Origami mechanologic

Benjamin Tremla, Andrew Gillmana,b, Philip Buskohla, and Richard Vaiaa,1

a
Functional Materials Division, Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433;
and bUES, Inc., Dayton, OH 45432

Edited by John A. Rogers, Northwestern University, Evanston, IL, and approved May 15, 2018 (received for review March 23, 2018)

Robots autonomously interact with their environment through a Components of Mechanologic

continual sense–decide–respond control loop. Most commonly, the Logic embedded into the structure of a soft robot is unlikely to
decide step occurs in a central processing unit; however, the stiffness replace the speed and information density of electronic logic;
mismatch between rigid electronics and the compliant bodies of soft rather, electronic and mechanical logic will cooperate to control a
robots can impede integration of these systems. We develop a robot. To develop mechanologic compatible with electronic logic,
framework for programmable mechanical computation embedded
we seek to emulate the language and structure of electronic digital
into the structure of soft robots that can augment conventional dig-
logic. This requires a mechanical bit to store information, logic
ital electronic control schemes. Using an origami waterbomb as an
experimental platform, we demonstrate a 1-bit mechanical storage
gates to operate on stored information, signal transmission
device that writes, erases, and rewrites itself in response to a time- mechanisms to connect logic gates, and an ecosystem of sensors
varying environmental signal. Further, we show that mechanical that interface with mechanical inputs. These components must
coupling between connected origami units can be used to program operate on an energy budget that can be harvested from the en-
the behavior of a mechanical bit, produce logic gates such as AND, vironment. A few components, such as signal transmission (10),
OR, and three input majority gates, and transmit signals between energy-harvesting sensors (11–13), and logic gates (14, 15) have

APPLIED PHYSICAL
mechanologic gates. Embedded mechanologic provides a route to been demonstrated individually. However, before a complete soft
add autonomy and intelligence in soft robots and machines. mechanological system can be established the components must

SCIENCES
be proven and integrated within a common platform.
origami | soft robotics | logic | active materials Here, we demonstrate origami as a platform capable of in-
tegrating these components into a mechanologic system. Origami

R obots are distinguished from machines on the basis of their

autonomy. The most successful robots, such as manufactur-
ing robots (1), the Mars rover, or Big Dog (2), use onboard
actuators have shown significant utility in the microrobotics
community, due to their precise motion control and amenability to
2D fabrication techniques (16, 17). Origami patterns are modular
computers as a coordinating intelligence and are mechanically (18), enabling units to be developed independently and combined
robust to support the technological ecosystem associated with to create more complicated functional structures. In addition,
digital electronics. For soft robotics, with applications in assisted localization of deformation to the fold lines mechanically protects
surgery (3), disaster response, and human rehabilitation and the facets, providing regions that can host electronic hardware.
augmentation (4), mechanical constraints may limit the integra- Advances in analyzing the nonlinear mechanics of origami have
tion of electronic components throughout soft structures, so there broadened the design space to include prediction of stable con-
is a need for alternative methods of incorporating computational figurations, in addition to analysis of the fold path (19–21). Be-
abilities into soft robots. Mechanical logic devices have a long cause origami patterns are scale-independent, insights into the
history, dating back to Leibniz’s step reckoner in 1672 and mechanics, design, and implementation of origami mechanologic
Babbage’s difference engine in 1822 (5), but hard mechanologic can be shared among disciplines, ranging from MEMS to de-
devices make use of gears, wheels, microelectromechanical sys- ployable structures, that exploit origami mechanisms.
tems (MEMS) (6), and even Legos to perform calculations.
However, these approaches do not easily integrate with
Significance
compliant machines.
Conventional electronic control of soft robots can be com-
plemented by soft mechanologic, where the inputs and outputs Autonomy separates robots from machines. Incorporating au-
tonomy into soft robots is an outstanding challenge due to the
are mechanical deformations of the robot’s structural frame-
mismatch between rigid electronics and the compliant bodies. In
work, distributed throughout a soft robot’s body, and perform
this work, we demonstrate origami as a platform for compliant
morphological computation locally, rather than passing all signals to
mechanical logic, containing mechanical bits, logic gates, and
a central processing unit (7, 8). This approach takes inspiration
signal transmission mechanisms that can supplement conven-
from animals, especially the octopus, which have distributed ner-
tional electronic controls. Furthermore, these processes can be
vous systems in their limbs not only to carry signals to a coordinating
responsive to and programmed by the environment via the in-
intelligence (i.e., brain) but also to act reflexively (9). This work tegration of adaptive materials. Thus, origami provides a
develops basic mechanologic units using origami as a platform. framework in which sensing, computation, and reflexes can be
Bistable waterbomb origami structures serve as mechanical memory seamlessly integrated into the compliant bodies of soft robotics.
units. Incorporation of environmentally responsive soft materials
that autonomously sense the local environment and transduce ex- Author contributions: P.B. and R.V. designed research; B.T. and A.G. performed research;
ternal signals into mechanical inputs produces composites that B.T. and A.G. analyzed data; and B.T., A.G., P.B., and R.V. wrote the paper.
write, erase, and rewrite the mechanical bit without any external The authors declare no conflict of interest.
power supply. We show that mechanical coupling between origami This article is a PNAS Direct Submission.
units transfers information and enables creation of mechanical logic This open access article is distributed under Creative Commons Attribution-NonCommercial-
gates that can be connected to form reprogrammable mechanologic NoDerivatives License 4.0 (CC BY-NC-ND).
circuits. The fundamental building blocks of an origami-based soft 1
To whom correspondence should be addressed. Email: richard.vaia@us.af.mil.
mechanologic system demonstrated here provide a platform for This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
further development and integration of distributed logic and re- 1073/pnas.1805122115/-/DCSupplemental.
flexes into soft robots and machines.

www.pnas.org/cgi/doi/10.1073/pnas.1805122115 PNAS Latest Articles | 1 of 6

 SI Appendix, Fig. S3. The internal energy of a single truss element
is given by

Z1
EA 2 G 2
U = l0 « + φ~ d ζ,
2 2
0

where l0 is the initial length of the truss, E is the Young’s modulus

(3 GPa), A is the cross-sectional area of the truss, G is the fold
stiffness (2·10−3 N·m/m), « is the axial strain in the truss, and φ
~ is
the rotation of the torsional spring. The first term represents axial
strain in the truss elements and accounts for facet stretching, while
the second term represents energy stored in the torsional spring
emanating from bending/folding. See SI Appendix, Supplemental
Note 2 for additional details of this model. The unit waterbomb
structure presented in Fig. 1 is composed of 16 truss elements
(solid and dashed lines in Fig. 1A), 8 of which correspond to folds
(dashed lines in Fig. 1A) and are modeled with nonzero fold stiff-
ness G. The fold stiffness is measured from the force displacement
behavior of a single PP fold (SI Appendix, Fig. S9), while the
Young’s modulus is taken from the manufacturer’s data sheet.
The cross-sectional area term is the product of the film thickness
(40 μm) and an effective truss width. This width is the only
adjustable parameter in the calculations. The dependence of
the force-displacement curve on the truss width parameter de-
Fig. 1. Bistable origami mechanomemory. (A) Fold pattern for a water- creases away from the snap-through event, indicating folding
bomb; dotted lines indicate mountain folds and dashed lines indicate valley dominated deformation. For a range of reasonable values (0.6–2 cm)
folds. (B) The 1 and 0 states of the waterbomb base, with the vertex height for this parameter, peak forces and the absorbed energy during
(h) on each structure indicated. (C) Mechanics of the snap-through reconfi- reconfiguration are within 30% of the measured values with the
guration. The hatched region indicates the range of calculated force- exception of the peak force involved in snapping from 0 to 1,
displacement curves due to an estimation of the effective truss width in which is overestimated by up to 110%. A truss width of 0.6 cm is
the governing equations. Green dots indicate the measured mechanical re- used for all further calculations. Good agreement between the ex-
sponse of a polypropylene waterbomb.
perimentally measured origami mechanics and a simple model aids
the design and analysis of the mechanologic devices presented below.
Satisfying an origami axiom for flat folding has been interpreted To produce a sense–decide–respond loop in an origami bit,
there is a need for materials that can respond to external stimuli
as a mechanical logic problem, with mountain and valley assign-
and harvest energy to write and erase the mechanical memory.
ment of a fold line as the mechanical 1 and 0 states (22). However,
The field of responsive soft materials provides a suite of materials
once folded these patterns are not dynamic or reprogrammable
capable of harvesting energy from the environment and trans-
because there is only one set of mountain–valley assignments
ducing environmental signals into mechanical responses. A wide
compatible with flat folding; any attempt to change a mountain to
variety of materials have been developed that respond to a range
valley (1 to 0) leads to mechanical frustration. To produce dynamic
of stimuli such as heat, light, magnetism, and humidity (28, 29).
mechanologic, the base unit must be able to switch between me- In this work, we use a humidity responsive polymer, poly(3,4-
chanical states without frustrating the system. Several bistable ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) as
origami patterns have been identified (20, 23, 24) which may satisfy a prototype responsive soft material. PEDOT:PSS is a conductive
this criteria. Here, we focus on the waterbomb base fold pattern as polymer commonly used in flexible and organic electronics.
a testbed because it serves as a model for the general bistability of PEDOT:PSS transduces a relative humidity (RH) change into a
origami vertices undergoing a vertex inversion process (24) and is a mechanical response. Upon absorption and desorption of water
common motif found in more complicated origami structures (25). vapor, PEDOT:PSS will swell and shrink, generating up to 4%
Fig. 1A shows the fold pattern for a waterbomb, as well as a model strain (30). The conductivity and hygromechanical response of
of the structure in its two stable configurations in Fig. 1B. During PEDOT:PSS provides a route to interface between mechanologic
reconfiguration between stable states, the mountain and valley distributed throughout the structure of a soft robot and conven-
folds stay mountain and valley folds and the structure undergoes tional electronic controls. The mechanical response of a com-
only a small change in projected area. We believe these properties posite of 24-μm-thick PEDOT:PSS on a 40-μm-thick PP film
allow the mechanical bit to switch between 1 and 0 states without follows bilayer bending mechanics, as predicted by Timoshenko
interfering with the ability of other connected units to reconfigure (31) (SI Appendix, Supplemental Note 1), indicating that contin-
in the multiunit structures presented below. uum approximations will be sufficient to predict the motion of
Fig. 1C shows measured and calculated force-displacement origami structures with distributed PEDOT:PSS transducers.
profiles of a waterbomb as a point load is applied to the vertex We demonstrate environmental responsivity and energy har-
of the structure driving reconfiguration. The waterbomb is vesting, mechanical state change, and fidelity of our nonlinear truss
folded from a 40-μm-thick, 4 × 4-cm square film of poly- model in Fig. 2. Placing PEDOT:PSS transducers at the fold lines
propylene (PP), with a mass of about 60 mg. The waterbomb is allows for validation of our origami model using a different loading
modeled as a truss system following the work of Schenk and condition than was used for calibration in Fig. 1. Depending on the
Guest (26) using the nonlinear formulation developed by Gillman location of the active material (outside vs. inside of folds), the
et al. (19, 27). The model is comprised of truss elements that form bending moment applied by the PEDOT:PSS can either open or
triangular origami facets, with a torsional spring added to fold close the folds. Representative images of the waterbomb are shown
lines to account for the stiffness of an origami fold, as illustrated in in Fig. 2 A–D, during both fold closing (B → A) and fold opening

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 logic structures. Instead, we return to the vertex inversion reconfi-
guration presented in Fig. 1 to provide the mechanical 1 and
0 states. The simplest logic gates take two inputs and compare them
to produce an output following a simple set of rules. In Fig. 3,
symmetric and antagonistic PEDOT:PSS transducers on the top
and bottom of the waterbomb vertex sense their local environment,
transduce the environmental stimulus into a mechanical input, and
compare them via a force balance at the vertex. If the waterbomb is
in a uniform RH environment, both actuators sense and respond to
the same signal, producing no net force and no change to the ori-
gami structure. However, in an RH gradient the PP layer restricts
diffusion of water vapor, forcing it to diffuse around rather than
through a waterbomb. As a result, the top and bottom sensors
detect significantly different local environments as shown in Fig. 3A.
The PEDOT:PSS actuator exposed to a lower RH exerts a larger
force on the vertex, bending the origami structure and, depending
on the initial waterbomb state, reconfiguring the structure.
Adding environmentally responsive actuators to a mechanical
bit elevates the composite structure from a mechanical memory
unit to an environmentally responsive logic gate. If we digitize
the signals sent to the top and bottom actuator as just high (1)
and low (0) RH and the two vertex configurations as 1 and 0,
then a waterbomb with a pair of antagonistic actuators at the

APPLIED PHYSICAL
Fig. 2. Environmental sensing and actuation of origami. (A–D) Reconfigura- vertex acts as a mechanical version of the logic gate known as an

SCIENCES
tion of waterbombs with PEDOT:PSS actuators on the inside (A and B) and SR latch. The SR latch is the fundamental logic gate for se-
outside (C and D) of fold lines. B is the equilibrium configuration which
quential digital logic (33). More precisely, because PEDOT:PSS
transforms into A, C, or D upon a change in the RH. All images are at the same
scale. (E) Change in the height of the vertex as the RH is reduced from an
exerts no force in response to environmental 1, and compressive
initial value of 85%. Letters indicate where the configurations shown in A–D force in response to environmental 0, PEDOT:PSS acts as a
occur. Squares indicate samples that undergo fold closing and circles indicate
samples that undergo fold opening and inversion. Filled and open symbols
indicate separate waterbomb samples. The dotted black line is a calculated
vertex height using the nonlinear truss model. (F) Cycling of waterbombs
between states B and A and states B and D repeatedly. Half cycles are the
reconfigured structure, A or D, while whole cycles are the stress-free state, B.

(B → C → D) transitions. Applying distributed bending moments

to the fold lines is a unique way to load an origami structure that
would be difficult to produce with conventional mechanical testing
equipment. As a result, the fold closing and opening reconfigurations
demonstrated here have not, to the best of our knowledge, been
studied previously. Fig. 2E compares the observed reconfiguration of
the structure to our origami model with bending moments applied to
the fold lines. Using the stress-free state (B) and the flat state (C) to
provide a scaling factor between the humidity-driven experimental
structure and our origami model, we see good agreement between
the calculated and experimentally observed origami mechanics.
After an initial change in the stress-free configuration likely due
to plastic deformation in the folds, the structure can undergo this
actuation cycle repeatedly, as shown in Fig. 2F.
The continuous relationship between humidity-driven bending
at the folds and linear actuation of the vertex is an analog-to-
analog transduction of an environmental input into a mechanical
output. For a waterbomb, the mechanical output manifests itself
as linear actuation of the vertex; however, changing the underlying
origami structure will produce other mechanical responses such as
twisting or large areal changes (20, 32). Recently, origami opti-
mization routines have been developed that take a set of possible
fold lines and develop an optimal fold pattern for a desired me- Fig. 3. A mechanical SR latch. (A) A waterbomb with actuators at the vertex
chanical response (21). The integration of environmentally trig- switches between 1 and 0 in response to a vertical humidity gradient.
gered distributed forces into the origami truss model shown here Steady-state COMSOL simulations show the RH distribution around a
highlights the opportunity to simultaneously optimize both the waterbomb. (B) Symbolic representation of the SR latch, where environ-
mental signals (dotted lines) are transduced to mechanical signals (solid
fold pattern and actuator placement for the rational design of
lines) by PEDOT:PSS. (C) State transition table for a waterbomb. T and B
dynamic origami structures. indicate the environmental signal detected by the top and bottom actuator,
respectively. Q is the state of the mechanical bit (vertex up or down). (D) An
Mechanologic Units environmentally responsive waterbomb writes, erases, and rewrites itself in
The origami actuator in Fig. 2 transforms via a fold inversion response to time varying environmental stimuli. The dotted lines indicate
mechanism, which may not be compatible with dynamic origami the equilibrium configuration of the 1 and 0 states.

Treml et al. PNAS Latest Articles | 3 of 6

NOT gate that senses and transduces an environmental input into a
mechanical input. These mechanical inputs on the top and bottom
 and Reset (R)
of the vertex are the Set (S)  signals for the SR latch,
which has the mechanical output (Q) of either the 1 or 0 state of
the waterbomb structure. Fig. 3B shows a symbolic representation
of the mechanologic device. The state transition table of the device
is shown in Fig. 3C; Qn indicates the current state of the water-
bomb (vertex up = 1, white and vertex down = 0, black), the en-
vironmental inputs into the structure, the humidity at the top (T)
and bottom (B) actuators are colored to match the color scale of
the simulated humidity distribution in Fig. 3A, and Qn+1 indicates
the subsequent state after sensing and responding to the environ-
ment. Fig. 3D shows the response of a waterbomb to a time-varying
environmental stimulus; the waterbomb writes, erases, and rewrites
itself by snapping between the 1 and 0 states in response to the
external environment, following the rules of its state transition
table. Video of this experiment is available in Movie S1. In addition
to serving as a mechanological memory unit, the environmental
energy harvesting of the PEDOT:PSS actuators, combined with the
structural energy storage and rapid release during snap-through,
can be exploited to drive autonomous locomotion, as demonstrated
in Movie S3 and SI Appendix, Supplemental Note 4.

Mechanologic Gates and Circuits

Complex logic circuits for sensing, memory, and computation are
built from logic gates that perform simple Boolean operations
such as AND, OR, and NOT. In electronic logic, logic gates
manipulate input voltages to produce an output voltage, which is
carried to other gates by wires. Mechanologic uses a mechanical
state to encode a 1 or 0, and so the inputs to and outputs of a
mechanologic gate must likewise be mechanical. In Fig. 4, we
explore mechanical coupling between waterbomb units as a means
of building Boolean mechanologic gates. Fold patterns for con-
necting one to four waterbombs to a central device unit are shown
in Fig. 4A. Smaller schematics enumerate all possible combina-
tions of states of the coupled waterbombs and are labeled using
binary notation starting from the left and moving clockwise
around the central gray unit (white = 1, black = 0). For example, a
5mer with the waterbombs in the one and three positions snapped
through is labeled 0101. The details of constructing and modeling
these complex origami structures are discussed in SI Appendix,
Supplemental Note 2. Each waterbomb in a network could be
triggered by a different stimulus, thus providing a means to con-
Fig. 4. Mechanical coupling in origami. (A) Fold patterns (colored) and
solidate different environmental stimuli to a decision point. possible states (black and white) of all possible nearest-neighbor coupled
Connected waterbomb units share a fold line and two facets waterbombs. Numbers in adjacent waterbombs indicate the order that
that serve to communicate the mechanical state of a waterbomb to states are listed in when labeled. White indicates waterbombs in the 1 state,
its neighbor. The essentials of mechanical coupling between con- black indicates waterbombs in the 0 state, and gray indicates the central
nected waterbombs can be seen in the 2mer (Fig. 4B). When a device unit for which the mechanics of snap-through are calculated. (B)
connected waterbomb is in the 1 state, reconfiguration of the Energy stored in the origami structure as the central waterbomb is recon-
central waterbomb becomes more difficult because opening of the figured from 1 to 0. (C) Energetic barrier to reconfiguration for all water-
shared fold between the waterbombs is resisted by the connected bomb configurations shown in A. By snapping neighboring units from 1 to 0,
the energetic barrier can be tuned across a wide range, which can be used to
waterbomb. The result is an increase in the energetic barrier to program the susceptibility of the central waterbomb.
snap-through of 11.6 μJ (33%) relative to a 1mer. In contrast,
when a connected waterbomb is a 0, the shared fold is held open
relative to an isolated waterbomb, as the 0 state has a less folded whether the 0s are next to or across from each other; for ex-
equilibrium state, and reduces the barrier to reconfiguration by 5.1 μJ ample, consider the 001 vs. 010 configurations of a 4mer.
(15%). Fig. 4C summarizes the effect of connecting additional The mechanical force applied by an embedded transducer, and
waterbombs and snapping connected waterbombs between 1 and hence energy transferred to a waterbomb unit, is constant for a set
0 states on the energetic barrier to reconfiguration of the central combination of responsive material and external stimulus. If we
device unit for all of the fold patterns and configurations in Fig.
consider the mechanical state of connected waterbomb units as
4A. To the first order, increasing the number of connected
waterbombs in a 1 state linearly increases the energetic barrier to inputs that modulate the energetic barrier to reconfiguration of
snap-through of the central waterbomb (14 μJ per connected the central device unit, which serves as an output, the origami
waterbomb), while snapping a connected waterbomb from 1 to structures in Fig. 4A can be used to create mechanologic gates.
0 linearly decreases the barrier to reconfiguration (17 μJ per Fig. 5A demonstrates an AND gate created from a linear 3mer
snapped waterbomb). When two connected waterbombs are 0s, with an environmentally sensitive actuator on only the center
the barrier to snap through varies by about 3 μJ depending upon waterbomb. In a humidity gradient (T = 0, B = 1), the center

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 another logic gate. As the mechanical coupling that modulates
the barrier to snap-through is local, propagation of this signal
over arbitrary distances is a challenge. Tiling of 3mer AND gates
provides one route to address this issue via a sequential snap-
through process. Fig. 5B schematically illustrates this process for
a linear chain of waterbombs, assuming an environmental stim-
ulus is present to provide the energy for snap-through (SI Ap-
pendix, Supplemental Note 3 and Movies S4 and S5). An initially
snapped-through waterbomb on the left side of a waterbomb
“wire,” which can be an externally programmed unit, sensor unit,
or the central device unit of a previous logic gate, reduces the
barrier to reconfiguration of its neighbor to the right. This
waterbomb snaps through and lowers the energetic barrier for its
neighbor, and so on down the line. The last unit of a waterbomb
“wire” can then serve as an input unit to a mechanologic gate.
The waterbomb-based mechanologic system presented here is a
mechanical implementation of 2D cellular automata (35). Quantum
dot cellular automata (QDCA) have been studied extensively as an
alternate to conventional field-effect transistor-based digital logic
(34). Like our implementation of origami mechanologic, QDCA
have a square unit cell and transfer local interactions through a logic
circuit via sequential reconfiguration. Designs for complex logic
circuits, including adders and multipliers, have been developed that

APPLIED PHYSICAL
may be adaptable to origami mechanologic (36, 37). For instance, if

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the transducer in the central waterbomb of a 5mer has a maximum
energy input between 55 and 70 μJ and one connected waterbomb
is reserved for transmitting the output, the 5mer will behave as a
three-input majority gate. When three three-input majority gates
are connected as shown in Fig. 5C the resulting seven input logic
circuit leverages the programmability of three input majority gates
to create a structure that can perform the four-input AND, four-
input OR, sum-of-products, or product-of-sums operations (37).
Fig. 5D diagrams a compact implementation of this structure in our
mechanologic platform, where gray squares indicate the device units
of the three-input majority gates. The unlabeled units between
majority gates act as wires to transmit the output of the left and
right gates to the central gate as discussed above.
Fig. 5. Logic gates and signal transmission. (A) Models of the equilibrium
states of a linear 3mer, along with corresponding photos of an experimental Discussion
3mer with PEDOT:PSS only at the center vertex. Photos on the left are at am- The demonstration of a mechanical bit, environmentally responsive
bient conditions; photos on the right are in a T = 0, B = 1 environment. Snap-
transducers, logic gates, and a signal transmission mechanism in a
through does not occur for the 11 state (red x) because the energetic barrier to
reconfiguration is too high. All images are at the same scale. (B) Sequential
single platform makes origami mechanologic a promising route to
propagation of reconfiguration in a waterbomb chain. The blue box highlights embed local computation and programmable reflexes into the
a waterbomb that has the local mechanical environment of a 01 linear 3mer. structural framework of soft robots. While the experimental dem-
When the light gray unit harvests energy from the environment and recon- onstrations in this work use only humidity-responsive actuators of a
figures, it alters the mechanical environment of its neighbor, resulting in signal constant size, the environmental responsivity of a soft robot can be
propagation. (C) Abstract logic diagram for a seven-input reprogrammable controlled at a unit by unit level by exploiting advances in additive
logic circuit. (D) Implementation of the logic circuit shown in C using manufacturing and the suite of stimuli-responsive materials to in-
waterbomb-based mechanologic. Input and logic gate waterbombs are labeled dependently control stimuli measurement, signal propagation, and
A–G and M, respectively. Empty waterbombs act as wires as illustrated in B.
logic operations. In addition, integration of environmentally re-
sponsive logic into the structural framework of a soft robot means
waterbomb is unable to snap through when coupled to two that even simple binary transitions not routed through a complex
mechanologic circuit can have a large impact on the shape or
waterbombs in the 1 state due to the raised energetic barrier to
mechanical properties of a soft robot’s body, for example pro-
reconfiguration. When one or both of the connected waterbombs
grammatically changing the compressive modulus of an origami
is a 0, the energetic barrier is reduced below the output of the
sheet (38).
environmentally sensitive actuator and the center waterbomb The implementation of mechanologic developed here is not
snaps. The full state transition table for this origami logic gate is without limitations. The set of Boolean logic gates accessible via
shown in SI Appendix, Table S1. Simultaneous control over the the structures in Fig. 4 does not include a NOT, NAND, or NOR
embedded actuator, which sets the threshold for reconfiguration, gate, all of which require the energetic barrier for reconfiguration
and the origami structure, which determines the number of inputs to increase when a connected unit is snapped from 1 to 0, rather
available, can be used to create a wide range of logic gates in- than decrease. Without one of these gates, the mechanologic
cluding AND, OR, and multiple input majority gates. Three input system developed here is not functionally complete, meaning that
majority gates are of particular interest because when one input is logic circuits with arbitrary truth tables cannot be produced.
used as a programming input they can be dynamically switched Furthermore, the 2D nature of origami limits circuit design and
between performing AND and OR functions (34). fan out of outputs of a logic gate, as a central device unit can only
To connect logic gates together into a complex logic circuit, have up to four total inputs and outputs. These limitations may be
outputs of one logic gate must be transmitted to the input of addressed through incorporation of other origami fold patterns or

Treml et al. PNAS Latest Articles | 5 of 6

may be circumvented in mechanologic systems based on alternate might be generated. We leverage the bistability of origami vertices
bistable building blocks. The selection criteria for an origami me- to store information mechanically in the origami structures. In-
chanical bit as well as the rules for coupling units together to tegration of environmentally responsive actuators into the origami
produce mechanical logic gates that have been developed here may structure enables autonomous sensing and transduction of an
transfer to the development of mechanologic in other bistable environmental signal into a mechanical signal, resulting in a self-
systems. However, it is likely that we have encountered only a powered mechanical SR latch. Mechanical coupling between ori-
subset of the criteria for a complete mechanologic system and that gami units that share folds and facets enables the creation of
other mechanologic platforms have advantages and constraints not Boolean mechanologic gates, signal transmission mechanisms,
encountered in our study of a waterbomb-based mechanologic. and complex mechanological circuits. The fundamental concepts
Ultimately, mechanologic cannot replace electronics and pro- demonstrated here, whether implemented using an origami
vide all controls for a soft robot. Instead, compliant mechanologic mechanologic language or another form of morphological com-
can be leveraged to augment and complement traditional robotic putation, provide a route to embedding reflexes and distributed
controls. Mechanologic provides an opportunity to reduce the intelligence in soft machines that will enable them to autono-
complexity of mechanical structure control by embedding an en- mously sense, respond to, and interact with their environment,
vironmentally powered sense–decide–respond loop locally in the thereby truly earning the title of soft robots.
structural framework. Significantly complex logic and long-term
memory are best left to electronics, and the rigid facets of ori- Materials and Methods
gami provide good places to mount electronic hardware. Advances Waterbomb samples were folded by hand from 40-μm-thick PP films. PEDOT:
in additive manufacturing of flexible electronics provide possibil- PSS was deposited onto the films via drop casting and patterned using the
ities for interaction between conventional electronic controls and procedure detailed in the SI Appendix, Fig. S8. Humidity gradients were
mechanologic, including transduction of an electrical stimulus into generated by a custom-built humidity chamber (see ref. 11 for details). Ex-
a mechanical response via joule heating of PEDOT:PSS (30) and tended discussion of the truss-based origami model, experimental proce-
transduction of a mechanical shape change into a resistance dures, and additional demonstrations of environmentally responsive origami
change of a flexible conductor (39). can be found in SI Appendix and Movies S1–S5.

Conclusions ACKNOWLEDGMENTS. We thank Nathan Price for his help in some data
collection. This research was completed at the Air Force Research Laboratory at
In this work we have used the waterbomb-based origami struc- Wright-Patterson Air Force Base with funding support from the Materials and
ture combined with environmentally responsive PEDOT:PSS ac- Manufacturing Directorate (RX) and the Air Force Office of Scientific Research.
tuators to demonstrate how a system of digital mechanologic B.T. acknowledges a National Research Council postdoctoral fellowship.

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