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Soft Modular Robotic Cubes: Toward Replicating Morphogenetic Movements of the Embryo

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In this paper we present a new type of simple, pneumatically actuated, soft modular robotic system that can reproduce fundamental cell behaviors observed during morphogenesis; the initial shaping stage of the living embryo. The fabrication method uses soft lithography for producing composite elastomeric hollow cubes and permanent magnets as passive docking mechanism. Actuation is achieved by controlling the internal pressurization of cubes with external micro air pumps. Our experiments show how simple soft robotic modules can serve to reproduce to great extend the overall mechanics of collective cell migration, delamination, invagination, involution, epiboly and even simple forms of self-reconfiguration. Instead of relying in complex rigid onboard docking hardware, we exploit the coordinated inflation/ deflation of modules as a simple mechanism to detach/attach modules and even rearrange the spatial position of components. Our results suggest new avenues for producing inexpensive , yet functioning, synthetic morphogenetic systems and provide new tangible models of cell behavior.
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RESEARCH ARTICLE
Soft Modular Robotic Cubes: Toward
Replicating Morphogenetic Movements of the
Embryo
Andrea Vergara
1
, Yi-sheng Lau
2
, Ricardo-Franco Mendoza-Garcia
2‡
, Juan
Cristo
´bal Zagal
1‡
*
1Departamento de Ingenierı
´a Meca
´nica, Universidad de Chile, Santiago, Chile, 2Escuela Universitaria de
Ingenierı
´a Meca
´nica, Universidad de Tarapaca
´, Arica, Chile
These authors contributed equally to this work.
‡ These authors also contributed equally to this work.
*jczagal@ing.uchile.cl
Abstract
In this paper we present a new type of simple, pneumatically actuated, soft modular robotic
system that can reproduce fundamental cell behaviors observed during morphogenesis; the
initial shaping stage of the living embryo. The fabrication method uses soft lithography for
producing composite elastomeric hollow cubes and permanent magnets as passive docking
mechanism. Actuation is achieved by controlling the internal pressurization of cubes with
external micro air pumps. Our experiments show how simple soft robotic modules can serve
to reproduce to great extend the overall mechanics of collective cell migration, delamination,
invagination, involution, epiboly and even simple forms of self-reconfiguration. Instead of
relying in complex rigid onboard docking hardware, we exploit the coordinated inflation/
deflation of modules as a simple mechanism to detach/attach modules and even rearrange
the spatial position of components. Our results suggest new avenues for producing inexpen-
sive, yet functioning, synthetic morphogenetic systems and provide new tangible models of
cell behavior.
Introduction
Cells are the fundamental building block of living organisms. During morphogenesis, cells are
able to contract, change their intercellular adhesion forces and even migrate, organizing them-
selves into different tissues that ultimately give rise to more complex structures and organs
[1,2]. Researchers have tried to build modular self-reconfigurable robots imitating the capacity
of cells to construct systems of varying morphology and function [3]. The development of this
type of robots might result in more versatile and robust machines, capable of adapting their
shape and function to account for new tasks, circumstances and even recover after damage [4].
Modular robots have been constructed using rigid materials, with cell-resembling docking
units often carrying computation, sensing, actuation and energy storage capabilities, and have
demonstrated self-reconfiguration, and even self-replication abilities under well-controlled
experimental conditions [57].
PLOS ONE | DOI:10.1371/journal.pone.0169179 January 6, 2017 1 / 17
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OPEN ACCESS
Citation: Vergara A, Lau Y-s, Mendoza-Garcia R-F,
Zagal JC (2017) Soft Modular Robotic Cubes:
Toward Replicating Morphogenetic Movements of
the Embryo. PLoS ONE 12(1): e0169179.
doi:10.1371/journal.pone.0169179
Editor: Josh Bongard, University of Vermont,
UNITED STATES
Received: March 9, 2016
Accepted: December 13, 2016
Published: January 6, 2017
Copyright: ©2017 Vergara et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: All relevant data are
within the paper and its Supporting Information
files.
Funding: Funded by Office of Naval Research
Global Grant Number N62909-16-1-2164. The
funders had no role in study design, data collection
and analysis, decision to publish, or preparation of
the manuscript.
Competing Interests: The authors have declared
that no competing interests exist.
While cells are inherently soft, current rigid implementations of modular robots fail at
reproducing fundamental cell behaviors that require elements to shrink, squeeze and stretch
while controlling connections to other units [8,9]. These capabilities are especially observed
during the morphogenetic movements of gastrulation, the initial shaping stage of the embryo
[10]. During this process, cells exhibit several mechanical behaviors (see Fig 1). Cells are able
to expand and contract, migrate, attach to each other (cell adhesion), and detach from each
other (cell delamination). Sheets of cells are able to bend inward (invagination), roll inward
(involution), spread by thinning (epiboly) and other mechanically complex behaviors like
detach and migrate freely (ingression) create longer but thinner arrays (intercalation), and
even converge and extend (convergent extension). These set of behaviors allow the generation
of infinite variation of living shapes, ranging from the primordial primitive streak to complex
structures of intricate organs such as the heart. Mechanical forces and behavior result in bio-
chemical changes that ultimately define function and structure of the cell [11]. Creating modu-
lar machines with the capability to replicate these movements will serve to better understand
the way nature creates shape as well as to advance toward artificial systems that can grow and
develop.
Recently a door to soft robotics was opened, and the new field is rapidly expanding with
results on new soft actuators, soft sensors and intelligent soft mechanisms [12]. These robots
are usually implemented with rubber, silicone or deformable material and are expected to
overcome some of the limitations of current rigid robotics. Soft robots are expected to be more
compliant, flexible, robust, light, stable, cheap and even simpler. For example, while many
components are today required for the implementation of a joint or a linear actuator, only one
Fig 1. Outline of some of the fundamental cell behaviors that take place during morphogenesis.
During expansion/contraction cells change their volume. During migration cells are able to travel to different
locations. Cell adhesion involves the capability of cells to bind to other cells or substrate. Cell delamination
involves splitting apart groups of cells. Cell invagination is a type of folding that creates a pocket. Cell
involution is the generation of an inward curvature that results in a new underlying layer. Cell epiboly involves
spreading of cell layers. During ingression cells detach from a main structure to migrate. During intercalation
cells from different rows interpolate creating longer but thinner arrays. Convergent extension involves cells
that converge in one direction to achieve extension in another perpendicular orientation.
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soft structure might be required using soft robotic technologies [13,14]. Soft robots can manip-
ulate delicate objects, conform to their surroundings, move in cluttered environments, and
exhibit dramatic shape deformation [15].
This paper describes the design and fabrication of soft modular robotic cubes based on
magnetic adhesion and pneumatic actuation. The parsimonious design of robotic units allows
complex group behavior that resembles, to a large extent, some of the key morphogenetic
movements of living cells. We demonstrate how soft modules can autonomously and purpo-
sively be detached and even self-reconfigured without relying on unit-embedded active
undocking mechanisms but instead using the coordinated inflation of modules. We also char-
acterize the mechanical behavior of modules and design walking controllers for three modular
configurations. Finally we characterize their behavior in reality and simulation.
Related Work
Onal and Rus introduced the concept of soft modular robots to literature [16]. They created a
soft actuator made of two silicone halves, a non-extensible and an extensible one, which per-
formed two-dimensional motion by bending in one direction when used alone or two direc-
tions when glued back-to-back to another actuator. The authors followed a modular approach
by bonding actuators into serial and parallel configurations that, in combination with control
sequences of electro-pneumatic valves, enabled different locomotion modes. Germann et al.
proposed an active electrostatic connection mechanism for joining extremely lightweight soft
modules [17]. On a different work his group also studied how chains made of soft ring-shaped
limbs can display predictable folding behaviors when released over a flat surface [18]. They
showed how chains constructed with different softness presets would lead to different curvilin-
ear shapes when retracted. Kwok et al. designed a magnetic connector to join soft robots with
hard components [19]. Their device uses an integrated expansive bladder to allow remote dis-
assembly. Morin et al. proposed techniques for fabricating inflatable cubes from thin elasto-
meric tiles [20]. The use of double-tapper dovetails served at increasing the contact area before
gluing tiles by their edges. They manually arranged cubes into different configurations using
soft peg/recess surface connectors. Locomotion capabilities of preassembled soft modular sys-
tems have been studied in simulation and real implementations of chained inflatable spheres
[21,22]. Rus and Vona introduced rigid modular robots able to achieve two-dimensional self-
reconfiguration thanks to expansion/contraction of their flat faces [23]. Before us, Yu et al.
visualized the potential of imitating fundamental cell movements with modular robots [24].
To validate their concept, they built the Morpho modular robot whose modules were linear
actuators made of rigid materials covered with fabric. The authors combined the modules into
assemblies that resulted in quick changes of shapes that they called “self-deformation”. Our
work presents a new soft modular system that is able to autonomously self-reconfigure and
reproduce various important cell behaviors. The design uses permanent magnets for inter-
module self-aligned bonding and relies on simple coordinated inflation of modules to achieve
remote assembly/disassembly.
Design and Construction
Our design was made with strong actuation, simplicity, and lightness in mind. We were
focused on producing a system that reproduces the general aspects of cell-environment in-
teraction rather than the complex physics of cell motility, adhesion or expansion. Simple
inspection of gastrulation in drosophila [9] led us to choose three basic requirements for mod-
ules: They should (1) allow control of expansion/contraction, (2) adapt their shape to fit sur-
rounding space and (3) have the ability to attach and detach to each other. We used a silicon
Soft Modular Robotic Cubes: Toward Replicating Morphogenetic Movements of the Embryo
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elastomer (Ecoflex 00–30, Smooth-on, http://www.smooth-on.com) to fabricate the robotic
modules with soft lithography [25]. The silicone is very soft and strong allowing for up to
900% strain before fracture. Fig 2 shows the fabrication process. Modules are 20×20×20mm
(8cc) elastomeric cubes with a hollow core to enable pneumatic actuation by inflation, and a
disc-shaped cavity on every face to hold Neodymium cylindrical permanent magnets (Dura-
mag 3000 Gauss NdFeB Neo magnet, 6mm dia ×2mm thk) that serve for docking (Fig 2C and
2D). Rigid 3D-printed frames were used to avoid magnets from collapsing toward the center
of the cubes, to provide a smooth transition between hard magnets and extremely soft silicone,
as well as to improve bonding by increasing the contact area between the different materials.
Frames fit tightly inside the disc-shaped holes of the soft body as shown in Fig 2D. The frames
and required molds were 3D printed with photopolymer resin (RGD240, Stratasys, http://
www.stratasys.com) using a high resolution 3D printer (ObJet 30, Stratasys, http://www.
stratasys.com). The liquid polymer precursor was mixed and then poured into the 3D printed
molds shown in Fig 2A and 2B.
The docking system results in homogeneous modules with gendered connecting faces,
where three faces release a north-pole magnetic field and the other three a south-pole field (Fig
2C). The induced soft lattice structure constraints each module face to find a reversed polarity
face in front. Modules can aggregate into arbitrary 3D shapes as long as their magnetic orienta-
tion matches the preexisting cubic lattice orientation and inter-module connection strength
allows shape preservation [26]. Connection strength evaluations (S3 Appendix) indicated that
up to eight modules can be vertically suspended on a single column and three modules cantile-
ver. Pneumatic actuation and magnetic docking are compatible choices with the soft nature of
Fig 2. Fabrication of soft robotic modules. The process begins by producing two silicone bodies using
multi-part 3D printed molds: the upper body (a) and the lower body (b). Removable pins hold the interior
discs used to create cavities on each face. The resulting silicone bodies are glued together and magnet
subassemblies are introduced inside the resulting disc-shaped cavities (c). The insert shows how magnets
are introduced inside a wrapping frame to enlarge contact surface with silicone and improve bonding. The
resulting module is finally shown in (d).
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the modules as they lack of internal mechanisms that would interfere with the elasticity other-
wise. The size of modules was chosen to be as small as possible to simplify the scalability of the
system.
The fabrication also relies in two multi-part molds. The first served for casting the upper
body (Fig 2A) of a cube and the second for producing the lower body (Fig 2B) of a cube. These
bodies are glued together using the same silicone resin that makes up the body. Curing liquid
polymer on molds takes 20 minutes at 60˚C; a process which otherwise might take up to four
hours at room temperature. Magnets are then inserted on each face and covered with a sealing
drop of silicone that prevents them from being pulled apart from the assembly. A final curing
stage is executed during additional 10 minutes at 60˚C. The final step consists on producing a
small air inlet on one vertex of the cube and then introducing a 3mm airline. The resulting
cube weights 10 grams (S3 Fig shows photo series of the manufacturing process).
Actuation is achieved by volumetric changes induced by computer-controlled pres-
surization of modules. Each module is connected to a dedicated pneumatic line driven by a
miniature diaphragm air compressor (Thinker, 60 kPa pressure, 60 mL/min air flow) for
pressurization and a solenoid valve (12v, 26 kPa max pressure, normally closed) for pressure
relief. The electro-pneumatic setup (see S1 Appendix and S4 Fig) considers independent cir-
cuits for each module. The activation signals of air pumps and relief valves are driven by an
Arduino Leonardo (http://www.arduino.cc). The low current signals were amplified with
2N2222 transistors.
Experiments
The following is a description of the different behaviors that where reproduced with the coor-
dinated actuation of the soft modules:
Expansion/Contraction
We characterized the capability of soft modules to expand and contract when controlling their
internal pressurization. We measured the volumetric expansion of cubes as function of their
internal pressure (see Fig 3A). An expansion of 106% respect to initial external volume results
when applying a pneumatic pressure of 15 kPa. We also measured the dynamic transient
response to a 137.9 kPa impulse (see Fig 3B) applied to the input hose over a very short period
of time. The figure shows how a rapid volumetric expansion (1277%) can be achieved after
200 ms.
Fig 3. Volumetric Response of Modules. a) Volumetric expansion vs pressure. b) Instantaneous volumetric
expansion response to a 138 kPa pressure impulse showing a rapid expansion of the module. Models
described on Eqs 1and 2are fitted to the data.
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Eq 1 models the normalized volumetric expansion as function of the static pressure P
0
inside a module. The constant ΔV
τ
describes the volumetric expansion at which accelerated
expansion takes place, and P
max
(P
0
<P
max
) is the maximum pressure which can be applied to
a module before failure.
DVchamberðPoÞ ¼ DVtln Pmax
Pmax Po
  ð1Þ
Eq 2 adds time dependency to the same model by considering the dynamics required to
build up pressure inside a module, P
0
=P
i
(1 –e
(-t/RC)
), resulting on an expression of the volu-
metric expansion as function of time t.RC is the time constant and P
i
is the maximum instan-
taneous pressure inside a module. We fitted both models to the experimental data (see model
on Fig 3A and 3B) resulting in the following values for the different constants: ΔV
τ
= 28.2%,
P
max
= 15.6 kPa for the static case and ΔV
τ
= 28.2%, P
max
= 138 kPa, RC = 2 ms, P
i
= 137.9 kPa
for the dynamic case. The later high level of pressure was only sustained during the very short
transient. S2 Appendix explains both models and details the methodology used during these
tests.
DVchamberðtÞ ¼ DVtln Pmax
Pmax Pi1et
RC
 
! ð2Þ
Adhesion
The soft modular units are able to attach to each other thanks to the magnetic force taking
place between their faces. We measured the attraction force between a pair of facing magnets
as function of distance and we fitted a quadratic model to the data. Equation S10 describes
resulting model. S7 Fig shows the experimental data together with the fitted model. Detailed
explanations of the measuring setup and model are presented in S3 Appendix.
Although the current locking mechanism still limits the scalability to only three modules
suspending cantilever, several modules can be connected when supported over a horizontal
surface or when floating on water. We tested the capability of a group of eight interconnected
modules to purposively incorporate and attach new units while moving horizontally. Fig 4
shows a sequence of images displaying how a group of six connected modules is able to travel
Fig 4. Cell adhesion during collective migration. A sequence of images displaying how a group of six
connected modules is able to travel (from right to left) thanks to the coordinated inflation of modules. At time
t = 8m:40s an adhesion occurs resulting in a new module incorporated to the group. The new seven-element
robot continues travelling sideways until a new module adheres at t = 18m:48s. Then the resulting eight-
element robot continues moving sideways.
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(from right to left) thanks to the coordinated inflation of modules. At time t = 8m:40s adhesion
between the group and a new module occurs. The seven-element robot continues travelling
along its own axis until a new module adheres at t = 18m:48s. The resulting eight-element
robot continues moving. As the worm-like system incorporates new modules to itself, they are
also incorporated to actuation by means of external coordination provided by a host computer
and a motion capture system (Optitrack, http://www.optitrack.com).
Collective Migration
Inflation of a single isolated module does not result in any motion. Therefore we tested the
locomotive capabilities of systems constructed using groups of soft modular robotic units. We
measured the performance of these systems under simulation (VoxCad, http://www.voxcad.
com) and then using real physical modules (see Fig 5). Details of the simulation implementa-
tion are presented in S4 Appendix. Sinusoidal volumetric sequences (Equation S11) com-
manded the inflation of simulated modules and binary sequences (Equation S12) commanded
the inflation of real modules. Signals were shifted ¼phase with respect to their immediate
neighbor’s actuation command (See S1 Appendix for details). Measured displacements of all
three systems are shown in Fig 6A for the simulated systems, and Fig 6B for their real physical
implementation. Displacement of System 1, or the worm-like system, took place predomi-
nantly in the longitudinal direction and was consistently fastest. Inspection of video sequences
(S1 Video) shows how peristaltic wave [27] propagation results in the overall displacement of
the system. System 2, or compound cube, shows a small displacement toward the bottom.
Finally, System 3, or legged, moves left and right without showing a noticeable total displace-
ment. Despite speed magnitude differences observed between simulation and reality (Fig 6)
one can appreciate how simulation allows predicting the overall trend of these systems.
Delamination
The ability to purposively detach modules is required to mimic the delamination capabilities
of living cells and is widely recognized as a requirement for achieving self-reconfiguration.
Fig 5. Instantaneous images taken during the locomotion of three different systems assembled using
soft modular robotic units. a) System 1, a worm configuration, b) System 2, a 2×2×2 deformable cube c)
System 3, a two legged machine. The timestamp is displayed on the left column in minutes:seconds format.
Corresponding simulated systems are displayed on top. Red arrows indicate an estimated displacement
vector.
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Usually providing a modular unit with actuation and control to enable detachment is expen-
sive since modules should be embedded with the circuitry and mechanical actuators for dock-
ing/undocking (e.g. electro magnets). We found that coordinated inflation/deflation of soft
neighboring modules can be used as an alternative method to detach specific areas of a soft
modular assembly. Fig 7 shows a sequence of images taken while a group of nine units
detaches certain elements thanks to the inflation of the central module. Despite the symmetry
of the actuation pattern, detachments take place on the lower right portion of the structure.
This symmetry break can be explained by small variations on the thickness of the silicone layer
that covers magnets. This mode of detachment is a remarkable property of these soft modular
Fig 6. Characterization of locomotion. Displacement as function of time recorded from the three simulated(a) and real
(b) systems shown in Fig 5. Experiments show consistency between the predicted behavior in simulation and measured
behavior in reality. For example, system 1 consistently shows the ability to travel faster and at constant pace.
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Fig 7. Cell Delamination. A sequence of images showing a behavior that resembles cell delamination on a
modular system constructed with nine units. The sequence illustrates how inflation on a central module
produces two detachments on the lower right portion of the image.
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robots and promises to become an alternative for discharging the onboard complexity of mod-
ular machines while enabling purposive localized detachment.
Invagination and Involution
We examined the potential of a group of 24 modules to reproduce the fundamental mechanics
of cell invagination and involution. These behaviors require modular structures to flex, a pro-
cess that can be reproduced by combining elements that expand while others dwindle. To
reduce module-surface friction we performed this experiment, as well as the remainder tests,
inside a vat containing water. The module buoyancy enabled lateral displacements while keep-
ing structures submerged at the bottom of the recipient. We assembled a soft beam made of
two parallel rows having twelve modules each, as shown in Fig 8. First we tested the capability
of the system to flex by inflating the lower row elements and keeping the upper row unactuated
(See Fig 8A). Then we tested the possibility of alternating the direction of curvature along the
beam. We used the inflation pattern shown in Fig 8B where the first and last three elements of
the upper row are inflated as well as the fourth up to the ninth element of the lower row. As a
result, the assembly transitioned from a rectangular to a curvy shape that shows two curvature
inflections. S4 Appendix shows an example of shapes that can be achieved when using eighty
simulated modules. These behaviors demonstrate the potential of a group of soft modular
robots to resemble to a great extend the cellular behaviors of invagination and involution.
Epiboly
A simple experiment to replicate epiboly consisted on arranging eight modules on a row and
then actuating over the arrangement to achieve linear extension. Fig 9 displays results from
applying this procedure. Initially the group of modules is unactuated. At t = 1s the eight
Fig 8. Cell invagination. Underwater experiments using a rectangular beam assembled using 24 soft
modular robots. a) Transition from rectangular to curved shape. b) Transition from rectangular to double
inflection curvature. Inflation patterns are displayed on a lower box using red for inflated modules and light
blue for unactuated modules. Time stamps are in the format seconds:centiseconds.
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modules are pressurized (b) reaching an axial extension of 29% with respect to initial length at
t = 2.05s.
Self-Reconfiguration
We explored the ability of groups of soft modular robots to reconfigure themselves into different
layouts. We built four modular setups by combining different number of actuated and unactuated
modules. The remaining figures illustrate sequences of images displaying the inflation of modules
and resulting reconfigurations for each setup. Each frame displays a time stamp together with a
box illustrating the pattern of inflated modules in red and resting modules in light blue. The fol-
lowing sub-sections describe each configuration together with the experimental findings.
Setup 11-actuated, 11-unactuated (11A-11U). Fig 10 displays a sequence of cell behav-
iors that enable the transition from an initial ‘C’ structure (a) to a final ‘O’ disposition (l). The
reconfiguration is achieved by first producing a curvature on the exterior portion of the struc-
ture (b) by activating eleven modules located at the periphery. As a result form this behavior a
group of modules adheres to their neighbors closing the ‘C’ into an ‘O’ (c). Then delamination
takes place (e) producing a vertical streak on the center of the structure. At this point the
peripheral modules are deactivated resulting in the migration of a group of four modules
toward the center (h-i). This results in a new stable configuration (j-l).
Setup 2-actuated, 14- unactuated (2A-14U). Fig 11 displays a sequence of cell behaviors
that enable the transition from an initial ‘C’ structure (a) to a final ‘T’ disposition (i). First the
lower-center module is inflated (b), this results in the closing of the ‘C’ with the transition of
Fig 9. Cell Epiboly. Underwater experiments with a row of eight soft modules. The sequence of images
displays a behavior that resembles the cellular behavior of epiboly. Initially modules are not pressurized. At
t = 1s modules are pressurized resulting in 29% linear extension of the array at t = 2.05s. Time stamps are in
the format seconds:centiseconds.
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two modules toward the left. The module deactivates (d). Next the upper-center module acti-
vates (e) and deactivates (h) resulting in the new stable ‘T’ shape (i).
Setup 3-actuated, 13- unactuated (3A-13U). Fig 12 displays an alternative actuation
sequence that results in equivalent topological change as previous situation (Transition from
‘C’ to ‘T’). In this case actuation takes place on two lateral and one central module. First the
two lateral modules are inflated (b) resulting in the closure of the ‘C’ toward the center. Then
the lateral modules are deactivated (d) and the upper-center module activates (f) and deacti-
vates (i) resulting in the new stable ‘T’ shape (i).
Setup 2-actuated, 6-unactuated (2A-6U). Fig 13 displays a case of reconfiguration
achieved with a reduced number of modules. Eight modules were initially configured into a
square missing one of its vertices (a). Two diagonally opposite modules inflate (b) producing
the anti-clockwise rotation and translation of the upper-center module toward the left. Simul-
taneously the left most center module moves upside right and rotates clockwise resulting in a
new inter-module attachment (c) with subsequent detachment (d). Finally modules are deacti-
vated and a new stable squared shape emerges (e-f).
Setup 2-actuated, 17-unactuated (2A-17U). In this case we investigated the possibility of
achieving different output configurations by keeping the same initial setup and just modifying
the actuation pattern. Fig 14 displays an initial ‘E’ configuration (a). Actuation on a lower-left
module (b) results in the partial displacement of one column from the right toward the center
(c). The displacement is then consolidated by the actuation of a lower-right module (d,e)
which results in the final ‘F’ configuration. Fig 15A displays the same ‘E’ initial configuration
as shown on Fig 14A. In this case the actuation order is inverted and the lower-right module is
first actuated (b). This results in the partial displacement of the central column toward the left
Fig 10. Self-Reconfiguration on configuration 11A-11U. Demonstration of self-reconfiguration on a group
of 22 modules submerged in water. a) The group is initially configured in a ‘C’ shape. At t = 1s the outer
modules are inflated (b) producing a closure of the shape (c). A delamination between four central modules
takes place at t = 5.4s (e). Deactivation of peripheral modules results in migration of a group of four modules
toward the center (h-i) resulting into a new stable configuration (j-l). Time stamps are in the format seconds:
centiseconds.
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Fig 11. Self-Reconfiguration on setup 2A-14U. Demonstration of self-reconfiguration on a group of 16
modules submerged in water. Initially a lower-center module is inflated (b) resulting in the closing of the ‘C’.
Subsequently the module deactivates (d). Then the upper-center module activates (e) and deactivates (h)
resulting in the new stable ‘T’ shape (i). Time stamps are in the format seconds:centiseconds.
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Fig 12. Self-Reconfiguration on setup 3A-13U. Demonstration of self-reconfiguration on a group of 16
modules submerged in water. The two lateral modules are first inflated (b) resulting in the closure of the ‘C’.
Lateral modules are then deactivated (d). Next the upper-center module activates (f) and deactivates (i)
resulting in the new stable ‘T’ shape.Time stamps are in the format seconds:centiseconds.
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Soft Modular Robotic Cubes: Toward Replicating Morphogenetic Movements of the Embryo
PLOS ONE | DOI:10.1371/journal.pone.0169179 January 6, 2017 12 / 17
(c). The displacement is then consolidated by the actuation of the lower-left module (d,e)
which results in a different final ‘C’ configuration.
Conclusion
This research demonstrates how simple pneumatically actuated soft modular robots can
achieve self-reconfiguration and mimic various cell behaviors observed during morphogenesis.
The fabrication method uses soft lithography for producing composite elastomeric hollow
cubes and permanent magnets as passive docking mechanism. Instead of relying on rigid
onboard-actuated docking mechanisms, we exploit the coordinated inflation/deflation of
modules as a mechanism to detach and rearrange the position of specific modules. While tra-
ditional approaches to modular robotics would suggest the need of embedding modules with
active latching mechanisms we observe how reconfiguration of units can be obtained thanks
to the coordinated inflation of modules. Previous studies have suggested forms of modular
reconfiguration on rigid heterogeneous robots without relying on active latching mechanisms
[28]. Our results demonstrate that reconfiguration can be achieved with passive latching on
Fig 13. Self-Reconfiguration on setup 2A-6U. Demonstration of self-reconfiguration on a small group of 8
modules submerged in water. Two diagonally opposite modules inflate (b) producing the anti-clockwise
rotation and translation of the upper-center module toward the left. At the same time the left most center module
moves upside right and rotates clockwise resulting in a new inter-module attachment (c) and subsequent
detachment (d). Finally a new stable squared shape emerges (e-f). Time stamps are in the format seconds:
centiseconds.
doi:10.1371/journal.pone.0169179.g013
Fig 14. Self-Reconfiguration on setup 2A-17U, First Actuation Pattern. First part demonstrating how
varying actuation pattern results in different configurations. A group of 19 modules is initially configured into an
‘E’ shape (a). In this case the lower-left module is first inflated (b) and then the lower-right module is inflated
(d,e). This actuation pattern results in a final ‘F’ shape. Time stamps are in the format seconds:centiseconds.
doi:10.1371/journal.pone.0169179.g014
Soft Modular Robotic Cubes: Toward Replicating Morphogenetic Movements of the Embryo
PLOS ONE | DOI:10.1371/journal.pone.0169179 January 6, 2017 13 / 17
even simpler homogenous modular robots, without having recourse to sophisticated mechani-
cal implementations.
Departing from the same initial configuration we showed how different final configuration
states can be consistently achieved when applying different control patterns.
While initial and final configurations are compatible with a rigid lattice we observe that self-
reconfiguration is in general achieved thanks to the capability of soft modules to break a rigid lat-
tice and sustain stable intermediate configurations that are only possible due to their elastic nature.
A thorough understanding of this self-reconfiguring process requires modeling the details of the
magneto-elastic interaction between modules, which is beyond the scope of the present study.
We also demonstrated how collective migration can be accomplished by a group of soft
modules. In this case modules are able to migrate in the same direction while maintaining
their inter-module connections. Similarly as in the case of living cells [29][30] we also verify
that modules migrate more efficiently in groups rather than by themselves.
Our experiments also showed how simple soft modules can reproduce to great extend the
overall mechanics of cell delamination, invagination, involution and epiboly. While other cell
behaviors still remain unexplored (ingression, intercalation, convergent extension, etc.) our
results already expose an interesting avenue for producing inexpensive, yet functioning, syn-
thetic morphogenetic systems.
Supporting Information
S1 Appendix. Actuation of soft robotic modules.
(PDF)
S2 Appendix. Modeling the expansion of soft modular robotic cubes.
(PDF)
S3 Appendix. Characterization of inter module connection strength.
(PDF)
S4 Appendix. Simulation of soft modular robotic cubes.
(PDF)
S1 Fig. Pneu-electic diagram displaying the connections used for modulating the internal
pressurization of soft modules. The air line of each soft module is driven by an independent
Fig 15. Self-Reconfiguration on setup 2A-17U, Second Actuation Pattern. Second part demonstrating
how varying actuation pattern results in different configurations. A group of 19 modules is initially configured
into the same ‘E’ shape (a) as in Fig 14A. In this case the lower-right module is first inflated (b) and then the
lower-left module is inflated (d,e). This inverted actuation pattern results in a different ‘C’ shape. Time stamps
are in the format seconds:centiseconds.
doi:10.1371/journal.pone.0169179.g015
Soft Modular Robotic Cubes: Toward Replicating Morphogenetic Movements of the Embryo
PLOS ONE | DOI:10.1371/journal.pone.0169179 January 6, 2017 14 / 17
pneu-electric circuit. Each circuit contains a diaphragm compressor for pressurization and a
solenoid valve for relief, each one is activated using a transistor driven by 5v digital signals pro-
duced by an Arduino board.
(TIFF)
S2 Fig. A simulation of eighty modules reproducing a double inflection behavior that
resembles invagination. Inflated modules are displayed in blue and unactuated modules are
shown with green. Time stamps are in the format seconds:centiseconds.
(TIFF)
S3 Fig. Photos taken during the fabrication of one soft module. 1. Filling molds with sili-
cone. 2. Taking parts out from the mold. 3. Cutting residual material. 4–6. Gluing together dif-
ferent parts. 7. Inserting magnet inside the frame. 8. Module showing one magnet sub-
assembly inside.
(TIFF)
S4 Fig. The actual pneumatic setup displaying solenoids, pneumatic pumps and lines.
(TIFF)
S5 Fig. Illustration of an unactuated empty module (left) and a heavily pressurized module
(right) displaying a volumetric expansion 700% superior to initial volume.
(TIFF)
S6 Fig. Illustration of the setup used for measuring volumetric expansion of modules. a)
Power source. b) Air pump. c) Manometer. d) Beaker. E) Module under water.
(TIFF)
S7 Fig. Attraction force vs distance measured for a pair of magnets (Duramag 3000 Gauss
NdFeB Neo magnet). The figure also displays the model (Equation S10) fitted to the data.
(TIFF)
S8 Fig. a) Attraction force measurement setup. Distance was modulated by adding paper
sheets (0.1mm thk) between magnets. The force was measured as the resulting weight required
to detach magnets. Adding drops of water to the canister served to increase weight. b) Vertical
arrangement of modules. c) Cantilever arrangement of modules.
(TIFF)
S9 Fig. Images taken during the rapid volumetric response to an impulse of 137.9kPa.
Time stamps are in milliseconds.
(TIFF)
S1 Video. Experiments of Self-Reconfiguration, Invagination and Locomotion.
(MP4)
S1 File. Supporting CAD.
(ZIP)
Acknowledgments
We thank laboratory assistance provided by Joakin Ugalde.
Author Contributions
Conceptualization: JCZ RFMG.
Soft Modular Robotic Cubes: Toward Replicating Morphogenetic Movements of the Embryo
PLOS ONE | DOI:10.1371/journal.pone.0169179 January 6, 2017 15 / 17
Data curation: AV JCZ RFMG YL.
Formal analysis: AV JCZ RFMG YL.
Funding acquisition: JCZ.
Investigation: AV JCZ RFMG YL.
Methodology: JCZ RFMG AV.
Project administration: JCZ.
Resources: JCZ.
Software: AV JCZ YL.
Supervision: JCZ RFMG.
Validation: AV JCZ.
Visualization: JCZ AV RFMG.
Writing – original draft: JCZ AV RFMG.
Writing – review & editing: JCZ AV RFMG.
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Supplementary resources (14)

... Adaptation has been shown to improve soft robot evolution in real-world (Vujovic et al., 2017) and simulated robots (Kriegman et al., 2018). Morphogenesis has been demonstrated on modular robotic platforms (Vergara et al., 2017). Understanding how to harness the power of developmental processes is a key step for progressing from simple soft robots to complex and intelligent machines that manifest behaviours driven by seemingly conscious action. ...
... Realising soft modular or self-assembling robots is less common, largely due to the inherent difficulties in fabricating and controlling continuum bodies. However, modular soft robots are seeing increasing use (Kriegman et al., 2020b), for example tensegrity systems (Zappetti et al., 2017), tendon-driven structures (Malley et al., 2017), and soft modular cubes for investigating morphogenetic movements of the embryo (Vergara et al., 2017). ...
... In reality, largescale physical experimentation methods are facilitating significant numbers of real-world evaluations. Automated (Chapter 6) and scalable (Kriegman et al., 2020b) methods show promise, as do modular and reconfigurable systems (Nygaard et al., 2018;Vergara et al., 2017). At a high-level, novel optimisation techniques can guide design exploration in silico and in reality. ...
Thesis
Roboticists increasingly look to biological systems for inspiration when designing and improving robotic systems. Simultaneously, building bio-inspired robotic systems can aid in the understanding of fundamental biological principles. In this context, the concept of embodied intelligence hypothesises that intelligent behaviours are the result of complex interactions between the brain, body (or morphology) and environment, rather than being driven purely by computational power in the brain. At the most basic level, embodied intelligence is driven by real-world physical interactions. By harnessing these interactions, unconventional `brainless' robotic systems have demonstrated complex behaviours driven purely by passive interactions. This thesis explores how complex behaviours emerge from interactions in two different low-level physical systems: falling paper and Bernoulli-balls. In falling paper systems, different paper shapes exhibit a range of behaviours when released into free fall. By altering morphological properties such as shape and weight, different behavioural modes can be triggered. In Bernoulli-ball systems, a ball is placed into a vertical airflow. If the morphological properties of the ball, for example size and density, and the environmental properties of the airflow, for example speed and width, are combined appropriately, the ball exhibits self-stable hovering within the airflow. In Part I, I investigate falling paper systems. I introduce the novel V-shaped falling paper system. The relationship between morphology and system behaviours is explored and a data-driven modelling approach is developed to understand this. I explore the nature of behaviour transitions in the system. Certain behaviour transitions appear random, while others are more deterministic, and this variability is linked to morphology. Different methods are developed to represent this. I investigate generalised falling paper systems via the development of an automatic experimental platform capable of fabricating, dropping, observing and modelling hundreds of different paper shapes. Since falling paper systems are challenging to model using conventional methods, combining a data-driven approach with automatic experimentation is powerful. In Part II, I investigate Bernoulli-ball systems. I explore the behaviour of a single Bernoulli-ball. A reduced-order model is derived to represent the main dynamics, and a minimalistic control policy is developed to modulate the ball hovering height by changing the airflow properties. I introduce the novel concept of a collective Bernoulli-ball: multiple hovering balls in a single airflow. This collective system exhibits a range of agent- and population-level behaviours, and these are investigated. The stability of, and relationship between, different behaviours is shown to be dependent on the balloon morphology and the environmental properties of the airflow. In summary, the work in this thesis relates to the emergence of non-trivial behaviours from low-level embodied physical systems. The main contributions are the investigation of novel dynamics in these systems and the development of methods for understanding, representation and design. Ultimately, the work represents a small step toward the goal of creating artificial lifeforms with increasingly complex behaviours.
... These constraints on computation are, by design, as much a promise from Turing's pioneering theory of the universe of computability as a constraint on where computability begins and ends (Pattee, 2007(Pattee, , 2001Sprevak, 2017). And this scaledependent inflexibility of computation is a primary reason for the continuing and growing controversy over whether computers are always appropriate metaphors for the mind (Bickhard, 2009;Bickle, 2015;Bravo et al., 2021;Brette, 2019;Chemero, 2009;Christensen and Bickhard, 2002;Cobb, 2020;Degenaar and O'Regan, 2017;Gibson, 1979Gibson, , 1966Hooijmans and Keijzer, 2007;Kelty-Stephen et al., 2022a;Kondepudi et al., 2017;Levin et al., 2021;Lyon et al., 2021;Matthews and Vosshall, 2020;Newen et al., 2018;Nielsen, 2019;Pattee, 1995Pattee, , 1974Raja, 2021;Rosen, 1991;Searle, 1990;Turvey and Carello, 2012;Vergara et al., 2017;Von Bertalanffy and Sutherland, 1974;Wood, 2019). Ultimately, we would like to be able to explain where the cognitive faculties of computation come from and when organisms engage or disengage them in day-to-day life. ...
... However, the Bernsteinian perspective has become more explicit about abundant degrees of freedom being a "blessing" (Latash, 2012). That is, with accruing evidence about the strict constraints on and repeated failures of computational models to explain or keep pace with contextsensitive performance (Bickhard, 2009;Bickle, 2015;Bravo et al., 2021;Brette, 2019;Chemero, 2009;Christensen and Bickhard, 2002;Cobb, 2020;Degenaar and O'Regan, 2017;Gibson, 1979Gibson, , 1966Hooijmans and Keijzer, 2007;Kelty-Stephen et al., 2022a;Kondepudi et al., 2017;Levin et al., 2021;Lyon et al., 2021;Matthews and Vosshall, 2020;Newen et al., 2018;Nielsen, 2019;Pattee, 1995Pattee, , 1974Raja, 2021;Rosen, 1991;Searle, 1990;Turvey and Carello, 2012;Vergara et al., 2017 Bertalanffy and Sutherland, 1974;Wood, 2019), the creative role of interactions across scale in developing coordination has come to appear increasingly more promising than strictly computational explanations of dexterity. For such a latter possibility, more degrees of freedom are going to provide a wider set of fluid configurations for supporting dexterity. ...
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Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor—that of the cascade. The time has come to confront Turing’s cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing’s cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.
... These constraints on computation are, by design, as much a promise from Turing's pioneering theory of the universe of computability as a constraint on where computability begins and ends (Pattee, 2007(Pattee, , 2001Sprevak, 2017). And this scaledependent inflexibility of computation is a primary reason for the continuing and growing controversy over whether computers are always appropriate metaphors for the mind (Bickhard, 2009;Bickle, 2015;Bravo et al., 2021;Brette, 2019;Chemero, 2009;Christensen and Bickhard, 2002;Cobb, 2020;Degenaar and O'Regan, 2017;Gibson, 1979Gibson, , 1966Hooijmans and Keijzer, 2007;Kelty-Stephen et al., 2022a;Kondepudi et al., 2017;Levin et al., 2021;Lyon et al., 2021;Matthews and Vosshall, 2020;Newen et al., 2018;Nielsen, 2019;Pattee, 1995Pattee, , 1974Raja, 2021;Rosen, 1991;Searle, 1990;Turvey and Carello, 2012;Vergara et al., 2017;Von Bertalanffy and Sutherland, 1974;Wood, 2019). Ultimately, we would like to be able to explain where the cognitive faculties of computation come from and when organisms engage or disengage them in day-to-day life. ...
... However, the Bernsteinian perspective has become more explicit about abundant degrees of freedom being a "blessing" (Latash, 2012). That is, with accruing evidence about the strict constraints on and repeated failures of computational models to explain or keep pace with contextsensitive performance (Bickhard, 2009;Bickle, 2015;Bravo et al., 2021;Brette, 2019;Chemero, 2009;Christensen and Bickhard, 2002;Cobb, 2020;Degenaar and O'Regan, 2017;Gibson, 1979Gibson, , 1966Hooijmans and Keijzer, 2007;Kelty-Stephen et al., 2022a;Kondepudi et al., 2017;Levin et al., 2021;Lyon et al., 2021;Matthews and Vosshall, 2020;Newen et al., 2018;Nielsen, 2019;Pattee, 1995Pattee, , 1974Raja, 2021;Rosen, 1991;Searle, 1990;Turvey and Carello, 2012;Vergara et al., 2017 Bertalanffy and Sutherland, 1974;Wood, 2019), the creative role of interactions across scale in developing coordination has come to appear increasingly more promising than strictly computational explanations of dexterity. For such a latter possibility, more degrees of freedom are going to provide a wider set of fluid configurations for supporting dexterity. ...
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Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor—that of the cascade. The time has come to confront Turing’s cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing’s cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.
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... Hence, metaphors capable of generating scientifically valid hypotheses about theory are not limited to logical machines like computers. Indeed, biological and artificial sciences alike have a yawning portfolio of models that are not logical but somewhat tangible, living, and embodied (Bravo et al., 2021;Matthews and Vosshall, 2020;Michael et al., 2021;Nielsen, 2019;Vergara et al., 2017). Much like the computer metaphor, these wilder models carry our best predictions forward into the future. ...
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... Hence, metaphors capable of generating scientifically valid hypotheses about theory are not limited to logical machines like computers. Indeed, biological and artificial sciences alike have a yawning portfolio of models that are not logical but somewhat tangible, living, and embodied (Bravo et al., 2021;Matthews and Vosshall, 2020;Michael et al., 2021;Nielsen, 2019;Vergara et al., 2017). Much like the computer metaphor, these wilder models carry our best predictions forward into the future. ...
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Modular soft robots have strong adaptability and versatility in various application contexts. However, the introduction of connection mechanisms will always either reduce the structural compliance or need extra actuation appendages, resulting in the complexity of the structure and system of the robot. To address these issues, herein, a compliant and passive connection strategy is demonstrated, which is accomplished utilizing the reclosable fasteners (RFs), and other varieties including hook‐and‐loop fasteners, as the connection mechanisms to the soft modules for the rapid assembly of various soft machines. The module is a pneumatic soft actuator with both ends designed with a multifaceted structure to attach the RFs in different orientations, resulting in various assembling patterns, including linear connection, orthogonal connection, and oblique connection. Moreover, an alignment mechanism is also designed to improve the alignment precision between two assembled modules. The versatility of the RF enables soft modules capable of assembling not only between identical modules but also with diverse additional accessories for various application scenarios. Different functional assemblies are demonstrated including soft grippers, soft walking robots, and shape‐morphing electrical devices. This approach to the connection mechanisms provides routes to new modular soft robots and devices. A detachable bonding mechanism is introduced to the modular assembly of soft robots and machines through various assembling patterns between two modules, including linear connection, orthogonal connection, and oblique connection. Different functional assemblies are demonstrated including soft grippers, soft walking robots, and shape‐morphing electrical devices. This approach to the connection mechanisms provides routes to new modular soft robots and devices.
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Conference Paper
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The field of modular self-reconfigurable robotic systems addresses the design, fabrication, motion planning, and control of autonomous kinematic machines with variable morphology. Modular self-reconfigurable systems have the promise of making significant technological advances to the field of robotics in general. Their promise of high versatility, high value, and high robustness may lead to a radical change in automation. Currently, a number of researchers have been addressing many of the challenges. While some progress has been made, it is clear that many challenges still exist. By illustrating several of the outstanding issues as grand challenges that have been collaboratively written by a large number of researchers in this field, this article has shown several of the key directions for the future of this growing field
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It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
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It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
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A soft robot, which consists of multi-deformable spherical cells, is constructed. According to the deflating action and the inflating action of the spherical cells, the size and the shape of each spherical cell can be changed. Thus, the soft robot can move in a narrow complicated passage. In the paper, a modular soft robot is built. The nonlinear relationship between the inflation radius ( \(R)\) of each cell and the inflation time ( \(t)\) is described to control the action of the spherical cell. The nonlinear dynamic moving process is analyzed with the deflating and inflating modes of each cell. The theoretical analysis of the forward locomotion is counted. Then, two special positions are described, and the moving conditions are presented in details. Last, a simulation and an experiment of three spherical cells are shown to emulate the moving process of the soft robot. It shows that the modular soft robot consisting of multi-deformable spherical modules can move forward with the nonlinear dynamic inflating and deflating process.
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This paper describes the fabrication of 3D soft, inflatable structures from thin, 2D tiles fabricated from elastomeric polymers. The tiles are connected using soft joints that increase the surface area available for gluing them together, and mechanically reinforce the structures to withstand the tensile forces associated with pneumatic actuation. The ability of the elastomeric polymer to withstand large deformations without failure makes it possible to explore and implement new joint designs, for example “double-taper dovetail joints,” that cannot be used with hard materials. This approach simplifies the fabrication of soft structures comprising materials with different physical properties (e.g., stiffness, electrical conductivity, optical transparency), and provides the methods required to “program” the response of these structures to mechanical (e.g., pneumatic pressurization) and other physical (e.g., electrical) stimuli. The flexibility and modularity of this approach is demonstrated in a set of soft structures that expanded or buckled into distinct, predictable shapes when inflated or deflated. These structures combine easily to form extended systems with motions dependent on the configurations of the selected components, and, when fabricated with electrically conductive tiles, electronic circuits with pneumatically active elements. This approach to the fabrication of hollow, 3D structures provides routes to new soft actuators.
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This paper describes a modular approach to creating soft robotic systems. The basis of these systems is an elastomeric actuation element powered by direct mechanical energy in the form of pressurized fluids. Fluidic elastomer actuators are fast and inexpensive to fabricate and offer safety and adaptability to robotic systems. Arrangements of these units can yield arbitrarily complex motions and achieve various functionalities. Actuation power can be generated on-board by a pneumatic battery, which harnesses the catalyzed chemical decomposition of hydrogen peroxide into oxygen gas, for mobile implementations. The modular nature of these robots enable distributed sensing and computation elements. Composition techniques of such soft robots are defined. Example systems are demonstrated and analyzed.
Conference Paper
A modular robot consists of a set of mechatronic modules that can be connected in many different ways, which makes it possible to build robots of many different shapes from the same basic set of modules. The main contribution of this work is an algorithm that, given the parameters of a module and the number of modules, efficiently can calculate how many different configurations and shapes can be built. These numbers are important because the first is a measure of the self-reconfigurability and the second, given there is a relationship between form and function, the versatility of a modular robot. As an experimental contribution, we enumerate the configuration and shape spaces of square, two-dimensional modules with all possible connector configurations. We proceed to three dimensions and enumerate the spaces of the theoretically interesting sliding cube module, and the M-TRAN and SuperBot modules. Several observations are made, an important one is that the shape spaces of the two physical modules are large even for a small number of modules (103 different shapes using 3 modules). This implies that it is not the lack of shape diversity that holds these modular robots back from being versatile. A result that suggests that if modules are designed right, versatility can potentially be reached even with few modules, which is contrary to the common belief in the community that more is better.