self-disassembly
using unique endcaps with magnets. While the mechanical design of endcaps increases the connection force between modules,
the configuration space of alignment also decreased. To completely detach two modules, helper modules, external forces,
or sandpaper are currently needed due to the strength of themagnetic force. New designs are necessary to improve selfdisassembly, such as adding actuators to increase the distance
between magnets to decrease the magnetic force [47] or using
an electromagnet. Another limitation of the current connector isthat the limited connection strength limits the scale of lattices andtheir range of motion. We are exploring new, stronger connector
designs.

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IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 8, NO. 8, AUGUST 2023

Each of the applications (e.g., tent, wheel, arm) show different
potentials, but need refinement to be practically useful. For
example, the tent deployment relies on low friction and a smoothground surface. The single-chain wheel exhibits distinct locomotion capability, but is not particularly stable. A double wheel
might provide such stability. The module-based arm provides
high deformation, but limitations of the connectors limit theweight of the objects that it can manipulate.
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