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ARTICLE
Legless soft robots capable of rapid, continuous,
and steered jumping
Rui Chen 1,9✉, Zean Yuan 1,9, Jianglong Guo 2,9, Long Bai 1,9, Xinyu Zhu1, Fuqiang Liu 3,
Huayan Pu 4✉, Liming Xin 5, Yan Peng 6, Jun Luo1,4, Li Wen 7& Yu Sun 8
Jumping is an important locomotion function to extend navigation range, overcome obstacles,
and adapt to unstructured environments. In that sense, continuous jumping and direction
adjustability can be essential properties for terrestrial robots with multimodal locomotion.
However, only few soft jumping robots can achieve rapid continuous jumping and controlled
turning locomotion for obstacle crossing. Here, we present an electrohydrostatically driven
tethered legless soft jumping robot capable of rapid, continuous, and steered jumping based
on a soft electrohydrostatic bending actuator. This 1.1 g and 6.5 cm tethered soft jumping
robot is able to achieve a jumping height of 7.68 body heights and a continuous forward
jumping speed of 6.01 body lengths per second. Combining two actuator units, it can achieve
rapid turning with a speed of 138.4° per second. The robots are also demonstrated to be
capable of skipping across a multitude of obstacles. This work provides a foundation for the
application of electrohydrostatic actuation in soft robots for agile and fast multimodal
locomotion.
https://doi.org/10.1038/s41467-021-27265-w OPEN
1State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China. 2School of Science, Harbin Institute of Technology
(Shenzhen), Shenzhen 518055, China. 3College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China. 4School of
Mechatronics Engineering and Automation, Shanghai University, Shanghai 200444, China. 5School of Computer Engineering and Science, Shanghai
University, Shanghai 200444, China. 6Research Institute of Unmanned Surface Vessel Engineering, Shanghai University, Shanghai 200444, China. 7School
of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China. 8Department of Mechanical and Industrial Engineering, University of
Toronto, Toronto, Canada.
9
These authors contributed equally: Rui Chen, Zean Yuan, Jianglong Guo, Long Bai. ✉email: cr@cqu.edu.cn;
phygood_2001@shu.edu.cn
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As an important locomotion function of terrestrial robots,
jumping or leaping is useful for them to effectively extend
their navigation range, overcome challenging obstacles,
and enhance their adaptability in unstructured environments1–3.
However, enhancing single-jump performance (jumping height
(JH) and jumping distance (JD)) of soft jumping robots to
improve their obstacle-crossing ability and accelerating jumping
frequency to increase their navigation efficiency at the same time
are two grand engineering challenges. Researchers have developed
soft or partially soft jumping robots capable of forward naviga-
tions and driven by integrated springs4–17, shape memory alloys
(SMAs)18–20, magnetic actuators21, light-powered actuators22,23,
dielectric elastomer actuators (DEAs)24–26, pneumatic
actuators27–29, chemical actuators30–33, motors34–36, and poly-
vinylidene difluoride (PVDF) actuators37. Some of them, which
are energy-storing jumping robots4–25, have excellent single-jump
performance, but always at the cost of navigation efficiency due to
the necessity of the additional elastic energy-storage process. The
prolongation of the energy-storage process increases the JH but
decreases the landing stability and reduces the jumping fre-
quency. On the other hand, soft jumping robots actuated by
pneumatic actuators27–29, chemical actuators30–33, and
motors34–36 have been demonstrated but have complicated
navigation strategies and structures. Lightweight soft hopping
robots based on DEAs26 and PVDF actuators37 can simply jump
by bending their body parts without additional energy-storing,
which can lead to rapid jumping frequencies, but their JHs and
JDs are not enough (<0.25 body height) to meet the requirements
of crossing obstacles.
Hydraulically amplified self-healing electrostatic (HASEL)38–41
actuators, which can achieve linear motion by electro-
hydrostatically changing the distribution of internal liquids, have
been demonstrated to achieve remarkable continuous actuation
performance with actuation strains up to 118%, strain rates of
about 7500% s−1, and a peak specific power of 156 W/kg. The
stacked quadrant donut HASELs presented by Mitchell et al.40
can achieve continuous vertical jumping by rapidly changing
internal liquid distribution with a JH of about 1.67 body heights.
This electrohydraulic actuation method, which can generate the
energy required for jumping in a very short time without the need
for a complicated energy-storing process, is a potential solution
for rapid obstacle-crossing robots. However, the diffusion-like
isotropic liquid flow of a donut HASEL actuator cannot generate
the energy of the forward jumping since the kinetic energy of the
liquid in all directions was canceled out, which caused the loss
and waste of energy. The jumping caused by the partial expansion
of the liquid pouch can only keep the partial actuator off the
ground and the backflow of the dielectric liquid relies solely on
gravity, making it slow to return to the original state after landing
(Supplementary Fig. 1a). Therefore, it is still challenging for
HASEL jumpers to (1) achieve enhanced single-jump perfor-
mance without stacking, (2) achieve rapid restoration, and (3)
generate forward jumping and steered jumping.
Based on the flexible electrical-driven liquid redistribution
method of HASEL series actuators38–41, the actuator structure
was redesigned to make liquid flow anisotropically, utilize the
kinetic energy generated by liquid redistributions, and achieve
forward jumping. In addition, using saddle-shaped bending based
on an elastically deformable frame-membrane structure to
achieve locomotion is common in DEAs42, which inspired us to
use rapid bending and rebound based on electrohydrostatic
principle and frame to enhance the jumping performance of
actuators. In this work, we propose an electrohydrostatically
driven tethered legless soft jumping robot (LSJR) with rapid,
continuous, steered jumping and obstacle-crossing capabilities
based on a soft electrohydrostatic bending actuator (sEHBA). We
show that the characteristic of sEHBA’s rapid response leads to a
short actuation time (~10 ms). The LSJR can be used to achieve a
JH of 7.68 body heights, a JD of 1.46 body lengths in a single
jump, and a continuous forward jumping speed of 390.5 mm/s
(6.01 body lengths per second) with a frequency of 4 Hz. We also
demonstrate that the integration of two LSJRs can readily achieve
rapid steered jumping. The turning speed of the dual-body LSJR
was able to reach 138.4°/s−1, which is the fastest among existing
soft jumping robots. Furthermore, we show that LSJR’s rapid
continuous jumping locomotion can cross various obstacles,
including slopes, wires, single steps, continuous steps, ring
obstacles, gravel mounds, and cubes of different shapes, some of
which are larger than the robot.
Results
Design concept and movement principle of the LSJR. In order
to use the anisotropic liquid flow to achieve forward jumping
caused by unbalanced energy, we heat-sealed a HASEL like
actuator into a semicircular separated HASEL (SCS-HASEL)
actuator composed of two semicircular liquid pouches based on
the zipping mechanism43 and it showed better jumping perfor-
mance (Supplementary Fig. 1b). Then, the dielectric liquid in the
rear semicircular pouch of the SCS-HASEL actuator was replaced
with an equal volume of air and the covered electrodes of the rear
semicircular pouch were removed so that the dielectric liquid can
flow anisotropically relative to the entire actuator. As expected, it
can be found that the special liquid–air layout can make the
liquid–air actuator jump forward even though the air pouch
dragged on the ground (Supplementary Fig. 1c). This was because
the electrodes squeezed the liquid dielectric to make it flow for-
ward quickly, thus giving it the initial kinetic energy that can be
used to provide forward kinetic energy to the liquid–air actuator.
The detailed experimental results can be seen in Supplementary
Movie 1.
By observing the three types of actuators above (Supplemen-
tary Fig. 1), it can be found that their jumps were all caused by the
partial expansion of the liquid pouch. This kind of jump was
unstable and unreliable, and the JH was insufficient. Furthermore,
the edges of the SCS-HASEL actuator and liquid–air actuator
were unrestricted so that every jump had randomness and the
initial state cannot be completely restored. Fixing a predeformed
frame on the edge is a well-known restriction method in DEAs42
and has not been used for HASEL series actuators. Combining the
frame to transform the linear motion of the electrohydraulic
actuators into a saddle-shaped bending motion provided the
possibility of an efficient type of jumping method. Therefore, the
non-prebending ring frame and the prebending ring frame were
combined to the SCS-HASEL actuator and the liquid–air
actuator, and then their single-jump performance was tested,
respectively (Supplementary Fig. 2). The left half of Supplemen-
tary Fig. 2 shows the moment (11.76 ms after applying voltage)
the actuators took off from the ground. The prebending frames
fixed on the edges of these actuators can guide the direction of
deformation, making the deformation of the actuators with
prebending frames more regular and closer to the saddle shape
than the actuators with plane frames and achieve better jumping
performance. The liquid–air actuator with a prebending frame,
which was also the sEHBA we needed, can jump higher and
further, and it can return to its original state immediately after
landing. Clearly, using the frame with more regular deformation
to touch the ground and generate jumping energy is a more stable
and reliable jumping mechanism than relying on the partial
expansion of the liquid pouch (Supplementary Movie 1).
In this paper, we propose an electrohydrostatically driven LSJR
(Fig. 1) that has rapid, continuous, steered jumping and obstacle-
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crossing capabilities based on the sEHBA. The special liquid–air
layout and the semicircular zipping structure can be used to make
the internal liquid flow anisotropically and rapidly to generate a
great amount of forward kinetic energy, which is offset and
wasted in HASEL actuators. Meanwhile, the prebending frame
fixed on the edge of the sEHBA can be used to guide the
deformation direction to achieve fast bending locomotion which
can be used to generate vertical and forward kinetic energy. The
special liquid–air layout and prebending frame structure greatly
enhance the jumping performance of electrohydraulic actuators
and enable rapid, continuous, and steered jumping without
stacking. The LSJR can jump simply by quickly liquid flowing and
body bending, thereby greatly shortening the propulsive interval
(~10 ms). The stored elastic energy associated with body bending
Fig. 1 LSJR detailed design and motion principle. a The LSJR consists of two plastic semicircular pouches printed with flexible electrodes. The front pouch
is filled with a dielectric liquid, and the rear is filled with air with the same volume. A flexible plastic ring frame is fixed on the edge and is prestrained. Note
that the rear air pouch functions to ensure that the pre-curved frame is consistent and maintains structural balance during the flight. bThe LSJR prototype
(1.1 g). Scale bar, 1 cm. cSchematic diagram of the LSJR jumping process. By the application of a high voltage to the two electrodes, the LSJR is energized to
bend itself to generate forces and energy for forward jumping. During the voltage application, Maxwell stress squeezes the dielectric liquid and makes it
flow laterally into the portion of the front pouch that is not covered by the electrodes (from the liquid outflow area to the liquid inflow area). dCross-
sectional views (e–e and f–f) of the LSJR: e–e denotes the deformation of the front pouch, whereas f–f shows the e–e deformation-driven whole-body
bending and jumping. eSnapshots of the LSJR jumping, where 10 kV is applied to the actuator. Scale bar, 2 cm.
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can help the robot quickly restore its original shape to avoid
affecting the next jump. The detailed design iterations are
demonstrated in Supplementary Fig. 3.
The LSJR consists of two flexible plastic semicircular pouches
printed with flexible electrodes that were connected with two
conductive tapes for potential electric wire connections (Fig. 1a).
The two pouches were made of biaxially oriented polypropylene
(BOPP) films. The front pouch was filled with a dielectric liquid
and the rear was filled with the same volume of air. A flexible
plastic polyvinyl chloride (PVC) ring frame was fixed on the edge
and prestrained. Note that the rear air pouch, which is similar to
the tail of animals and is used to maintain the balance of the
jumping and landing posture, played an important role in the
whole structure of the LSJR. To further enhance the jumping
performance of LSJR, the air in this pouch can be replaced with
helium or other less dense and non-explosive gas. The prototype
of an LSJR (1.1 g) is shown in Fig. 1b. The detailed fabrication
process can be seen in “Methods”.
The LSJR is energized to bend itself to generate forces and
energy for forward jumping. After the application of a high
voltage to the electrodes, Maxwell forces attract the electrodes,
squeezing the dielectric liquid from the outflow area to the inflow
area with no electrode coverage (Fig. 1c). The rapid and
anisotropic flow can generate a horizontal initial kinetic energy.
The increased electrostatic force between the electrodes of the
front pouch causes a rapid liquid flow, which increases the
thickness of the cross-section F-F and decreases its lateral length
from X
1
to X
2
, as the pouch is inextensible. This deformation,
plus the pre-strain of the ring frame to keep the bottom electrode
from touching the substrate and facilitate the further bending of
the frame during actuation (cross-section G-G), pulls the front
and rear ends closer to each other (Fig. 1d). The instantaneous
partial deformation of the frame results in instant bending of the
overall frame, which propels the robot body into the air.
Snapshots of a rapid (~10 ms) take-off process is presented in
Fig. 1e. After take-off, the initial horizontal velocity of LSJR is
determined by the horizontal ground reaction forces at the frame
ends. The forces are caused by the moving dielectric liquid flow
and frame bending. The initial vertical velocity of the LSJR is
determined by the vertical ground reaction forces at the frame
ends, which are caused by the frame bending. During the leaping
state, the ring frame quickly releases its elastic energy, and the
dielectric liquid flows back, restoring the robot to the original
state in preparation for the next jump after landing. Note that the
low-profile robot design makes both the jumping and landing
stable with no capsizing. The detailed theoretical analysis of the
locomotion mechanism is demonstrated in Supplementary
Note 1.
Single-jump characterization. JD and JH are two important
performance measures that can be used to characterize the
jumping performance of the LSJR. If the same robot material and
size are maintained, the electrode area/nonelectrode area ratio,
magnitude of the voltage application, the mass of the load, and
the ring frame prebending level are important parameters influ-
encing the jumping performance of the LSJR. Figure 2a shows the
untethered single-jump process and related parameters. The two
aluminum electrodes connected to the tail of the LSJR were freely
placed on two copper electrodes (top left inset in Fig. 2a), aiming
to eliminate the influence of electric wires on the jumping per-
formance. Note that (1) three LSJRs with the same parameters
were fabricated, and the differences in the JD and JH results were
all within 10%, and (2) for each jumping experiment, 10 repeated
tests were performed in the same laboratory environment, and
average and one standard deviation values of each 10 results were
reported. Furthermore, applying a voltage of the same polarity
would cause the charge to be retained and to accumulate inside
the actuators, which would prevent the actuators from fully
returning to their initial position, thus affecting the results of the
next experiment. Therefore, the polarity would be reversed and a
waiting time of 60 s would be used to alleviate charge retention
after each experiment (top right inset in Fig. 2a).
We define r=electrode area:nonelectrode area (of the front
pouch) and fabricated three robots with r=2:1, 1:1, and 1:2.
Figure 2b, c shows that the robot with r=1:1 produced a larger
JD and JH. At a low voltage (0~3 kV), the robot deformed slowly,
and the deformation force was not large enough for jumping.
Average values of JD =95.0 mm (1.46 body lengths) and
JH =30.7 mm (7.68 body heights) were achieved when the
applied voltage was 10 kV and r=1:1. Carrying a 1 g load (0.91
body weight) decreased the JD (56.0 mm) and JH (20.0 mm) to
59% and 65% of the no-load condition, respectively, bringing a
jumping performance reduction of 38%. Carrying a 2 g load (1.82
body weight) decreased the JD (33.7 mm) and JH (8.1 mm) to 35
and 26% of the no-load condition, resulting in a jumping
performance reduction of 70%, which was nearly twice that of a
1 g load condition. We used different body heights (BH) to
represent different prebending levels and fabricated three robots
with BH =2, 4, and 6 mm. Figure 2d, e shows that the robot with
BH =4 mm produced a larger JD and JH. In addition, the LSJR
with 2 mm BH had a greater average relative jumping height
(RJH) of 9.4 when 10 kV was applied, whereas the average RJHs
of the LSJR (BH =4 mm) and the LSJR (BH =6 mm) were 7.7
and 4.2, respectively. Comparing the experiment results (Fig. 2b,
c) of the LSJR (r=2:1, load =0 g), the LSJR (r=1:1, load =0 g),
and the LSJR (r=1:2, load =0 g), an apparent difference in their
JHs but a very small difference in JDs can be found. According to
Supplementary Note 1, the amount of dielectric liquid flow had a
much greater impact on the initial horizontal velocity v
x
than on
the initial vertical velocity v
y
. The bigger ratio r, which can affect
the size of the electrode coverage area, led to a bigger volume
ΔV
oil
of dielectric liquid flow, a faster velocity v
oil
of dielectric
liquid flow, and the faster bending rate of the ring frame. It
caused a bigger horizontal initial kinetic energy of the moving
dielectric liquid flow and greater vertical ground reaction forces,
leading to a bigger JD and JH. However, the excessive r(e.g.
r=2:1) not only affected the flexibility of BOPP films and
hindered the normal bending of the frame, reducing the vertical
ground reaction forces, but also led to a smaller ΔV
oil
and a lower
v
oil
, reducing the horizontal initial kinetic energy of the moving
dielectric liquid flow. Therefore, the ratio (r=1:1) was the most
appropriate in this experiment.
Continuous jumping on different substrates. Rapid continuous
forward jumping is a useful locomotion capability. Continuous
forward jumping speed (CFJS) is an important performance
feature characterizing a continuous forward jumping robot. If the
same robot is used, the substrate surface roughness, actuation
frequency, and magnitude of the applied voltage are important
parameters influencing the jumping performance of the LSJR.
Sufficient substrate surface roughness prevents the robot from
slipping during continuous motions, and an appropriate actua-
tion frequency enables a quicker continuous movement. Note
that (1) for each jumping experiment, 10 repeated tests were
performed in the same laboratory environment, and the obtained
results were reported as the average and one standard deviation,
and (2) the polarity was reversed to alleviate charge retention.
It is shown in Fig. 1e that applying 10 kV to the robot for 10 ms
or more was a necessary condition for a successful jump. This
resulted in a jumping time of almost 250 ms (Supplementary
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Movie 2) and a typical actuation frequency of 4 Hz. Therefore, we
set the power-on time to 10 ms and selected a series of test
frequencies, i.e., 8, 4, 2, 1, 0.5, and 0.25 Hz, to test the influence of
actuation frequency. In the experiments, the LSJR moved for four
cycles at each frequency, and CFJS was calculated. In Supple-
mentary Movie 3, we demonstrated continuous forward jumping
locomotion of the soft robot on four substrates, i.e. a glass plate, a
paper plate, a PVC plate, and a wood plate, with different surface
roughness (Supplementary Fig. 10). Figure 3a–d shows that at
4 Hz and 10 kV, the robot achieved a greater average CFJS =
390.5 mm/s (6.01 body lengths per second) on the wood
substrate, whereas an average CFJS =95.6 mm/s (1.47 body
lengths per second) was achieved on the glass plate because it was
difficult for the smooth glass plate to provide sufficient friction.
Fig. 2 Single-jump characterization results. See also Supplementary Movie 2. aUntethered single-jump process and parameters. The top left inset shows
the electrical connections. The top right inset is the voltage application strategy in the experiment. bThe relationship between JD and applied voltage under
different loads (0, 1, and 2 g) and different electrode area/nonelectrode area ratios (2:1, 1:1, and 1:2). cThe relationship between JH and applied voltage
under different loads (0, 1, and 2 g) and different electrode area/nonelectrode area ratios (2:1, 1:1, and 1:2). dThe relationship between JD and applied
voltage at different body heights (2, 4, and 6 mm). eThe relationship between JH, RJH, and applied voltage at different body heights (2, 4, and 6 mm).
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Fig. 3 Continuous jumping on different substrates. See also Supplementary Movie 3. aThe relationship between CFJS and actuation frequency on the
glass plate, where the slowest average CFJS =95.6 mm/s (1.47 body lengths per second) was obtained at 4 Hz and 10 kV. bThe relationship between CFJS
and actuation frequency on the paper plate. cThe relationship between CFJS and actuation frequency on the PVC plate. dThe relationship between CFJS
and actuation frequency on the wood plate, where the fastest average CFJS =390.5 mm/s (6.01 body lengths per second) was obtained at 4 Hz and 10 kV.
eThe voltage application strategy and the corresponding robot motion states. fComposite image of the initial position and four landing points in
continuous jumping on the PVC plate when CFJS =250.1 mm/s at 4 Hz and 10 kV. The angle deviation of each jump was less than 8°. Scale bar, 5 cm.
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As the actuation frequency increased, the CFJS increased. At a
frequency higher than 8 Hz, after the LSJR took off and left the
substrate, another actuation cycle started while the robot was still
in the air. Each actuation cycle should only occur after the LSJR
had landed smoothly; otherwise, the next jumping performance is
impaired. Figure 3e shows the constant voltage application
waveform and the corresponding robot states. Applying a voltage
of the same polarity would cause the charge to be retained and to
accumulate inside the actuators, which would prevent the
actuators from fully returning to their initial position. Reversing
the polarity mitigated charge retention within the actuator during
continued cycling. The voltage application period was required to
be long enough to prevent the LSJR from entering the next
actuation cycle before landing. Therefore, changing the voltage
waveform in real time through visual recognition and other
means and making the LSJR enter the next actuation cycle
immediately after landing may provide solutions to the random-
ness of flight time and further increase the CFJS. Figure 3f
demonstrates the initial position and four landing points during
continuous forward jumping on the PVC plate with a speed of
250.1 mm/s (3.85 body lengths per second). The angle deviation
of each jump was less than 8°, which means that the robot can
achieve a reasonably good straight-line movement. More details
on the LSJR’s motion precision can be seen in the Supplementary
Note 2 and Supplementary Movie 8.
Steered jumping of a dual-body LSJR. Steered jumping is a
useful function for animal locomotion in unstructured and
complex terrains. It is desirable for soft jumping robots to
replicate this ability. Two LSJRs were connected abreast, resulting
in a dual-body LSJR (Fig. 4a, b) with the ability to adjust its
locomotion direction42. Applying a voltage (V
1
) to one unit of the
LSJRs causes the unit to jump: it deforms, generates forward
kinetic energy, and bears ground friction forces. The center of
gravity of the dual-body LSJR is not in the direction of the initial
speed and friction forces, resulting in turning behavior (each cycle
achieves a turning angle of α, as shown in Fig. 4a). Selectively
controlling V
1
on the left and right LSJRs results in steered
jumping. To illustrate the turning performance of the dual-body
LSJR, it was made to turn at least 60° on each of the four sub-
strates. Figure 4c shows that the robot on the wood plate achieved
a greater turning speed (TS). An average TS =138.4°/s was
achieved at 10 kV and 4 Hz, which, to the best of the authors’
knowledge, is the fastest among existing soft jumping robots. An
average TS of only 27.9°/s was achieved on the glass plate at 10 kV
and 4 Hz because the surface was smooth. Figure 4d demonstrates
Fig. 4 Turning results of the dual-body LSJR. See also Supplementary Movie 4. aSchematic diagram of the dual-body LSJR turning process, which
consists of the rest state, the turning state, and the landing state. Over each voltage cycle, the robot turns by an angle of α.bCenter of gravity of the dual-
body LSJR. cThe relationship between TS and applied voltage on the four substrates. dComposite image of the initial and final positions during a
continuous turning procedure on the PVC plate with a speed of 65.0°/s. The robot took 1.23 s to turn 80° at 10 kV and 4 Hz. Scale bar, 5 cm.
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the initial and final positions during a continuous turning pro-
cedure on the PVC plate with a speed of 65.0°/s at 10 kV and
4 Hz. Sufficient substrate surface roughness not only prevents the
robot from slipping during continuous motions but also hinders
the movement of the unpowered LSJR and thus the turning
behavior. Therefore, a potential solution is to apply a large V
1
to
one LSJR and a small V
0
to the other LSJR. This will lead to a
greater jump by one unit, thus resulting in turning behavior, and
will be considered in our future work. More details on the LSJR’s
motion precision can be seen in Supplementary Note 2 and
Supplementary Movie 8.
Obstacle-crossing ability of the LSJR. A main function of a
jumping robot is obstacle avoidance so that it can conduct
explorations, inspections, and reconnaissance tasks in complex
and unstructured environments. Both the single-body and dual-
body LSJRs can be used to achieve decent obstacle-crossing
capability, as shown in Figs. 5and 6(Supplementary Movies 5
and 6). Under an applied voltage of 10 kV and an actuation
frequency of 4 Hz, the single-body LSJR was found to (1) climb
on the glass plate (tilt angle of 3°) with a CFJS of 16.3 mm/s (0.25
body lengths per second), (2) jump cross an electric wire (dia-
meter of 6.3 mm), (3) jump across a square step (8 mm high), and
(4) jump across continuous steps (consisting of the square step
and a 5 mm high round step). In crossing tests with an obstacle
height interval of 4 mm, the maximum height that the LSJR can
cross was 14 mm for cuboids, and 18 mm for triangular prisms
and cylinders, as shown in Supplementary Fig. 11 (Supplementary
Movie 7). Affected by the leaping posture and wires, the
Fig. 5 Single-unit LSJR obstacle crossing at 10 kV and 4 Hz. See also Supplementary Movie 5. aClimbing on the glass plate (tilt angle of 3°) with a CFJS
of 16.3 mm/s. bCrossing an electric wire (diameter of 6.3 mm). cJumping across a square step (height of 8 mm). dJumping across continuous steps
(heights of 8 and 5 mm). Scale bar, 5 cm. eComposite image of the LSJR’s locomotion on a gravel mound (gravel size: 3–6 mm). Scale bar, 2 cm.
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maximum obstacle height that the LSJR can cross was less than
the max JH. In order to further prove the robot’s ability to
overcome obstacles in realistic unstructured environments, we
made a gravel mound with many gravels (size: 3 to 6 mm), and
tested LSJR’s locomotion on the gravel mound (Fig. 5e). The
steered jumping (simultaneous jumping and turning) capability
of the dual-body LSJR made it (1) jump across a 5 mm high
round step and (2) jump across a ring object with a height of
8 mm, an inner diameter of 77 mm, and an outer diameter of
83 mm. It was challenging for the single-body LSJR to avoid the
ring obstacle. The collaborative movement of two LSJR units
results in much greater flexibility and improved obstacle-crossing
ability for soft jumping robots, thus making the robot more
adaptable to complex terrains.
Discussion
We proposed an electrohydrostatically driven, low-profile (0.85-
mm-thick), lightweight (1.1 g), modular, and cost-effective teth-
ered LSJR based on a sEHBA. The robot features capabilities of
rapid, continuous, and steered jumping, load-carrying, and
obstacle-crossing through a simple control strategy. The
inspiration for the design of the sEHBA stemmed from the
electrohydrostatic jumping of HASEL actuators40 and the peri-
odic saddle-shaped bending caused by the predeformed frame of
DEAs42. In the design process, a mechanical analysis model and a
dielectric liquid’s center of gravity moving equivalent model were
built to guide the optimization of size parameters.
Most existing soft jumping robots (Table 1)havealargeJHbut
require a long actuation/energy-storage time and righting time, which
leads to a slow CFJS and lack of flexibility. A few soft jumping
robots26,37 have a high actuation frequency and high speed mobility,
but they can only achieve a small JH (<0.25 body height), which is
not suitable for overcoming challenging obstacles. Our LSJR used the
special liquid–air layout and the edge-fixing prebending frame to
achieve rapid continuous forward and steered jumping locomotion
caused by periodic saddle-shaped bending and anisotropic liquid
flow, which made up for the limitations of HASEL actuators40,
including (1) unachievable forward and steered jumping, (2) weak
single-jump performance without stacking, and (3) incapability for
rapid restoration. As a result, the LSJR had a short actuation time
(~10 ms) and was able to achieve a JH of 7.68 body heights, a JD of
1.46 body lengths in a single jump (Fig. 2and Supplementary
Movie 2), and a CFJS of 390.5 mm/s (6.01 body lengths per second)
with a frequency of 4 Hz (Fig. 3and Supplementary Movie 3). The
angle deviation of each jump can be controlled within 8° in con-
tinuous forward jumping locomotion. The integration of two LSJRs
was able to readily achieve rapid steered jumping (Fig. 4and Sup-
plementaryMovie4).TheTSofthedual-bodyLSJRwasableto
reach 138.4°/s, which is the fastest among existing soft jumping
robots. Experiments also verified that LSJR’s rapid continuous
jumping locomotion could be applied to cross many obstacles,
Fig. 6 Dual-body LSJR obstacle crossing. See also Supplementary Movie 6. aStraight jumping across a round step (height of 5 mm). bSteered jumping
across the round step (height of 5 mm). cJumping across a ring obstacle (height of 8 mm, inner diameter of 77 mm, and outer diameter of 83 mm). Scale
bars, 10 cm.
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Table 1 Comparison between this work and some soft forward jumping robots.
Soft
jumping robots
Energy-storing
jumping
Actuation
methods
Weight (g) Jumping distance Jumping height Propulsive
interval time (s)
Landing
stability
Straight line
jumping
capability
Direction-
adjusting
capability
Unit cost
Kovač(2013)7Yes Spring 14.00 ≈2.55 BD ≈3.44 BD ≥5.00 Medium Low Directional
jumping (∞
directions)
High
Zhakypov
(2019)18
Yes SMA 9.70 3.97 BL 2.50 BH >24.00 High High No High
Huang (2018)19 Yes SMA 3.00 ≈2.00 BL 1.00 BH ≈3.00 High High No High
Hu (2018)21 Yes Magnetic N/A ≈1.63 BL 2.44 BL >10.00 Low Medium Steered jumping
(≈15.0°/s)
N/A
Ahn (2019)22 Yes Light N/A 8.00 BL 5.00 BH ≥100.00 High High No N/A
Hu (2017)23 Yes Light N/A N/A 5.00 BH ≈10.56 High High No N/A
Duduta (2020)25 Yes DEA 0.90 1.34 BL 1.16 BL ≥6.00 High High No Low
Zhao (2019)26 No DEA 6.50 ≈0.29 BL <0.25 BH ≈0.03 High High No Low
Ni (2015)27 No Pneumatic N/A ≈0.64 BL ≈0.64 BH ≥0.75 High High No
High
Liu (2020)29 No Pneumatic 0.45 ≈0.90 BL ≈0.80 BL ≥0.28 High High No
Low
Tolley (2014)30 No Chemical 510.00 7.50 BH 7.50 BH ≥0.03 Low Low Directional
jumping (3
directions)
High
Loepfe (2015)31 No Chemical 2100.00 2.78 BD 1.11 BD ≈4.50 Medium Low No High
Bartlett (2015)32 No Chemical Tethered: 478.60 Tethered: N/A Tethered: 2.35 m ≥2.45 High Low Directional
jumping (3
directions)
High
Untethered: 964.60 Untethered:
0.50 BL
Untethered:
6.00 BH
Churaman
(2011)33
No Chemical 0.314 ≈21.78 BL 80 mm ∞Low Low No Low
Li (2017)34 No Motor 250.00 2.57 BL 1.00 BH ≈10.00 Medium Low Steered jumping
(≈0.6°/s)
High
Mintchev
(2018)36
No Motor 37.00 ≈3.35 BD 2.86 BD ≈3.00 Medium Low No High
Wu (2019)37 No PVDF ≈0.06 ≈0.11 BL <0.25 BH <0.01 High High Steered jumping
(≈0.8°/s)
Low
This work No sEHBA 1.10 1.46 BL 7.68 BH ≈0.01 High High Single-body: No Low
Dual-body: steered
jumping (138.4°/s)
Notes: BL body length, BH body height, BD body diameter, N/A not available. Landing stability, straight line jumping, and unit cost were evaluated in three (high, medium, and low) levels. The following are the detailed level judgment criteria:
●Landing stability:
(1) High. After the robot lands, it does not roll and does not need artificial/self-righting before the next jumping.
(2) Medium. The robot is capable of self-righting. After landing, it rolls a distance and sometimes needs self-righting based on its posture.
(3) Low. The robot is not capable of self-righting. After landing, it rolls a distance and sometimes needs artificial-righting based on its posture.
●Straight line jumping capability:
(1) High. There is no need for artificial direction adjustment in continuous forward jumping process. Connecting several continuous landing points as a line, it is basically a straight line.
(2) Medium. The robot needs artificial direction adjustment in continuous forward jumping process. Connecting several continuous landing points as a line, it is basically a straight line.
(3) Low. The landing points have some randomness in continuous jumping process. Connecting several continuous landing points as a line, it is a curve.
●Unit cost:
We estimate the unit price based on the main material and component price (from a Chinese e-commerce website) of the robot.
(1) High. The unit price exceeds 10 RMB.
(2) Low. The unit price does bot exceeds 10 RMB.
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including slopes, wires, single steps, continuous steps, ring obstacles,
gravel mounds, and cubes of different shapes. The maximum height
of the robot can reach up to 18 mm (Figs. 5and 6, Supplementary
Movie 5, Supplementary Fig. 11 and Supplementary Movies 6 and 7).
The jumping performances of the LSJR rely on not only the
applied voltages but also the surface textures of various substrates
(Supplementary Fig. 10). Under the same applied voltage (10 kV,
4 Hz), the glass substrate with the smoothest surface provided the
lowest friction among all substrates, leading to a lower CFJS of
95.6 mm/s (1.47 body lengths per second) and a lower TS of
27.9°/s. This currently limits the application of the robot to
jumping on relatively smooth surfaces but can be mitigated if
electroadhesion is applied by adding additional passive electrodes
to the rear pouch.
The LSJR can be applied to detect and record environmental
changes such as temperature and ultra-violet light by attaching a
light and soft temperature sensor/paste and photochromic dyes
(Supplementary Fig. 15 and Supplementary Movie 9). Through
integrating other sensors, it is expected to detect more environ-
mental factors, such as pollutants in industrial environments and
civil buildings. In addition, future work may also include (1)
study of the scalability and parametric optimization of the sEHBA
to achieve better jumping performance, (2) development of an
untethered LSJR and its applications, and (3) investigation of
sEHBA’s other soft robotics applications such as wall-climbing
robots, swimming robots, and flapping wing robots.
Methods
Materials of the LSJR. The inextensible pouch shell was made by heat-sealing two
16-μm-thick BOPP films (Jiazhixing Co., China) and injected with air and a
dielectric liquid made of 25# mineral transformer oil (Aokelai Lubricants Co.,
China). BOPP has reasonably good dielectric breakdown strength (~700 V µm−1)
and tensile strength (~300 N mm−2)44. The dielectric liquid has favorable dielectric
properties and low viscosity45. The electrodes were screen printed on the BOPP
films using LN-GCI-3 graphene conductive inks (Jining Leadernano Tech., China).
The plastic ring frame was fabricated by laser cutting a 0.5-mm-thick PVC sheet
(Lizhiyuan Plastic Industry, China), which has good mechanical properties and low
density46. All materials are low in cost and easy to procure.
Fabrication procedure of the LSJR. The fabrication procedure of an LSJR involves
nine major steps (Supplementary Fig. 4). First, we screen printed conductive inks
onto BOPP films using a screen-printing machine (Mingming Screen-Printing
Equipment Co., China) (Supplementary Fig. 5). The electrodes were cured at room
temperature for 12 h, resulting in a flexible graphene electrode with a thickness of
20 µm. Second, we stacked two BOPP-electrode composite films with the electrodes
facing outwards and put them on a Teflon high-temperature cloth as a load-
dispersing layer. Third, the soldering iron was set to 200 °C to heat-seal the BOPP
films, creating two semicircular pouches (both 55 mm in diameter) and leaving two
fill ports in the seal of each pouch. Fourth, we filled the front pouch with the
dielectric liquid of 1 mL and the rear pouch with the same volume of air by using
two syringes. Fifth, we squeezed the air bubbles out of the front pouch and heat-
sealed the two fill ports to prevent fluid compression. Sixth, we lifted the four
corners of the top BOPP film in sequence and placed the laser-cut flexible PVC
ring frame (thickness of 0.5 mm, inner diameter of 58 mm, and outer diameter of
62 mm) between the two BOPP films. Seventh, we fixed the edge position of the
three-layer composite membrane and moved the soldering iron on the films to
deform the ring frame and heat-seal it following the rebound trajectory. In this
step, the prebending levels of the final LSJR can be controlled by moving different
distances (d). Eighth, we heat-sealed along the inside and outside circles of the
predeformed frame and removed the pushpins to rebound the frame to generate
prebending. Finally, excess BOPP film was cut away, and two aluminum tapes were
attached to the ends of electrodes to create a completed LSJR with a total body
weight of 1.1 g and a full body length of 65 mm.
Experimental control strategy of the LSJR. After electrical connections were
made to the LSJR, applying a high voltage to the LSJR for 10 ms enabled it to
complete a jump. In the single-jump tests, after it took-off, the aluminum pieces at
the tail detached from the copper electrodes fixed on the ground, thereby cutting
off the voltage. The voltage waveform was a square wave and the duty cycle was
1:6001, as shown in the top right inset of Fig. 2a. Voltage reversal and a wait time of
60 s were conducted to alleviate the residual charge issue. Different voltages caused
different jumping distances and JHs. In the continuous locomotion tests, the wires
were used for electrical connection instead of using a separable aluminum–copper
contact structure. The voltage waveform was a square wave and the duty cycle was
adjustable, as shown in Fig. 3e. The power-on time of the robot in each cycle was
10 ms. Different voltages and frequencies caused different continuous forward
jumping speeds. In the direction-adjusting tests, two LSJRs were abreast connected
and the voltage was selectively applied to one of them. The electrical connections
were made the same as in the continuous locomotion tests. The voltage waveform
was a square wave and the frequency was 4 Hz. The power-on time of the robot in
each cycle was 10 ms. Different voltages caused different turning speeds. In the
obstacle-crossing tests, the electrical connections were the same as those in the
continuous locomotion tests and direction-adjusting tests. The voltage waveform
was a square wave and the frequency was 4 Hz. The voltage was 10 kV and the
power-on time of the robot in each cycle is 10 ms.
Experimental set up of the LSJR. For single-jump tests, a high-speed camera
(2F01, Revealer, China) was used to capture the motions. For other low-speed tests,
a Nikon D3400 DSLR camera and an Apple iPhone XR were used to record the
movements. For substrate surface morphology characterization, a 3D Laser Scan-
ning Confocal Microscope (OLS4000, Olympus Corp., Japan) was used to measure
the areal surface texture. Adobe Premiere (version 7.0.0) and Adobe Photoshop
(version 19.1.4) were used to process the videos and to obtain the experimental
data. An EMCO high-voltage amplifier (E101CT, EMCO High Voltage Co., USA)
was used with two high-voltage relays (CRSTHV-14KV-A, CRST, China), con-
trolled by a DMAVR-128 board (Ningbo Xinchuang Electronic Technology Co.,
China), to energize the LSJR.
Data availability
The authors declare that data supporting the findings of this study are available within
the paper and its Supplementary Information files.
Received: 23 June 2021; Accepted: 10 November 2021;
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Acknowledgements
This work was supported by the National Key Research and Development Project of
China (grant no. 2020YFB1313000) and the National Natural Science Foundation of
China (grant nos. 52075051 and 51975070). J.G. wants to thank Prof. Jonathan Rossiter
for supporting this work whilst working at SoftLab Bristol, University of Bristol, under
grant EP/M020460/1. In addition, he wants to thank Prof. Jinsong Leng for the support
while working at HITSZ. We also thank Yi Sun and Thomas Bamber for the initial review
of the paper, and Wenbo Liu for the assistance in experiments.
Author contributions
R.C. conceived the research. R.C. and Z.Y. jointly designed and implemented the soft
electrohydrostatic bending actuator. J.G. refined the legless soft jumping robot concept,
and proposed the robot design rationale and refined paper novelty clarifications. Z.Y. and
X.Z. conducted the structural design, device manufacturing and experiments. Z.Y., R.C.,
L.B. and X.Z. analyzed and interpreted the results. Z.Y. drafted the manuscript. Z.Y., X.Z.
and J.G. designed and optimized the figures, tables, and videos. Z.Y., J.G., L.W. and Y.S.
wrote the abstract, introduction, and discussion part, and fully revised the whole
manuscript. L.B., F.L., H.P., L.X., Y.P. and J.L. reviewed and commented on the paper.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41467-021-27265-w.
Correspondence and requests for materials should be addressed to Rui Chen or Huayan
Pu.
Peer review information Nature Communications thanks Manolo Garabini and Cecilia
Laschi for their contribution to the peer review of this work. Peer reviewer reports are
available.
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