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APPLIED SCIENCES AND ENGINEERING Copyright © 2023 The

Authors, some
A modular strategy for distributed, embodied control of rights reserved;
exclusive licensee
electronics-free soft robots American Association
for the Advancement
of Science. No claim to
Qiguang He†, Rui Yin†, Yucong Hua, Weijian Jiao, Chengyang Mo, Hang Shu, Jordan R. Raney* original U.S. Government
Works. Distributed
Robots typically interact with their environments via feedback loops consisting of electronic sensors, microcon- under a Creative
trollers, and actuators, which can be bulky and complex. Researchers have sought new strategies for achieving Commons Attribution
autonomous sensing and control in next-generation soft robots. We describe here an electronics-free approach NonCommercial
for autonomous control of soft robots, whose compositional and structural features embody the sensing, License 4.0 (CC BY-NC).
control, and actuation feedback loop of their soft bodies. Specifically, we design multiple modular control
units that are regulated by responsive materials such as liquid crystal elastomers. These modules enable the
robot to sense and respond to different external stimuli (light, heat, and solvents), causing autonomous
changes to the robot’s trajectory. By combining multiple types of control modules, complex responses can

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be achieved, such as logical evaluations that require multiple events to occur in the environment before an
action is performed. This framework for embodied control offers a new strategy toward autonomous soft
robots that operate in uncertain or dynamic environments.

INTRODUCTION steps. The same problems arise for microrobots or other robots
Soft robotics has become a notable area of research in recent years, with unique form factors that might be incompatible with conven-
with the potential to enable robots with a number of promising tional electronics (37).
characteristics (1, 2), such as resilience to large deformation (3, Nature provides inspiration for the design of autonomous capa-
4), safe human-machine interaction (5, 6), environmental adapt- bilities based on embodiment rather than traditional electronics.
ability (7, 8), novel and adaptable locomotion strategies (9, 10), Instead of using electronic components, biological systems interact
and resistance to impact (11, 12). Versatile deformable structures with the environment via physical intelligence, directly embodying
and actuating materials have been adopted in the design and fabri- many of the sensing, processing, and actuating functions in spatially
cation of soft robots, including pneumatic and hydraulic actuators distributed features of the physical body (37, 38). Embodying phys-
(13–15), dielectric elastomer actuators (16, 17), liquid crystal elasto- ical intelligence provides unique advantages, including simplicity
mers (LCEs) (18–20), magnetic actuators (21, 22), and hydrogels and scalability (38, 39). This strategy has been recently applied to
(23, 24). Numerous useful functionalities have been demonstrated soft robotic systems (40, 41). For instance, Drotman et al. (42) de-
in soft robots, including gripping (25, 26), crawling (27, 28), veloped untethered soft-legged quadruped robots that reverse their
jumping (29, 30), and shape adaptability (31, 32). direction of motion when a wall is contacted. Rothemund et al. (43)
However, to sense and respond to the environment, most soft designed and fabricated a mechanical bistable valve that enables
robotic systems rely heavily on traditional mechatronics (fig. S1): simple logic circuits and demonstrated how these can be applied
Solid-state sensors capture inputs from the environment; these in soft grippers and crawlers. In parallel, nascent ideas in mechan-
signals are routed to an electronic processor; the processor then ical metamaterials have been developed that blur the distinction
uses the inputs to make decisions and issue commands to actuators. between robotics and materials (44, 45). These mechanical metama-
These sensing, control, and actuation feedback loops require terials embody transduction and control functions in their engi-
complex integrated systems that may limit the function and form neered architecture, allowing the materials to use environmental
factor of the robot (16, 27, 33, 34). Typically, these mechatronic inputs for mechanical computation and autonomous adaptation
devices consist of rigid electronic components and peripheral cir- (46–50). For example, recent work has demonstrated environmen-
cuits that can be bulky, expensive, and mechanically incompatible tally responsive mechanical logic (48, 51, 52), including an artificial
with soft materials (35). In addition, these electronics may be unde- “flytrap” that can autonomously actuate when it senses specified en-
sirable for work in certain harsh environments, e.g., due to the po- vironmental stimuli.
tential for spark ignition (mines and nuclear reactors) or in In this work, we build on the above advances in intelligent me-
environments in which metal may be incompatible or limiting chanical metamaterials and embodied logic to create an electronics-
(magnetic resonance imaging machines, water, and other solvents) free soft autonomous robot (Fig. 1).
(36). Moreover, for applications in which the robot is intended to We accomplish this by designing modular control units that in-
directly change shape or function in response to its environment, corporate soft responsive materials, such as LCEs that respond to
an electronic sensing, control, and actuation strategy can be ex- heat or light (via the photothermal effect), hydrogels, and silicones
tremely complex and requires a large number of transduction [polydimethylsiloxane (PDMS)], and distributing these units
throughout the soft body of the robot (Fig. 1).
The robot body itself consists of a kirigami-inspired architecture
Department of Mechanical Engineering and Applied Mechanics, University of
Pennsylvania, Philadelphia, PA 19104, USA.
based on the rotating squares mechanism (53–55), which serves as a
*Corresponding author. Email: raney@seas.upenn.edu flexible and convenient platform for the reconfigurable, modular
†These authors contributed equally to this work.

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Fig. 1. Design of an electronics-free soft autonomous robot. (A and B) A schematic and image, respectively, of the soft robot. (C) The soft robot comprises multiple
types of control modules (with responsive materials), a kirigami-inspired body, a pneumatic actuator (mechanical valve is optional), and feet (to enable locomotion). (D)
Autonomous motion of the soft robot in response to various external stimuli (light, heat and solvent). Scale bar (B), 5 cm.

control units (Fig. 1). The control modules constrain the local rota- removed from the kirigami body, imparting different functionality
tion of the kirigami when activated by stimuli-responsive materials. to the robot. Each of these modules integrates stimuli-responsive
The behavior of the robot in response to environmental inputs is materials, which act as sensors for stimuli such as light, heat, and
a function of the spatial distribution (and interactions) of the solvents (Fig. 2). These materials can activate or deactivate mechan-
control modules. The trajectory of the robot is thereby governed ical constraints, which in turn induce bending in the kirigami
by a distributed computational event, comprising a logical combi- during pneumatic actuation. The placement of these control
nation of distinct environmental inputs. This framework provides a modules in the kirigami thereby enables the robot to sense and
new strategy for achieving autonomous, electronics-free soft robots respond to these stimuli, and, based on the location and type of
that can operate in dynamic or uncertain environments following a control modules, to autonomously change its trajectory of locomo-
variety of control objectives. tion (Fig. 2). In this work, we mainly focus on the use of LCEs to
sense and respond to heat or light. However, the design principle
can be applied to a broad range of external stimuli using multiple
RESULTS responsive materials (see the Supplementary Materials for
Design and operational principle examples).
The design of the electronics-free autonomous robot is shown in Several important parameters affect the behavior of the kirigami
Fig. 1. This robot comprises four components: a kirigami-inspired robot and the efficacy of the control modules, including the hinge
body, a pneumatic actuator (equipped with a bistable mechanical thickness of the kirigami, the constraints applied to the square units,
valve), multiple types of control modules (with integrated respon- and the size of the kirigami. Before deciding on a final set of param-
sive materials), and feet to enable locomotion. The pneumatic actu- eters for the robot, we experimentally and numerically character-
ator is sandwiched between two layers of the kirigami. It can ized the effect of these parameters, with details provided in the
generate periodic extension and contraction when pressurized air Supplementary Materials. In brief, we built a discrete model that
is applied, which in turn expands or contracts the kirigami body. treats the kirigami squares as rigid bodies and the thin hinges as
The kirigami body accommodates the changing dimensions of the elastic springs (fig. S3). The discrete model is then nondimension-
actuator via the internal rotation of the squares. The bistable valve alized to identify the fundamental parameters that intrinsically
(Fig. 1) is optional (see discussion later), but it can translate a cons- dictate the mechanical behavior of the kirigami platform, thus pro-
tant pressure source into a periodic inflation/deflation of the pneu- viding useful guidelines for the design of the kirigami body (figs. S4
matic actuator (43); hence, an electronic pressure controller is not and S5). We also performed finite element analysis (FEA), which
required. The feet underneath the body of the robot enable it to has the advantage of validating the experimental data more precise-
move forward due to anisotropic friction between the robot and ly, but which is computationally expensive, and therefore less effi-
ground (fig. S2) (43). Control modules can be added, moved, or cient than the discrete model for parametric studies (figs. S6 to S8).

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Fig. 2. Operating principle of electronics-free soft autonomous robots. Multiple control modules (with responsive materials) allow the soft robots to respond to their
surrounding environments (heat, light, and solvents). Control modules activate in response to local stimuli, which mechanically constrain the actuating kirigami, causing
changes to the curvature of the robot, and, as a result, to its trajectory.

Results from these methods are discussed where appropriate below noting that the modularity of the control units enables a robot to
and described in more detail in the Supplementary Materials. achieve different moving strategies in response to a given set of en-
The inflation/deflation cycle of the pneumatic actuator powers vironmental stimuli, without the need of fabricating a new robot.
the locomotion of the robot. When no relevant stimuli are Furthermore, new control modules could be designed, beyond
present, inflation of the pneumatic actuator causes rotation of the those that we have introduced in this work, which could enable
kirigami squares and associated lengthening of the robot body. new types of responses or enable responsiveness to additional
The extension of the platform is dependent on the pressure in the stimuli. The responsive materials in the control modules sense
pneumatic actuator. We define the extension ratio (ε) as ε ≡ (l − L)/ and actuate when they encounter relevant environmental stimuli.
L × 100%, where L is the length of the initial state and l is the length In this way, the control modules that are distributed throughout
of the pressurized state. We measure the extension ratio (ε) as a the robot influence its shape, thereby enabling it to autonomously
function of the applied pressure, both for the pneumatic actuator change its trajectory.
and for the assembled robot (without any control modules, We experimentally and numerically characterized how different
Fig. 3A). To accurately quantify this relationship, the pressure in mechanical constraints on the rotation of the kirigami squares affect
the pneumatic actuator for these tests is precisely controlled using the bending angle (figs. S11 to S13). The first example of a control
a custom fluid control system (fig. S9). The ability of the kirigami to module, shown in Fig. 3C, locally prevents the kirigami from
extend with the actuator is a function of hinge thickness. We char- opening if light or heat is applied. This is enabled by a strip of
acterized this effect experimentally and numerically (using both our carbon nanotube doped liquid crystal elastomer (CNT-LCE) in
discrete model and FEA). The experimental results show that the control module, which contracts if heat or light is present
smaller hinge thicknesses (1 mm) can generate a large extension above a given threshold (see figs. S14 to S20 for detailed character-
ratio (27%) without causing buckling of the pneumatic actuator izations). As shown in Fig. 3C, if the light and heat in the environ-
(fig. S10). Both the discrete model and FEA agree with experiments, ment are minimal, the CNT-LCE does not contract (the control
i.e., that the hinge thickness should be as thin as possible to allow module is not active), allowing the kirigami squares to rotate
efficient extension (e.g., fig. S10) (56). As shown in Fig. 3A, when freely everywhere. This leads to uniform extension of the robot
the pressure is below 25 kPa, the extension ratio of the pneumatic body as the pneumatic actuator inflates (no bending). If the temper-
actuator is comparable to the robot. Further increasing the pressure ature is elevated, the CNT-LCE strip contracts, causing the control
may lead to buckling of the actuator, resulting in bending of the module to locally inhibit the motion of the squares, producing
robot body. This can cause the robot to turn. The maximum oper- bending when the robot is actuated. To quantify this effect, we mea-
ational pressure of the pneumatic actuator is therefore set to 25 kPa. sured the bending angle α as a function of temperature (Fig. 3C). At
The autonomous robot is designed to achieve sensing and a given pressure, the bending angle of the robot is larger when the
control solely from the action of the control modules. The behavior temperature is higher, because the LCE actuates to a larger strain
of the robot in response to a particular stimulus depends both on (fig. S15). The length of the CNT-LCE strip is a critical design pa-
the types of control modules present in the robot and on their lo- rameter (fig. S21). In addition, the bending angle of the robot was
cation. Multiple types of control modules are developed to provide measured during repeated inflation/deflation cycles (fig. S22),
different moving strategies. They can be easily attached to or showing no obvious degradation of the control module.
removed from the body of a given robot (Fig. 3B and movie S1), By simply changing the type of control module, the robot can
showing the simplicity of the entire robotic system. It is worth behave entirely differently in response to the same environmental

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Fig. 3. Physical shape changes of soft autonomous robots in response to environmental inputs. (A) The extension ratio ε of the pneumatic actuator and the robot
(without any control modules) as a function of applied pressure. (B) Multiple types of modular control units are developed. They can be easily attached to or removed
from the body of the robot. (C) As one example, a control module can sense and respond to heat or light. (D) In this example, a different control module design causes the
robot to bend away from heat or solvents. (E and F) In another example, a control module is designed to bend the robot so that its end will align toward a light. Scale bars
(A), (C), (D), (E) and (F), 2 cm.

stimulus. For example, Fig. 3D and fig. S23 show a control module side. If the control module is illuminated more on one side than the
that causes the robot to bend in the opposite direction than the pre- other, the CNT-LCE strip on that side contracts more than the strip
vious example. on the other side. As a result, the robot bends toward the light
The relationship between the bending angle α and pressure is source (Fig. 3E). Note that as with all responsive materials, there
plotted in Fig. 3D. In addition to heat, the LCE can contract is an operational range for the relevant stimuli (e.g., temperature)
when exposed to other stimuli, such as the toluene, due to a outside of which the materials will not behave as designed (e.g.,
nematic-isotropic phase transition (57–59), resulting in bending the robot will not bend when the temperature of the LCEs is so
of the robot when pneumatically actuated (Fig. 3D). high that both have fully contracted). If the light is directly in
A third type of control module is shown in Fig. 3 (E and F). Here, front of the robot (Fig. 3F), then the two CNT-LCE strips contract
two CNT-LCE strips are used in the module and distributed to each

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equally, so the robot does not bend. The extension ratio (ε) of the large variety of other stimuli, including magnetic fields (22) and
robot is measured and shown in Fig. 3F. pH (60).
It is worth noting that the robot exhibits relatively slow locomo-
Autonomous changes to trajectory in response to tion speed (1 mm/s). This rate was chosen to accommodate the slow
environmental inputs response time of the actuating materials that regulate the control
Feet are added to the bottom of the robot to translate the cyclic in- modules. For example, at the millimeter to centimeter length
flation and deflation of the pneumatic actuator into locomotion. As scales of this design, the CNT-LCE composites actuate in response
shown in movie S2, the robot walks straight if no control modules to light on the order of 100 s. Hence, at these length scales, the robot
are present. should move at a rate such that its immediate environment changes
In Fig. 4, we show the effect of the control modules of Fig. 3 on at comparable time scales. Whether or not this time scale is “fast
the trajectory of the robot. First, we demonstrate how the robot can enough” or “slow enough” depends on the application and the in-
autonomously steer its trajectory closer to light or heat (Fig. 4A and trinsic time scale of the environment. The response time can be
movie S3) using the control module of Fig. 3C. When no apprecia- changed by patterning the responsive materials, or changing their
ble heat or light is present in the local environment, the robot walks length scale, potentially down to millisecond time scales (51).
forward. However, if the control module receives a large flux of heat However, the response time is also coupled with the mechanical
or light, then the CNT-LCE strip contracts, inhibiting the squares in properties of the responsive materials. Reducing the length scale

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contact with the module from opening when the pneumatic actua- of the responsive materials may reduce the force that they can
tor inflates. The rest of the robot body can still expand, however, exert on the kirigami. This may, in turn, require that the compliance
inducing bending. The trajectory of the robot therefore bends of the kirigami be structurally increased (e.g., via thinning of the
toward the stimulus (Fig. 4A). The trajectory of the robot is hinges or of the kirigami itself ) to maintain mechanical
shown in Fig. 4 (B and C) as a function of the power of the heat compatibility.
source (Fig. 4B) and as a function of the distance between the
robot and the light source (Fig. 4C). Since the CNT-LCE contracts Embodying multistimuli-responsive logic via
more at higher temperatures, the bending angle of the robot is larger control modules
when the power is higher or the distance is smaller. To confirm the As shown above, the control modules are designed to produce me-
repeatability of the trajectories for a given set of conditions, we chanical constraints within the robot body, altering how it deforms
tested some trajectories up to 20 times with the same light condi- and thereby its trajectory. The mutual interactions produced by
tions, finding minimal trajectory variations. The standard deviation multiple control modules throughout the body can be very
of the trajectories in these trials was less than 5% of the body length complex. However, these interactions also offer a strategy for imple-
of the robot (fig. S24). menting more nuanced control objectives, despite the lack of elec-
As in Fig. 3, simply by changing the type of control module, we tronics in these robots. The competing actions of multiple control
can cause the trajectory to bend away from the stimulus. Figure 4 (D units can be viewed as a computational event that is distributed
to F) shows trajectories of the robot that occur when the control throughout the robot body.
module of Fig. 3D is used instead of the module of Fig. 3C. This To demonstrate this behavior more concretely, we consider a
module inhibits the rotation of the squares on the side of the simplified example in which control modules are only placed
robot that is opposite to the stimuli. This causes the robot to auton- along the robot’s right or left side (near the center) and only heat
omously steer its path away from stimuli (Fig. 4D and movie S4). or light are used as inputs. Since heat or light can be applied to
These trajectory changes are quantified in Fig. 4 (E and F). either side, there are four total environmental inputs: heat applied
The third type of control module, introduced in Fig. 3 (E and F), to the left side (“input A”), light applied to the left side (“input B”),
allows the robot to steer itself directly toward a stimulus, as demon- heat applied to the right side (“input C”), and light applied to the
strated in Fig. 4 (G and H) and movie S5. right side (“input D”). Boolean values of “1” or “0” for a given input
Note that this same module also enables steering in dynamic en- indicate that the input is, or is not, present, respectively. We also
vironments, e.g., in which the intensity or location of the light define an “output” value, for which “0” indicates that the robot is
sources is changing (fig. S25). moving forward along a straight trajectory, while output values of
Last, we note that all of the control modules above have made use “1” and “−1” indicate that the robot is steering left or right,
of LCEs. However, in principle, the LCEs in the control modules can respectively.
be replaced with other responsive materials, such as hydrogels and With four boolean inputs, there are a total of 16 possible com-
PDMS, enabling analogous robot responses in the presence of water binations of input values. The output associated with each combi-
or other solvents, respectively (figs. S26 to S28). In this work, as a nation of inputs is determined by the choice of control modules
simple proof of concept, we made control modules with hydrogels placed at the input sites. The aggregate effect of all control
and silicones instead of LCEs. These control modules were sub- modules determines the map from the inputs to the outputs.
merged in water (hydrogels) or nonpolar solvents (silicones) for 2 These relationships can be summarized in “truth tables,” as
hours and 15 min, respectively, and then reattached to the robot shown, for example, in fig. S31.
body. As shown in fig. S26, the flexible strip generates tension due As a first simple example, we configure the robot using only one
to the swelling of the materials, which prevents the opening of the control module (the module of Fig. 3C), placed on the left side of the
kirigami. As a result, the kirigami bends when the actuator is inflat- robot. The complete truth table for this configuration (for all 16
ed (figs. S27 and S28). We demonstrate this behavior in figs. S29 and combinations of inputs) is shown in fig. S31A. Heat and/or light
S30. Given the large number of stimuli-responsive materials that can be sensed on the left side of the robot (e.g., inputs A and B
have been developed, the control modules could respond to a are allowed to be either 0 or 1). However, since there is no

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Fig. 4. Autonomous changes to trajectory in response to environmental inputs. (A) The schematic and experimental images show that the robot can autonomously
steer its trajectory closer to light or heat. (B) The trajectories (displacement and steering angle) of the robot as a function of the power of the heat source. (C) The
trajectories (displacement and steering angle) of the robot as a function of the distance y (in millimeter scale) between the light source and the initial trajectory of
the robot. (D) The second type of control module causes the robot to autonomously steer away from a heat source or the solvent toluene. (E and F) The trajectories
(displacement and steering angle) of the robot under different stimuli (heat or toluene). (G) The third type of control module causes the robot to autonomously steer
directly toward a light source. (H) The trajectories (displacement and steering angle) of the robot in environments with different locations of the light source. Scale bars
(A), (D), and (G), 5 cm.

control module on the right side of the robot, changing the values mechanical lock on the right side of the robot. It does not sense or
for inputs C and D has no effect on the robot. Hence, we can use an respond to stimuli, but instead causes the robot to bend right by
abbreviated truth table to fully define the response of the robot (see default when the pneumatic actuator inflates, even without environ-
fig. S32). This configuration behaves as an “OR” operation. When mental stimuli (i.e., the output is −1 even when the inputs A = B = C
the robot is exposed to heat or light from the left side (i.e., input A = D = 0). Consequently, the robot steers right when heat or light are
and/or input B are nonzero), the robot bends due to the contraction below the threshold. The complete truth table for all possible inputs
of the CNT-LCEs, causing it to steer left (fig. S33). is shown in fig. S31B. However, as in the previous example, since the
Next, we add a second control module to the robot, as shown in inputs on the right side are not sensed, the values of inputs C and D
Fig. 5A. The new module is a passive control module that acts like a have no effect. The abbreviated truth table is shown in Fig. 5A and

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Fig. 5. Embodying distributed, multistimuli-responsive logic via interaction of multiple control modules. Interactions of multiple control modules can be complex
(see complete truth tables in fig. S31). Here are a few simplified examples: (A) The combination of a “mechanical lock” control module and the CNT-LCE module of Fig. 3C
causes the robot’s steering to obey a NOR response. (B and C) Experimental images and trajectories, respectively, of the robot with different heat/light inputs. (D) In
another example, a “mask” control module is used in conjunction with the CNT-LCE module of Fig. 3C to steer in accordance with an AND strategy [for the environment
shown in (E)]. (E and F) Experimental images and trajectories, respectively, of the robot with different heat/light inputs. (G) In another example, two identical control
modules (actuated by heat or light) are distributed symmetrically along the two sides of the robot body, which enable the robot to realize XOR response. (H and I)
Experimental images and trajectories, respectively, of the robot with different heat/light inputs. Scale bars (B), (E), and (H), 5 cm.

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fig. S34. If the control module on the left side is exposed to heat and/ environment. Light and heat sources are placed along both sides
or light (i.e., input A and/or input B are nonzero) the squares across of the robot’s path. In the first example, we evenly distribute
from the lock are also inhibited from opening when the pneumatic control modules (with CNT-LCE strips) throughout the soft body
actuator inflates. In this case, the mechanical constraints on the two of the robot, as shown in Fig. 6A. This specific design causes the
sides cancel one another, causing the robot to remain straight when robot to be “attracted” by the heat and light sources. This results
the pneumatic actuator is pressurized, giving a straight trajectory in a “zigzag” trajectory, as shown in Fig. 6B and movie S9. A differ-
(Fig. 5, B and C, and movie S6). This configuration behaves as a ent moving strategy can be achieved by rearranging the control
“NOR” operation. modules, as shown in Fig. 6C. In this case, the control modules
More complex examples of mechanical logic can be achieved are only placed along one side of the robot, including modules
with other combinations of control modules. For example, the de- that bend the trajectory toward stimuli (i.e., Fig. 3C) and a
cision for the robot to turn can obey AND logic by adding a mask module that bends the trajectory away from stimuli (i.e., Fig. 3D).
module (an opaque polydomain LCE) exterior to the CNT-LCE This design causes the robot to steer left whenever heat or light are
control module used in the previous examples, as shown in encountered (Fig. 6D and movie S9). Next, we use three different
Fig. 5D and figs. S31C and S35. When the temperature is greater modules to give the robot an AND response, as shown in Fig. 6E.
than 150°C, the mask layer (opaque polydomain LCE) becomes These include control modules that bend the trajectory toward
transparent (fig. S36), as demonstrated previously (61). If only stimuli (i.e., Fig. 3C), a mask module (i.e., the polydomain LCE

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heat is applied to the left side of the robot (i.e., inputs A = 1 and of Fig. 5D), and the module that causes the robot to steer directly
B = 0), the mask layer becomes transparent, but also blocks toward stimuli (i.e., Fig. 3, E and F). When this configuration is
enough of the heat that the CNT-LCE module inside does not acti- used, the robot first moves toward the light, causing the body to
vate. Consequently, the robot walks forward along a straight trajec- steer left. Then, the robot moves straight forward, due to the
tory (Fig. 5, E and F). The same thing occurs if only light is applied effects of the mask module. As the robot begins to sense the light
(A = 0 and B = 1), since the mask layer remains opaque. Only when source to the right, the trajectory begins to turn right (see Fig. 6F
heat and light are both present on the left side (A = B = 1) will the and movie S9). The autonomous motion of the robot can be repro-
robot steer left (see Fig. 5, D to F, and movie S7), since the heat grammed simply by changing the distribution and types of control
causes the mask module to become transparent, allowing the light modules in the kirigami robot body. The error bars in the trajecto-
to reach and activate the inner control module. As with all active ries of Fig. 6, (B, D, and F) are the standard deviations of the posi-
materials, there is a particular time scale and intensity range that tions upon performing the experiments three times.
defines their operational relevance. In this case, we have to tune Last, we note that while the robot itself does not have onboard
the distance between the robot and light source to prevent overheat- electronics, it is tethered to a pneumatic device that is electronically
ing from occurring too rapidly. Note, in this example, inputs C and controlled. However, as has been previously demonstrated by others
D have no effect, since no control modules are present on the right (42), the pneumatic controller can be eliminated by integrating a
side of the robot. However, if the two control units on the left were bistable valve with the robot (Fig. 7). When the membrane of the
duplicated on the right side, the same AND logic with respect to valve bends upward, it blocks the pneumatic tube inside the top
inputs C and D would govern whether the robot steers right (and chamber. As a result, the pressurized air flows into the actuator, in-
in the case in which all inputs A = B = C = D = 1, the two sides would flating the pneumatic actuator. Once the pressure of the top
cancel, allowing the robot to proceed straight ahead). Moreover, the chamber reaches a critical pressure Pc, the membrane snaps, the
AND response of Fig. 5 (D to F) can be made into a NAND response air tube in the top chamber is no longer blocked, and the pressur-
by adding a mechanical lock to the right side (as demonstrated in ized air can flow out to the atmosphere, deflating the pneumatic ac-
figs. S31D, S37, and S38). In this case, the robot will only move tuator (Fig. 7A). This bistable valve thereby converts a constant
straight ahead if both heat and light are present on the left side, oth- pressure input to a periodically varying pressure output, providing
erwise it will turn right. the necessary sequential inflation-deflation of the pneumatic actu-
As a final example, we consider using two of the CNT-LCE ator (Fig. 7B). With the bistable valve and the control modules, this
control modules of Fig. 3C, one on each side of the robot robot can autonomously change its trajectory in a complex manner
(Fig. 5G and fig. S39). The robot bends only when exactly one without any electronics (Fig. 7C, figs. S40 and S41, and movie S10).
side of the robot is subjected to light or heat (for example, A = 1
and B = C = D = 0 or A = B = C = 0 and D = 1), causing the
robot to steer left or right (Fig. 5, H and I). If the control DISCUSSION
modules on both sides are actuated (e.g., A = 1, B = C = 0, and D In this work, we have shown how a kirigami-based soft robot can
= 1), the two effects cancel, and the robot continues to move straight autonomously navigate through an environment using modular
forward. The complete truth table for this system is shown in fig. control units distributed throughout its body. These control
S31E. See also movie S8. modules can make use of different types of responsive materials, en-
We again note that all of the different behaviors described above abling the robot to sense and respond to stimuli such as light, heat,
were obtained using the same robot. Only the type and locations of water, and solvents. Different control responses can be imparted to
the modular control units were varied. the robot simply by changing the positions and types of control
modules. We also showed that simple computational capabilities
Examples of autonomous trajectory changes in robots (e.g., “turn toward heat, but only if light is also present”) can be em-
integrated with multiple control modules bodied in the robot via the interactions of multiple control units.
Last, we demonstrate autonomous trajectory changes of the elec- Last, by also incorporating a mechanical bistable valve, the robot
tronics-free robot as it passes through a more complex can autonomously navigate without any electronic components.

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Fig. 6. Demonstration of repeatable autonomous trajectory changes for the robot configured with different control modules moving through environments
with multiple stimuli. (A, C, and E) show the robot configured with different modular control units. (B, D, and F) show experimental images and trajectories that result
from these designs. Scale bars (A), (C), and (E) 2 cm. Scale bars (B), (D), and (F), 5 cm.

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photolithography, two-photon polymerization, etc., which may

broaden the application of the proposed control strategy to biomed-
ical engineering and other areas making novel use of small soft
robots. Future work can also investigate the use of the proposed
control strategy under a broader range of environmental stimuli.
In addition, we note that most of the analysis, modeling, and exper-
imentation assumed that the robot exists in a two-dimensional (2D)
world (i.e., stimuli are in the same plane as the robot body).
However, in principle, there is no such restriction, and 3D effects
could certainly be included in the future. For example, fig. S42 illus-
trates one mechanism that could translate out-of-plane phenomena
into trajectory changes of the robot. Last, although we only demon-
strate control of trajectory in this work, such electronics-free sense-
control-act response loops could be readily adopted to change the
function, morphology, or other behaviors of robots.

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MATERIALS AND METHODS
Fabrication of the pneumatic actuator
The fabrication process of the pneumatic actuator is based on (62)
(see fig. S43). Briefly, we design a mold using SolidWorks and print
it using a MakerGear M3 3D printer. The uncured silicone precur-
sor (Ecoflex 30, Smooth-On Inc.) is poured into the mold and cured
Fig. 7. The integration of a bistable valve with the autonomous robot. (A) The for 24 hours. This results in a silicone elastomer tube with a helix
working mechanism of the mechanical bistable valve. When the membrane bends concave fiber groove. Then, we wrap a kevlar fiber following the pre-
upward, it blocks the pneumatic tube inside the top chamber. As a result, the pres- designed helix trace on the tube to constrain the radial expansion of
surized air flows into the actuator, inflating the pneumatic actuator. Once the pres-
the actuator resulting in axial extension. The two ends of the kevlar
sure of the top chamber reaches a critical pressure Pc, the membrane snaps, the air
tube in the top chamber is no longer blocked, and the pressurized air can flow out
fiber are fixed to the silicone using Sil-poxy (Smooth-On Inc.).
to the atmosphere, deflating the pneumatic actuator. (B) The bistable valve trans- Using this approach, the fiber angle can be precisely controlled.
lates a constant pressure input to a periodically varying pressure output (supplied The total height of the helix is 120 mm, the pitch is 8 mm, and
to the pneumatic actuator). (C) Demonstration of autonomous motion in response the diameter is 19 mm. This corresponds to a total length of 1806
to various light and heat sources. Scale bar (C), 5 cm. mm for the kevlar fiber. After that, the silicone tube (wound with
fiber) is reinserted into the mold. Additional uncured precursor is
Previous work has demonstrated the use of a similar bistable valve injected into the mold to seal the kevlar fiber. After 24 hours, the
to autonomously reverse the moving direction of a robot when it silicone tube is taken out and sealed with two caps using Sil-poxy.
walks into a wall (42), a clear example of an autonomous interaction Last, a fitting is inserted into the cap, which is connected to the ex-
of a robot with its environment. In our work, we develop a collec- ternal pneumatic source.
tion of modular control units that enable the robot to sense and
respond to multiple environmental stimuli (light, heat, water, and Fabrication of kirigami platform
solvent). These control modules are interchangeable, providing a As shown in fig. S44, the uncured silicone precursor (Dragonskin
wide variety of robot-environment interaction inputs and program- 10, Smooth-On, Inc.) is poured into the 3D-printed mold. Then,
mable moving strategies. Our framework opens up a new strategy we ensure all excess silicone is removed. After 24 hours, the cured
for working toward full autonomy in soft robotic systems. specimens are taken out and prepared for further use.
The current version of the soft robot is tethered to an external
pneumatic source. We note, however, that the robot could be Assembly of the electronics-free soft autonomous robot
made untethered, following strategies already outlined in the liter- The entire structure of the soft robot is shown in fig. S45. The pneu-
ature, especially since the robot only requires a constant pressure matic actuator is sandwiched between two layers of kirigami. The
source thanks to the bistable valve. The robot could provide its vertical columns (made from silicone) are placed at both sides of
own pneumatic source via a chemical reaction, such as hydrogen the pneumatic actuator to constrain the actuator during extension.
peroxide (39) or by carrying a small compressed gas source (42). For the connection between the kirigami and the pneumatic actua-
Another current limitation of this robot is its large physical size tor, 3D printed parts (R11, EnvisionTec) are designed and fabricat-
(the squares in the kirigami are centimeter scale), which is the prac- ed (fig. S45). All the squares can freely rotate and open when
tical result of our current manufacturing technique. We note, pressurized air is applied to the pneumatic actuator.
however, that the mechanical response of the kirigami body and
the basic control strategy (i.e., using variable mechanical constraints Fabrication of the control modules
to manipulate that mechanical response) are scale independent. The control modules include silicones, responsive materials (LCEs,
Hence, similar robots could, in principle, be scaled to smaller hydrogels, and/or PDMS), rigid rods, and 3D-printed parts. The sil-
length scales using advanced manufacturing methods such as icone layer of the kirigami is fabricated by pouring the mixture of
silicone precursor and dye (Ecoflex 30, Smooth-On Inc.) into the

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mold. The silicone is peeled off from the mold after 24 hours. For We prepare the LCE film following (63) with a few modifica-
the 3D-printed part, we use a digital light processing printer (Envi- tions. Ten grams of liquid crystal mesogen RM257 and 0.078-g of
sionTec) to fabricate the rigid parts. The detailed fabrication and photoinitiator HHMP are added to toluene. The mixture is dis-
assembly of each control module can be found in figs. S46 to S51. solved in an oven at 85°C. A 0.03-g MWCNTs can also be added
The control modules can be repeatedly switched on and off by suit- into the mixture to make the LCEs light-responsive. A 1.9017-g
able inputs in the environment, with no discernible change in per- chain extender EDDET, 1.52-g cross-linker PETMP, and 0.0324-g
formance (figs. S22 and S24). The practical maximum operational catalyst DPA are added to the mixture. The mixture is stirred and
temperature of the control module is set to 150°C. Further increas- degassed and poured into a glass mold (1 mm thickness). After 24
ing the temperature will cause softening of the 3D-printed parts. hours of curing, the solvent (toluene) is evaporated from the LCE in
Other materials could be substituted to increase this operational an oven set to 85°C for 12 hours. This results in a loosely cross-
temperature, if that were necessary for a particular application. linked, polydomain LCE thin film. To align and fix the alignment
of the liquid crystal mesogen, the loosely cross-linked LCE is
Mechanical integration of the control modules with the soft stretched to λ = 2 and exposed to ultraviolet (UV) irradiation for
autonomous robot 1 hour. This results in a monodomain LCE. LCE strips can be
Integration of the control modules with the soft robot is shown in made by cutting the monodomain LCE sheet. The actuation perfor-
fig. S52 and movie S1. The top and bottom layers of the control mance of the LCE is shown in fig. S15. If a polydomain LCE is

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module (blue color in fig. S52) are attached to the kirigami body desired (e.g., as in the mask control module), then it is placed
of the robot. Eight cylindrical pins (diameter, 4 mm) are used to under the UV light for 1 hour without stretching, finishing the
connect the control module and kirigami robot. The process can second cross-linking step.
be easily performed in reverse to remove a module.
Synthesis of hydrogels
Fabrication of the mechanical bistable valve Acrylamide (>99%; Arcos, USA), alginate (FMC Biopolymer, LF
The mechanical bistable valve receives a constant pressure as input 10/60, USA), N,N0 -methylenebis (acrylamide) (MBAA) (Sigma-
and outputs a periodic pressure variation due to an internal insta- Aldrich, USA), ammonium persulfate (>98%; Sigma-Aldrich,
bility, as reported previously (43). We fabricate the bistable valve USA), N,N,N0 ,N0 -tetramethylethylenediamine (TEMED) (>99%;
based on (42). We pour the silicone precursor (Dragonskin 10, Sigma-Aldrich, USA), and calcium sulfate dihydrate (98%; Sigma
Smooth-On Inc.) into a 3D-printed mold and cure. Air tubes are Aldrich, USA) are used without further purification.
glued to the membrane in the middle of the valve using Sil-poxy The double network hydrogel is synthesized following (64) with
(Smooth-On Inc.). The cap of the valve is subsequently glued to some modification (65). An 8-g acrylamide, 1-g alginate, 0.0048-g
the main body of the bistable valve. Last, we connect the cross-linker MBAA, and 0.02-g thermal initiator are dissolved into
air pathway. 51 g of deionized water. The mixture is stirred for 2 hours until all
the components are fully dissolved. The mixture is marked as sol-
The measurement of the elongation, bending angle, and ution 1. Then, 0.02-g initiator accelerator TEMED and 0.1328-g
trajectory of the soft robot ionic cross-linker calcium sulfate dihydrate are dissolved into 5 g
The pneumatic actuator of the robot is pressurized using a custom of deionized water. The mixture is sonicated for 2 min and
fluid control system to precisely control the pressure (fig. S9). To marked as solution 2. After that, solution 1 and solution 2 are
measure the elongation ε and bending angle α of the robot, we mixed and poured into a 3D-printed polylactic acid (PLA) mold
use a digital camera (Canon 80D) to capture images of the robot with dimensions 5 mm by 4 mm by 10 mm. The specimen is left
during its inflation. We characterized the bending angle of the at room temperature (24°C) for 24 hours, covered by a glass slide,
robot at each pressure by analyzing the images, using ImageJ. The to polymerize the gel.
results are shown in Fig. 3.
To measure the trajectory of the soft robot, we use a digital The measurement of the actuation strain of the CNT-LCE
camera to record the video. We extract the video frames images and LCE film
from the video after one cycle. We track the center point of the A hot plate is used to measure the actuation strain of the CNT-LCE
robot to keep track of its location (using ImageJ). The results are and LCE film at different temperatures. At each temperature, we
shown in Figs. 4 to 6. wait 3 min to ensure the length of the LCEs has reached an equilib-
rium. The length is measured by taking an optical image (Canon
Synthesis of LCEs 80D) then using ImageJ. The results of the actuation strain are
1,4-Bis-[4-(3-acryloyloxypropyloxy)benzoyloxy]-2-methylbenzene shown in fig. S15.
(RM257) (Wilshire company, 95%), (2-hydroxyethoxy)-2-methyl-
propiophenone (HHMP; Sigma-Aldrich, 98%), 2,20 -(ethylene- The response speed of the CNT-LCE film
dioxy) diethanethiol (EDDET; Sigma-Aldrich, 95%), The actuation strain of the CNT-LCE film versus time is shown in
pentaerythritol tetrakis (3-mercaptopropionate) (PETMP; Sigma- fig. S18A for different light intensities. In the experiment, we change
Aldrich, 95%), dipropylamine (DPA; Sigma-Aldrich, 98%), and the distance between the light source and the CNT-LCE film. When
multiwalled CNTs (MWCNT, Sigma-Aldrich, >98%) are used as re- the light is switched on, the actuation strain of the CNT-LCE grad-
ceived without purification. We use a glass mold and VHB (3M, ually increases, eventually reaching a steady-state plateau value after
4905 and 4910) as spacer for controlling the thickness of the 100 s. After the light is switched off, the actuation strain drops to 0
LCE sample. within 160 s. During these tests, we also measure the maximum
surface temperature of the CNT-LCE film using an infrared (IR)

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This PDF file includes: 24. Y. Zhao, C.-Y. Lo, L. Ruan, C.-H. Pi, C. Kim, Y. Alsaid, I. Frenkel, R. Rico, T.-C. Tsao, X. He,
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Figs. S1 to S52 drogel. Sci. Robot. 6, eabd5483 (2021).
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