SOFT ROBOTICS
Volume 00, Number 00, 2023
Mary Ann Liebert, Inc.
DOI: 10.1089/soro.2023.0030

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Spikebot: A Multigait Tensegrity Robot with Linearly
Extending Struts
Jinwook Jeong,1 Injoong Kim,1 Yunyeong Choi,1 Seonghyeon Lim,1 Seungkyu Kim,1 Hyeongwoo Kang,1Dylan Shah,2 Robert Baines,2 Joran W. Booth,2 Rebecca Kramer-Bottiglio,2 and Sang Yup Kim1

Abstract

Numerous recent research efforts have leveraged networks of rigid struts and flexible cables, called tensegrity
structures, to create highly resilient and packable mobile robots. However, the locomotion of existing tensegrity
robots is limited in terms of both speed and number of distinct locomotion modes, restricting the environmentsthat a robot is capable of exploring. In this study, we present a tensegrity robot inspired by the volumetric
expansion of Tetraodontidae. The robot, referred to herein as Spikebot, employs pneumatically actuated rigid
struts to expand its global structure and produce diverse gaits. Spikebot is composed of linear actuators thatdually serve as rigid struts linked by elastic cables for stability. The linearly actuating struts can selectively
protrude to initiate thrust- and instability-driven locomotion primitives. Such motion primitives allow Spikebot
to reliably locomote, achieving rolling, lifting, and jumping. To highlight Spikebot’s potential for robotic
exploration, we demonstrate how it achieves multi-dimensional locomotion over varied terrestrial conditions.
Keywords: tensegrity, soft robotics, puffer fish, pneumatic actuation, multigait

One particularly interesting class of structures, namely
tensegrities that consist of rigid struts and compliant cables,
has been shown to be the optimally lightweight structure
under compressive loads,10 leading researchers to develop a
new field of tensegrity robotics.11–13
Most tensegrity robots to date have adopted a six-strut
topology with a roughly spherical shape, known as Jessen’s
icosahedron, and exhibit a controlled rolling locomotion byshifting the center of gravity14–16 outside of the polygon ofstability. The center of gravity of icosahedron tensegrity

Introduction

By combining the benefits of rigid and soft components, biological systems dynamically change theirstiffness and gait, allowing them to easily navigate complex
environments. Taking cues from systems as varied as thehuman musculoskeletal system to the carapace-plastronstructure of turtles,1–4 engineers have begun creating hybrid
systems that combine the benefits of soft and rigid systems tocreate efficient and lightweight robots.5–9
1
2

Department of Mechanical Engineering, Sogang University, Seoul, Republic of Korea.
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut, USA.

 Jinwook Jeong et al. 2023; Published by Mary Ann Liebert, Inc. This Open Access article is distributed under the terms of the Creative
Commons License [CC-BY] (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly cited.

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robots has previously been achieved by modifying tensile
forces of cables,17–19 adjusting the length of the struts,20,21 or
inflating membranes that constitute faces of the polyhedron.22,23
For example, earlier versions of tensegrity robots utilize
motors attached to the end of their struts to control cabletensions,18,19 allowing the robot to be geometrically unstable
and roll. Subsequent studies have expanded the motion
primitives of tensegrity robots to vibration,24,25 flying,26,27
and shape memory.28–30
However, such motion primitives have limited the speed
and efficiency of tensegrity robots, because the deformationof the overall shape often consumes more energy than what isneeded for locomotion. In addition, the deformation of theinternal cavity reduces the robots’ payload-carrying capabilities.
To achieve higher locomotion speeds, several studies reported jumping locomotion using additional bulky actuators,26,31 allowing potential gains in overall mission energy
efficiency and speed. Yet, as demonstrated to date, jumping
tensegrity motions tend to be unstable and suffer from low
repeatability.
A key feature of tensegrity robots is their rigid struts. Since
the struts provide ample space to implement conventional
actuation mechanisms, a tensegrity may be equipped withlinear actuators to unlock a novel locomotion mode. Up tonow, the actuation of struts has only been exploited to induce
structural deformation of tensegrity robots. Consequently,
tensegrity robots have been unable to fully utilize actuation

JEONG ET AL.

originating from their struts15 and seamlessly implement
other types of conventional actuators.
To overcome these limitations and create a tensegrity capable of multiple repeatable locomotion modes, we present a
new motion primitive for tensegrity robots that is decoupledfrom structural deformation. Inspired by the Tetraodontidae,
which takes in external fluid to realize the rapid volumetric
expansion of a globe,32 we propose a tensegrity robot (furthermore referred to as Spikebot) that can extend its rods outof its nominally convex hull while retaining its original internal shape. Node-originated extension of rods creates asimilar effect to volumetric expansion of the tensegrity,
serving as an effective and efficient locomotion primitive.
The new locomotion primitives attained by Spikebot solve
notable challenges of deformation-based tensegrity robots,by enabling rapid rolling and jumping behaviors. Spikebot iscapable of selectively actuating each strut at high velocity toelicit several locomotion gaits. We characterize the stability
and controllability of each locomotion gait, and showcase theutility of Spikebot as a mobile robot over several terrestrial
conditions, including inclines and obstacles.
Design and Manufacture
Tetraodontidae-inspired design of tensegrity

Spikebot mimics the fluid-driven volumetric expansion33–35 of a Tetraodontidae, as shown in Figure 1. The

FIG. 1. Overview of a multigait tensegrity robot referred to herein as Spikebot, inspired by the volumetric expansion of
Tetraodontidae. (a) The working principle behind the volumetric expansion of Tetraodontidae and Spikebot, respectively.
Spikebot utilizes the linear extension of each strut to realize spatial expansion similar to that of Tetraodontidae. (b)Schematic of the multi-mode locomotion of Spikebot capable of in-plane (x–y direction) rolling and out-of-plane (zdirection) jumping motions.

TENSEGRITY ROBOTICS

Tetraodontidae intakes fluid to rapidly and efficiently morph
its body shape. Likewise, Spikebot increases its bounding
volume by extending its pneumatically-actuated struts(Fig. 1a). By utilizing independently controlled linear actuators, we locally distribute changes in bounding volume to
impart diverse locomotion modes, such as rolling andjumping (Fig. 1b).
Manufacture and control of Spikebot

Figure 2 showcases the overview of Spikebot, which employs a Jessen’s icosahedron-shaped tensegrity structure thatconsists of 6 struts and 24 cables. To manufacture Spikebot,
pneumatic linear cylinder actuators with 45 mm stroke(MC10 by SYM, Korea) are purchased and connected tosolenoid valves (KS320s by KCC Ltd., Korea) via pneumatic
tubes of 2 mm in diameter. A strut is prepared by connecting
two of the pneumatic cylindrical actuators with a polylactic
acid (PLA) coupler, and a PLA cable holder secures eachcable with the same angle and length (Fig. 2a). The struts areconnected by elastic cables to uphold the three-dimensional

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structure, and therefore, the linear extension of the struts
results in the spatial expansion of the robot.
A 16-channel relay module (SZH-RLBG-052, by SMG-A,
China) is used to control the total of 12 linear actuators within
Spikebot (Supplementary Fig. S1), and a compressor(OFS600-8, by Compworld, Korea) is used to generate andcontrol the pneumatic pressure to operate each actuator. In
addition, a microprocessor (Arduino Uno) is used to control
the relay module and the actuators by serial communication.
This control circuit allows for selective actuation of the struts
for both their extension and retraction motion and speed(Fig. 2b; Supplementary Fig. S2).

Geometrical characteristics of Spikebot

Spikebot has 20 faces, each characterized either as a closed
face (cables connected at all corners) or as an open face(cables connected at two corners), as shown in Figure 3. As
Spikebot locomotes, the base plane (the plane in contact withthe ground) shifts between each of these 20 faces.

FIG. 2. The overall structure of Spikebot and the selective actuation of its struts. (a) Spikebot consists of 24 elastic cables
and 6 rigid struts with two independent linear pneumatic actuators that can each extend a rod to enable motion. (b)Representative actuation states of Spikebot, including the fully retracted (left) and fully extended states (middle), along withselectively extending a single actuator (right).

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JEONG ET AL.

FIG. 3. Geometrical characteristics of Spikebot and two distinct types of the face that can serve as the base plane. (a)Spikebot is constituted of 20 faces that are shaped as either closed faces (cables connected at all corners) or open faces(cables connected at two corners). The dimension of each face type is determined by the length of the struts l and the
distance between two parallel struts d. A strut can be extended by the length e, at the node of the base plane (the face incontact with the ground), to create the thrust necessary for the locomotion. (b) Two different base plane types (closed face
vs. open face) and the comparison of thrusts in a direction normal to the ground In. When the open face serves as the baseplane, the ground-normal thrusts In varies depending on the actuation node (In1 6¼ In2 ¼ In3 ), that is different from the case of
closed face (In1 ¼ In2 ¼ In3 ).

The geometrical characteristics of Spikebot can be quantified from the length of the struts l, the distance between twoparallel struts d, and the extension length of the strut e(Fig. 3a). The strut is usually extended from a node of thebase plane to create the thrust necessary to roll Spikebot in the
opposite direction of the extension.
Depending on whether the base plane is a closed face or an
open face, the robot’s thrust may induce different types of
motion. In detail, as shown in Figure 3b, the closed face isshaped as an equilateral triangle and the thrusts normal to theground In are identical from all three nodes. On the other
hand, the open face is nominally an isosceles triangle, giving
rise to two distinct amplitudes of the ground-normal thrust In
from its nodes (Supplementary Fig. S3).
Such unique geometry of base planes determines the motion primitive as well as the controllability of Spikebot,
thereby allowing the control strategy of Spikebot to beadapted on the fly.
Results and Discussion

Spikebot can engage in diverse types of locomotion bymodulating the sequence and/or speed of strut extensions. In
this study, we showcase and mathematically model threedifferent types of locomotion: thrust-induced rolling, instabilityinduced rolling, and thrust-induced jumping (Fig. 4). Spikebot
readily combines these locomotion modes, demonstrating versatility as a mobile robot in several environments.

Thrust-induced rolling

Actuation of a strut from the base plane creates thrustsufficient to roll Spikebot about its center of gravity (Fig. 5).
This thrust-induced rolling motion is different from widespread rolling mechanisms of tensegrity robots that harness
structural instabilities. Namely, since Spikebot’s thrustinduced rolling is governed by the force induced from extending struts to impact the ground, Spikebot maintains its
structural stability and can therefore fully utilize its internal
space for payloads. Such structural stability during locomotion also benefits its ability to withstand external collision byelastic tension cables absorbing the impact energy.
Moreover, since the speed and stroke of each strut can beselectively controlled, Spikebot diversifies and unlocks therolling locomotion of tensegrity robots. In detail, Spikebot
can execute rolling motion regardless of its base plane types(closed face vs. open face). In general, icosahedron-shaped
tensegrity robots have been known for three rolling types
depending on their initial base plane and final base plane after
a rolling motion: closed base-to-open base (CO step), open
base-to-closed base (OC step), or open base-to-open base
(OO step).
Among these three steps, CO steps are particularly difficultfor icosahedron tensegrity robots to accomplish by structuraldeformation because the closed-base planes are highly stable
attributed to their equilateral triangle shape. However, as
shown in Figure 5a, Spikebot is capable of realizing all threesteps, including the CO step, because the extending strut

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FIG. 4. Multi-mode locomotion that Spikebot can execute. Spikebot is capable of three types of locomotion: thrustinduced rolling (top), instability-induced rolling (middle), and thrust-induced jumping (bottom). Thrust-induced rolling isachieved by an extending strut pushing it along a desired direction. Instability-induced rolling is realized as one or two struts
retract from the fully extended initial state, allowing the robot to passively tip toward the retracted actuator. Finally, thrustinduced jumping is a result of rapidly extending several actuators, propelling the robot off the ground in a desired direction.

creates sufficient thrust to overcome the structural stability
granted from the closed base plane.
Pressure applied to extending strut is an important control
factor to achieve reliable rolling motion. Figure 5b depicts
the outcome prevalence rate of the thrust-induced rollingwith respect to the pressure applied to the extending strut thatis directly related to the extension speed (Supplementary
Fig. S2). Each rotation step is accomplished by extending asingle strut located opposite side in the direction of rolling,
and the successful rolling case is defined as when the baseplane of Spikebot is switched to the adjunct face. Similarly,
the excessive rolling case and the unsuccessful rolling caseare defined when the base plane is switched more than once
and when the base plane is unchanged, respectively.

The experimental results reveal that the rolling efficiency
of Spikebot varies with the rolling types, and CO step is themost reliable among the total three rolling types with the
maximum outcome prevalence rate of >95%. The effect of
the inlet pressure on achieving the CO step is less notable
than OC step and OO step.
On the other hand, both OC step and OO step arehighly dependent on the inlet pressure, with each type ofrolling still having a range of optimal inlet pressures that canachieve outcome prevalence rate >90%. So, by modulating
the inlet pressure according to the initial base plane andthe rolling direction, the thrust-induced rolling of Spikebot
can be subsequently executed to realize continuous rolling
motion.

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JEONG ET AL.

FIG. 5. Characteristics of the thrust-induced rolling of Spikebot. (a) Timelapse image of Spikebot executing a rolling
locomotion by extending a strut. The rolling is referred to as ‘‘CO step’’ since the robot starts on a closed face (depicted as a
red triangle) and rolls to an open face (depicted as a yellow triangle). (b) The three canonical rolling motions (CO step, OC
step, and OO step) and their success rate as a function of actuator pressure. The actuator pressure governs the speed ofextending struts, and the resulting success rate is highly dependent on the types of rolling motion.

Instability-induced rolling

Spikebot can additionally realize rolling motion by harnessing geometrical instability (Fig. 6). The instability can be
induced from the initial fully actuated state of Spikebot—
where all struts on the base plane are extended outward—byretracting one strut (Fig. 6a). As a result of the strut retraction,
Spikebot rotates about the remaining two extended struts andeventually impacts the ground with sufficient momentum toroll to the adjacent face.
Figure 6b depicts the change of the base plane (from DABC
to DABC¢) and the resultant shift of the center of mass (c:o:m)within the base plane (from D1 to D2). Because Spikebot is
skewed in contact with the re-established base plane DABC¢,the location of its c:o:m within the base plane D2 is notably
shifted toward the edge, thereby spurring the subsequentrolling motion.
Compared with thrust-induced rolling, instability-induced
rolling is advantageous because the motion is independent of
the actuation force (i.e., pressure). In detail, the instability isgained from reshaping the orientation and area of the baseplane, demanding no actuation force afterward, ultimately
resulting in an energy-efficient rolling motion. However, theinstability-rolling of Spikebot is limited in its versatility because the rolling motion is only achieved when the base plane
is on the open face.
The success rate of the instability-induced rolling marks
100% with the open face as the base plane, but on the other
hand, Spikebot is lack of creating enough momentum to rollwhen the closed face serves as the base plane. Figure 6c illustrates the shift of c:o:m, in response to the instability,
where the shifting length D1 D2 directly scales with the momentum granted to Spikebot after the initial rotational motion.
Since the shifting length D1 D2 is a function of the distance
between two parallel struts d and the extension length of thestrut e (Supplementary Fig. S4), we note that more pronounced rolling can be achieved by increasing the ratio e=d.
Thrust-induced jumping

When two or more actuators are extended from the baseplane, the resultant thrust is sufficient to cause Spikebot tojump, as shown in Figure 7. Thrust-induced jumping produces horizontal H and vertical V displacement components,

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FIG. 6. Overview of the instability-induced rolling of Spikebot. (a) Timelapse image of Spikebot rolling from the baseplane of fully extended struts. Retracting a previously extended strut gives rise to the rolling motion from an open face(emphasized by a yellow triangle superimposed on the image) to a closed face (emphasized with a red triangle). (b)Schematic of the locomotion principle that entails the augmentation of the base plane and shift of the center of mass (fromD1 to D2) with respect to the base plane. (c) Illustration of the base plane that shows the shift of c:o:m in response to the strut
retraction. The c:o:m shift (D1 D2 ) becomes apparent with increasing extension length e and decreasing strut distance d(Supplementary Fig. 4), thereby creating pronounced rolling motion.
yet the base plane remains unchanged (Fig. 7a). In this study,
Spikebot’s jumping is examined only when an open face isserving as the base plane.
In the case of jumping with a closed face as the base plane,
the V component is negligible compared with that when an
open face serves as the base plane. Such difference injumping ability is presumably due to a lower ground-normal
thrust In created from the base plane when a closed face is incontact with the ground (Supplementary Fig. S4).
With an open face serving as the base plane, the jumping
motion of Spikebot can be achieved with various strut configurations. The strut configurations are determined bywhether each strut is retracted or extended at the initial state
before jumping, and we examine three types of strut configurations in this study (Fig. 7b).
Type 1 jumping is executed by simultaneously extending
all struts on the ground, and Type 2 jumping is controlled byextending only two struts while the other strut remains retracted. Type 3 jumping is similar to Type 2 jumping, but thepreviously retracted strut remains extended. Such variationsof strut configuration are designed to control the jumping
characteristics of Spikebot with a focus on its horizontal H
and vertical V displacement.
Figure 7c summarizes jumping characteristics of Spikebot
with the actuation schemes cited earlier. Both V and H
components are measured for five independent jumps withincreasing inlet pressure that directly scales with the thrustfor jumping. In general, the higher the thrust, the greater thevalue of both components.
However, the Type 1 jumping scheme reveals that the H
component can be reduced with increasing thrust, presumably because of the rod in the vertex that creates thrust in the
opposite direction. In detail, above a certain pressure
threshold, the front extending strut in the locomotion direction pushes off the ground, inducing a moment that raises thefront of SpikeBot.
As a result, the thrust produced from the rear extending
struts primarily contains a vertical component, rather than ahorizontal component, thereby reducing H and increasing V.
Such hindrance of H translation is mitigated in the Types 2
and 3 jumping schemes. Likewise, Spikebot’s ability totranslate in both V and H direction expands the locomotion
space of the tensegrity robot to three dimensions, enhancing
the capability of Spikebot as a mobile robot.
Demonstrations

Spikebot is adaptable to various environments because it
can modulate between diverse locomotion modes, maintaining mobility in various situations. We showcase the consistent mobility of Spikebot as it overcomes several obstacles
in controlled settings (Fig. 8; Supplementary Movie S1).

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FIG. 7. Characteristics of the thrust-induced jumping of Spikebot. (a) Timelapse image of Spikebot that jumps in vertical(V) and horizontal directions (H). The base plane is retained as an open face. (b) Illustration of three different types ofjumping motion, initiated from different strut configurations. (c) Travel distance in vertical and horizontal directions
obtained from each jumping locomotion as a function of actuator pressure. Increased pressure leads to larger displacements,
although the benefit depended strongly on the jumping type. The error bars indicate the standard deviation of six trials.

Figure 8a reveals that Spikebot rolls in two-dimensional
space by repetition of thrust-induced rolling.
Each rolling motion is rapid and achieved with 100%
success rate, demonstrating Spikebot’s better ability to explore a large area of exploration than the conventional tensegrity robot (Supplementary Fig. S5). Moreover, since theexcessive rolling mechanism can increase the locomotion
speed while the instability-induced rolling can serve as another locomotion principle, Spikebot is expected to enhancethe efficiency of two-dimensional locomotion by the combination of diverse thrust- and instability-induced rolling
motions.

We also demonstrate Spikebot’s ability to traverse an inclined slope, which has been a challenging task for several
deformation-driven tensegrity robots. Figure 8b shows theinclined rolling of Spikebot against a slope of 8 by utilizing
thrust-induced rolling.
Such inclined locomotion is difficult to realize by
instability-induced rolling because the inclined base plane
reduces the shift of c.o.m. during actuation, but thrustinduced jumping shows comparable performance with thrustinduced incline rolling. Increasing the extension speed ofstruts is expected to assist Spikebot in locomoting higher
angle slopes with the enhanced impact energy.

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9FIG. 8. Demonstration of Spikebot locomoting various environments. (a) Spikebot maneuvering over flat ground in bothx- and y-directions. Left: top-down view of the experiment. Right: The path traced by Spikebot’s center of gravity during the
locomotion sequence, along with annotations emphasizing which face was in contact with the ground during periods ofrelative equilibrium. (b) Inclined locomotion of Spikebot achieved from the thrust-induced rolling of ‘‘OC step.’’ Such
incline motion can be also realized by thrust-induced jumping. (c) Spikebot that overcomes an obstacle through a couple ofthrust-induced jumping motions. Combinations of in-plane locomotion and jumping are expected to unlock the locomotion
space of Spikebot, spurring its utility as a mobile robot.
Lastly, we examine the effectiveness of three-dimensional
space locomotion of Spikebot. Figure 8c shows that Spikebot
can leap over an obstacle along its locomotion path via thrustinduced jumping. As the locomotion principle of thrustinduced rolling suggested (Fig. 7c), the jumping motion
simultaneously creates both vertical and horizontal locomotion and allows Spikebot to leap over an object.
Such locomotion in three-dimensional space is expected to
upscale the practical utility of Spikebot, which can overcome
irregular shapes and obstacles of terrain. In sum, robotic demonstrations herein suggest that Spikebot can be a viable robot to
explore diverse terrestrial environments because of its diverse
locomotion modes that complement current tensegrity robots.
Conclusions

Inspired by Tetraodontidae, we have herein presented
Spikebot, a tensegrity robot that is capable of selectively
actuating each strut to spatially expand, locomoting in threedimensional space by rolling and jumping. Three different
motion primitives are investigated, and their combination allows increased options for path finding and subsequent realization of efficient and dynamic navigation over varied terrain.
Such path-finding ability is expected to unlock the functionality of the robot in exploring unmanned space and severe

environments. One of the noteworthy benefits of Spikebot is
its ability to maintain an unaltered internal space, by expanding solely on the external side. This unique characteristic
creates a stable and protected internal payload volume during
operation, for carrying scientific payloads or navigation
sensors, for example.
We demonstrate SpikeBot’s ability to explore multidimensional space in several controlled settings with varied
terrain. In future work, we plan to increase Spikebot’s utility
as a field robot by implementing an untethered actuation
system. We surmise the realization of an untethered actuation
system could be accomplished by replacing pneumatic linear
actuators with battery-powered actuators paired with a bistable mechanism capable of rapidly releasing stored elastic
energy.
In addition, field compatibility should be tested by deploying the robot with sample payloads, under several dynamic deployment strategies (e.g., mid-air discharge). In allcases, we contend that the design and motion primitives of
Spikebot covered herein will facilitate the practical use oftensegrity robots on the field.
Author Disclosure Statement

The authors have no competing interests to declare.

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JEONG ET AL.

Funding Information

This work is supported by the National Research Foundation of Korea (Grant No.: 2021R1F1A1056999 and RS-202300218379) and Sogang University (Grant No.: 202110009).
Supplementary Material

Supplementary Figure S1
Supplementary Figure S2
Supplementary Figure S3
Supplementary Figure S4
Supplementary Figure S5
Supplementary Movie S1
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Address correspondence to:Sang Yup Kim
Department of Mechanical Engineering
Sogang University
Seoul 04107
Republic of Korea
E-mail: sangyupkim@sogang.ac.kr