SOFT ROBOTICS
Volume 00, Number 00, 2021
ª Mary Ann Liebert, Inc.
DOI: 10.1089/soro.2020.0170

Tensegrity Robotics

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Dylan S. Shah,1,*,i Joran W. Booth,1,*,ii Robert L. Baines,1 Kun Wang,2 Massimo Vespignani,3Kostas Bekris,2 and Rebecca Kramer-Bottiglio1

Abstract

Numerous recent advances in robotics have been inspired by the biological principle of tensile integrity—or‘‘tensegrity’’—to achieve remarkable feats of dexterity and resilience. Tensegrity robots contain compliant
networks of rigid struts and soft cables, allowing them to change their shape by adjusting their internal tension.
Local rigidity along the struts provides support to carry electronics and scientific payloads, while global
compliance enabled by the flexible interconnections of struts and cables allows a tensegrity to distribute impacts
and prevent damage. Numerous techniques have been proposed for designing and simulating tensegrity robots,
giving rise to a wide range of locomotion modes, including rolling, vibrating, hopping, and crawling. In thisstudy, we review progress in the burgeoning field of tensegrity robotics, highlighting several emerging challenges, including automated design, state sensing, and kinodynamic motion planning.
Keywords: tensegrity, robotics, soft robotics, resilient robots
Numerous tensegrity robots have been proposed that utilize a wide range of mechanical designs, locomotion modes,
and sensing modalities. For example, some tensegrity robots
can adjust the length of either their struts15 or cables,16,17 tochange their resting shape and induce motion by shifting theircenter of mass. Others harness thrust generated by jetpacks,18 vibration,19 or propellers.20 Tensegrity robots often
exhibit passive compliance, allowing their structure to absorb
energy, while providing robustness to damage and pressure.21
Passive deformation may also be exploited to absorb impacts
from unintended falls or extraterrestrial landing (Fig. 1C).16
In this review, we survey recent progress and highlight
grand challenges for the field of tensegrity robotic locomotion. Although we separate key concepts for organizational
clarity, we would like to simultaneously convey the interdisciplinary nature of this field, by discussing interactions
between the relevant fields of study. We begin by discussing
the mechanical design of tensegrity robots and then overview
existing locomotion methods, sensing techniques, and approaches for control and motion planning. While there havebeen great advancements in each area thus far, fundamental

IntroductionT

ensegrities are composed of rigid compressive elements (struts) and flexible tensile elements (cables),connected to create a compliant yet stable network (Fig. 1).1
The inclusion of rigid components and the overall low stiffness (or high ‘‘softness’’2) of the structure endows tensegrities with desirable properties found in both classically‘‘rigid’’ and ‘‘soft’’ robots. Tensegrities have served to inspire art, model biological structures like the human skeleton,
and to provide designs for lightweight and strong architecture.3–5 In fact, tensegrities can form the minimal-massstructure required to sustain a given compressive6 or bending7 load, exhibiting great potential for use as lightweight
deployable satellites and other structures.8 Tensegrities haveeven been explored for use as robotic grippers,9 manipulators,10 and shoulder joints for manipulator arms.11 While thescope of the tensegrity literature is vast, in this review, we
focus on locomoting tensegrity robots. We refer to other reviews, when applicable, for further details on nonlocomoting
tensegrities.1,3–5,12–14

1

School of Engineering and Applied Science, Yale University, New Haven, Connecticut, USA.
Computer Science Department, Rutgers University, Piscataway, New Jersey, USA.
3
KBR Wyle Services, Llc, NASA Ames Research Center, Moffett Field, California, USA.
*These authors contributed equally.
i
ORCID ID (https://orcid.org/0000-0003-3943-6170).
ii
ORCID ID (https://orcid.org/0000-0002-7380-3416).
2

1

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2

SHAH ET AL.

FIG. 1. Tensegrity concepts wereoriginally applied to create (A) artwork3 and (B) lightweight architectural structures.4 (C) Recently,
roboticists have built tensegrity robots that can withstand significant
impacts, such as falling from theroof of a building.16 Labels 6 and 7
point to nodes 6 and 7, respectively,
to help visualize the spinning trajectory followed by the tensegrity as
it fell from the roof of a building.
Color images are available online.

challenges remain, ranging from automated codesign ofsensors, actuators, and the underlying mechanical structures;
improved sensors and algorithms for state estimation; andreal-time path planning algorithms. As research progresses,
we expect tensegrity robots to achieve unprecedented mobility in extreme environments.
Structural Design

There are myriad ways to connect compressive and tensile
elements to create tensegrity structures.1 Various materials
could be used for the compressive and tensile elements,
depending on the desired balance between competing design objectives (cost, strength, weight, etc.). Fortunately,
there are numerous tools to aid in the structural design oftensegrities, including analytic frameworks22 and robot
simulators.23,24 In this study, we summarize the design oftensegrity structures, that is, the selection and placement of
struts and cables.
In the taxonomy delineated by Skelton, tensegrities can beclassified by the number of rigid bodies in contact.6 For example, class 1 tensegrities such as the six-bar icosahedronthat forms the structural basis of numerous tensegrity robots16,21,23,25,26 (Fig. 2A) have only one rigid body contacting each node; no two struts are fixed in contact (however,they could incidentally contact during normal motions).
Class 4 ‘‘t-bar’’ tensegrities (resembling the kites built by
Snelson,3 but pinned at the two struts’ intersection) havefour struts connecting at a single node and are proven as
the minimal mass structures for compressive loadingDownloaded by YALE UNIVERSITY from www.liebertpub.com at 11/07/21. For personal use only.

TENSEGRITY ROBOTICS

3

FIG. 2. Many methods exist for designing tensegrity robots, using combinations of automated tools and designer intuition.
(A) Hand-designed six-bar icosahedron with graphite composite tubes and passive helical springs.21 (B) Hand-designed
three-bar crawling tensegrity structure.29 (C) evolutionary algorithms can operate on an abstract connectivity graph togenerate novel tensegrity designs of varying size and numbers of struts and cables.30 Additive manufacturing and rubberbands were used to physically realize the designs. (D) Modular elastic prototyping nets for quickly manufacturing the cables
for a tensegrity.31 Left: assembly process. Starting with a modular lattice (i), rods are sequentially added (ii–v), to create anequilibrium icosahedron shape. Right: additional manufactured structures, including a spine robot (top) and a cube-likeshape (bottom). (E) Direct encoding of cable and strut lengths, in addition to connectivity, can be paired with evolutionary
algorithms to generate tensegrity designs.32 Color images are available online.
conditions,6 suggesting that further developing techniques
for automated design of tensegrity structures could lead tomechanically optimal robots. Although most tensegrities arecomposed of a single base topology, some tensegrities havenested hierarchies of fundamental strut-cable arrangements6
or a base pattern repeated serially.27 In addition, researchers
have recently proposed changing the stiffness of tensegrities
on-demand by switching between a class 1 and a class 2
topology, highlighting the key role that topology plays inperformance, even with the same set of parts.28
Since each member in a tensegrity primarily only experiences tension or compression, designers often treat the tensegrity as a simple truss.1 Mechanically, this simplification
allows for a high degree of controllability, reliability, andtunability. The truss model also allows for the developmentof analytic models of deformation, alleviating the need for amore complex finite-element simulation. Many methods
have been proposed for form-finding (finding the rest configurations) of tensegrities (as reviewed by Tibert and Pellegrino,22 and Juan and Tur,13) and analyzing their dynamic
properties.12 Importantly, the stiffness of the overall tensegrity structure can be adjusted by increasing the prestress(or resting tension) in the tensile elements.

To reduce prototyping cost and time, tensegrity topologies
can be designed in an autonomous or semiautonomous
manner in a robot simulator. For example, Paul et al. used
evolutionary algorithms (EAs) to specify the number and sizeof rods in addition to the inter-rod connections (Fig. 2B, E).32
To further generalize the design process, Rieffel et al. designed an EA to generate graphs that represent the connectivity of tensegrities and allowed the simulator to determine
the resting shape (Fig. 2C).30 In these examples of EAs intensegrity design, the simulation environments and searchalgorithms were formulated to ensure that generated tensegrity structures could be manufactured. However, there is
not a generalized framework for determining if or how simulated solutions will transfer to functional robotic hardware.
Promisingly, Zheng et al. recently proposed a robustness
metric for estimating the likelihood of achieving sim-to-realtransfer for tensegrity designs.33
Tensegrity hardware design is often achieved through a
combination of human intuition and mechanical models(Fig. 2A, B).21,29 Once a topology has been selected, actuatorand sensor placement is often decided heuristically, which
can lead to inefficient or redundant designs. Fortunately,
several researchers have proposed iterative methods forDownloaded by YALE UNIVERSITY from www.liebertpub.com at 11/07/21. For personal use only.

4choosing where to place sensors and actuators within the
networks of cables and struts, in an effort to balance thecompeting requirements of low cost and high performance.34–36 Many materials for struts and cables have been
used, including metal and fishing line (Fig. 2B),27,29 aluminum and paracord,16 graphite composite tubes and passive
helical springs (Fig. 2A),21 and acrylic pipes paired withrubber bands.37 The stiffness of the tensegrity can even bechanged to some degree through the use of prestress in thecables and adjusted in an application-specific manner to improve robot performance. For instance, a tensegrity-inspired
fish robot used prestretched cables to stiffen its body and improve its swimming speed.38 Researchers have even begun
exploring the use of variable-stiffness materials and mechanisms39 in tensegrities, allowing robots to change the bendingor tensile stiffness of their members and thereby modify theirdynamics. For example, Zappetti et al. used a low-melting
point alloy to change the stiffness of a stationary three-bar
tensegrity,40 while Friesen et al. controlled the stiffness of theirtensegrity-inspired arm by adjusting its cable tension.11
Connecting the cables and struts in a tensegrity isstraightforward for simple structures such as a three-bar
prism, but quickly becomes complicated. For example, thecanonical six-bar icosahedron tensegrity truss has 24 cables
that need to be attached. During assembly, the cables’ natural
tension makes the structure deform into shapes that are difficult to work with. To simplify assembly, one group proposed modular lattices that reduce assembly time from hours
to minutes for moderately-complex designs (Fig. 2D).31
Zappetti et al. proposed a three-dimensional (3D) printed
lattice structure that was used to make icosahedron modules,41 while Lee et al. simultaneously 3D printed polylactic
acid (PLA) struts alongside a dissolvable mold that was later
filled with silicone to make the tensile cables.42 Other researchers have proposed 3D printing tensegrities and thenreplacing some printed connections with cables, although thistechnique has not been used to create locomoting tensegrity
robots.30 Additional design considerations for selecting tensegrity hardware include impact resilience,16 cost,35 andmodularity.19
Simulation

Many studies have used simulation to generate and evaluate designs of and control policies for tensegrity robots.
There are three main families of simulation tools used in thiscontext: (1) the more traditional physics engines, which are
based on first-principles, analytical models, and numericalapproximations; (2) analytical formulations, which solve
systems of differential equations that represent the dynamics
of a tensegrity structure; and (3) the emerging family ofdifferentiable physics engines, which aim to learn a physicalmodel directly from data. In this section, we introduce popular physics engines, discuss several tensegrity robot simulators, and describe the newer differentiable simulators. A
high-level comparison of several popular simulators is shownin Table 1. More detailed descriptions of each simulator arepresented throughout this section.
Simulators based upon traditional physics engines use firstprinciples from physics to predict the future motions of objects. Since tensegrity assemblies are composed of rigid struts
and compliant cables, tensegrity simulators usually include a

SHAH ET AL.

collision detector and both rigid body and soft body dynamics
components. Rigid body physics engines, such as the popularbullet248 and Open Dynamics Engine (ODE),49 can efficiently calculate rigid-body motions in parallel. Soft-body
physics engines implement various solution methods, ranging from the bounding box-based bullet348 to finite element
method (FEM)-based Vega-FEM50 and simulation open
framework architecture (SOFA).51 These engines can accurately model deformable objects, making them an ideal
choice to model soft bodies such as tensegrity cables, skins,
and strut endcaps.
The soft and compliant properties of tensegrities can be
simulated by extending or combining different physics engines(such as ODE, MuJoCo,52 or bullet2). For instance, the earlytensegrity simulation environment by Paul et al.29 was built
upon ODE and supports cables as virtual objects that aremassless, volumeless, and do not have any contact characteristics. More recent work by Wang et al.53 built a tensegrity
robot over the MuJoCo physics engine.52 Both Caliper43 andthe open-source NASA Tensegrity Robotics Toolkit (NTRT)24
extend bullet2 with support for compliant cables. NTRT provides relatively comprehensive support for tensegrity robot
modeling and has consequently become the most popular
choice for the development of gaits in simulation.
Starting from analytical formulations of the statics anddynamics of a tensegrity structure, several researchers haveachieved higher level tasks such as topology optimizationand controller design.54,55 These analytical models makesimplifications, such as treating the struts as cylinders, preventing rotation along the axis of the struts, ignoring endcaps,
and assuming that there are no collisions between cables. For
instance, TensegrityMATLABObjects (TMO)44 is a Matlabbased tensegrity simulator, which supports strut-groundcollision and friction-less contact. Software for Tensegrity
Dynamics (STEDY)45 and Modeling of Tensegrity Structures (MOTES)46 are Matlab-based comprehensive tools thatuse nonminimal Cartesian coordinates to describe the dynamics of the system. VirtualTensegrities56 is a Java-based
simulator that can visualize multiple tensegrity structures yet
neglects collisions.
As an example of how multiple simulators can be used tomodel a single robot design, consider the SUPERball v2 robot16 (Fig. 3), which is composed of six struts and 24 cables.
During design, and for predicting dynamic motions using
analytic models, TMO44 simulator is often used to reduce
cost, development time, and operational risk. Subsequent
controller development and modeling can be done in higher
level simulators such as MuJoCo53 and NTRT.24 Importantly, TMO can only model dynamic motions and contacts between struts and the ground, while neglecting friction,
strut–strut contact, and cable contacts. MuJoCo can additionally model strut–strut contact and friction, but only
NTRT can detect collisions between cables and other components. This capability has helped facilitate successfultransfer of locomotion policies from NTRT to reality.57
Although complicated motions can be generated in simulation, policy transfer from simulation to reality is plagued byinconsistencies. Mitigating this so-called ‘‘reality gap’’ between simulation and hardware typically requires an iterative
process where simulator parameters are tuned after running
experiments on physical robots to more accurately reflect realconditions. For example, hardware validation of the NTRTTENSEGRITY ROBOTICS

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Table 1. Comparison of Various Tensegrity Robot Simulators
Cable
Simulator
Paul et al.29
Caliper43
NTRT24
TMO44
STEDY45
MOTES46
Wang et al.47

Physics engine

Mass

Contact

GroundReaction

FrictionRod
Reaction

Friction

Differential

ODE
Bullet2
Bullet2
MatlabMatlabMatlab
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The main differences of the tensegrity simulators are in (1) the physics engine that the simulator is built on (where MATLAB refers tocustom physics engines programmed using MATLAB); (2) modeling of the cable (mass and contact with other objects); (3) modeling of thecontact between the robot and the ground (reaction force and friction force); (4) modeling of the rod-rod contact (reaction force and friction
force); (5) differentiability.
MOTES, Modeling of Tensegrity Structures; NTRT, NASA Tensegrity Robotics Toolkit; ODE, Open Dynamics Engine; STEDY,
Software for Tensegrity Dynamics; TMO, TensegrityMATLABObjects.

simulator has been performed for spine-like tensegrity robots58 and a six strut icosahedron robot.23 These studies
identified system parameters that could be tuned to increase
the accuracy of NTRT and improve its applicability to realsystems. To reduce the data requirement during policy generation, Zhu et al. used a Bayesian optimization identification
framework with a parameter projection to a lower dimensional space through embedding.59,60 Nevertheless, system
identification techniques assume that the underlying analytical or numerical model is conceptually correct and the reality
gap can be effectively eliminated by tuning the model’s parameters. Frequently the model is imperfect, and significant
reality gaps persist, even after tuning model parameters.
To further diminish the reality gap, researchers have begun
building physics engines predicated on a differentiable
model, such as a deep neural network. Differentiable models
help to reduce data requirements, increase the policy update
frequency from per-trajectory to per-time step, and allow the
robot to learn system dynamics directly from data. One
method for defining differentiable physics engines is tomodel system components as moving particles that interact.61
Each element in a scene (robot and environment) can be split
into multiple modules, and the simulator can then generate agraphical representation of module interactions. Two classes
of interactions can be defined: fixed system topology andtemporary connections for collisions. This framework gives

rise to an interaction network that depicts the interactions ofdifferent modules.
Recently, Wang et al. proposed the first differentiablephysics engine focused on tensegrity systems. It uses interaction networks, as well as first principles from physics.47,53
Namely, the differentiable physics engine models cable tensions as spring forces that depend linearly on an unknown
coefficient that needs to be learned from data. The friction andthe reaction forces, however, are more complex and involve
nonlinear components modeled by neural networks. The
combination of first principles and interaction networks results
in a more data-efficient, explainable, and modular pipeline forsystem identification. One limitation of the differentiablephysics engine of Wang et al. is that it considers cables asvirtual objects with no mass, volume, or contact. An inherent
limitation of all differentiable engines is that they assume thatsystem dynamics are totally unknown—even though thegoverning equations of motion are often well understood—andtry to learn the dynamics exclusively from data.
Locomotion

A rich variety of locomotion modes have been demonstrated for tensegrity robots (Fig. 4). Many of the tensegrity
robots we reviewed move by rolling, or what Kim et al. referto as ‘‘punctuated rolling,’’ since the motion is characterized

FIG. 3. SUPERball v216 (A) hardware, and its model in (B) the Tensegrity MATLAB Objects (TMO) tensegrity simulation framework,44 (C) the MuJoCo physics engine,53 and (D) the NASA Tensegrity Robotics Toolkit (NTRT). TMO
can simulate dynamic motions, while MuJoCo can additionally detect rod-rod collisions, and NTRT can even detectcollisions between cables and other components. Color images are available online.

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FIG. 4. Representative examples of locomotion strategies utilized by tensegrity robots. Since actuation and topology areoften tightly coupled with the locomotion strategy, these are also indicated for each example. Color images are available
online.
6

TENSEGRITY ROBOTICS

by discrete, sequential impact events between the strut ends
and the ground.62 Other tensegrity robots locomote byswimming, hopping, climbing, flying, vibrating, or crawling.
Often, actuator choice and robot topology are tightly coupledwith the desired mode of locomotion. For example, climbing
robots are best suited to tower structures, whereas rolling isbest suited to symmetric topologies approximating a sphere,
such as the widespread six-bar icosahedron.

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Rolling

Rolling tensegrities achieve motion by displacing theircenter of gravity so that it is outside their polygon of stability(the vertical projection of the nodes that are in contact withthe ground). The result is a tipping from face to face. Since
the mass of a tensegrity is often concentrated in the rigid
struts that form the structure, rolling tensegrities must be
capable of large structural deformations.
Deformations are typically produced by changing the lengthof tensile elements along the edges of a tensegrity, which inturn shifts the struts and causes the structure to topple. To
achieve a rolling locomotion mode, many tensegrity robots
feature motors mounted on their rigid struts to contract thecables that serve as the edges of the tensegrity.23,25,62–67 Other
actuators have been demonstrated for changing the length ofthe edges, including linear servos in series with springs,15,17,68
liquid crystal elastomer threads activated with near-infrared
light,69 shape memory alloy springs,37 silver-coated twistednylon,70 and McKibben pneumatic actuators.26,71,72 Most
rolling tensegrity robots are six-strut class 1 structures with an
icosahedron resting shape. A few two- and three-strut rollingtensegrities have been shown in simulation, but none was
implemented in hardware.55,73 We have observed the rolling
locomotion approach used on robots with characteristic lengthscale of meters (e.g., Superball16) down to a few centimeters(e.g., Wang et al.’s light-powered tensegrity69), with speeds on
the order of a few body lengths per minute (3.5 BL/min16 and1.15 BL/min69).
While most rolling tensegrities modulate the lengths of theirtensile elements to roll, several other strategies have been
demonstrated. For example, the TT-4mini has custom linear
actuators as its struts and passive elastic elements as its edges.17
Baines et al. designed reconfigurable planar membrane actuators that form the faces of tensegrity robots, capable of extending in-plane to change the tensegrity’s shape, or bulging
out of plane to tip the tensegrity.74 In-plane extending membranes were demonstrated on a 6-strut icosahedron, whereas
out-of-plane membranes were demonstrated on a rolling 12-barrhombicuboctahedron, 4-strut cube, a 10-strut dodecahedron,and various others. Curved two-strut tensegrities introduced by
Kaufhold et al.75–77 and Rhodes and Vikas78 roll by shifting
masses along tracks embedded in the curved struts.
Crawling

Several tensegrity robots are capable of deforming theirstructure to use a subset of their strut ends as feet, achieving
gaits resembling those of legged animals. All reviewed
crawling tensegrities either relied on winch and cable actuation27,29 or were only realized in simulation.79–82 For example,
Masic et al. simulated a class-II tensegrity tower composed offour-bar prism segments.79 Paul et al. demonstrated threebar27,29 and four-bar29 crawling robots in simulation and7

hardware, resulting in robots 36 cm long, with resulting speedsof 2 BL/min.29 SunSpiral and colleagues introduced theTetraSpine, a class of multisegment spine-like robots that
could walk and climb over objects in the NTRT simulator, andsome progress was made toward building real robots with asimilar design.80,83 A later study on similar simulated robots
led to high-DoF multisegment spine-like robots that used
central pattern generators (CPGs) to attain various crawlingand snake-like gaits.81 Zappetti et al. demonstrated winchdriven, modular six-bar icosahedron tensegrities that could beconnected in series to yield a crawling robot.41,84
As evidenced by the research referenced above, crawlingtensegrities can be made of either single controllable segments or multiple segments that collaborate to control their
ground contact and locomote. By expanding the range ofshape primitives to include additional geometries, such as the
deployable class-II tensegrity tower with pentagonal modular
sections introduced by Veuve et al.,85 additional locomotion
gaits could be attained.
Vibration

Vibrating tensegrities locomote by harnessing oscillating
elements, such as linear electromagnets or eccentric mass
motors, to dynamically excite the whole tensegrity structure.41,82,86–89 The locomotion mode is characterized bycomplex coupling between multiple physical phenomena,
including asymmetrical friction pairings and dynamic‘‘hopping’’ that ultimately yields motion along a surface. For
example, by dynamically exciting its structure, a two-bar
tensegrity could vibrate in different directions.89 Other icosahedron tensegrity robots could drift along a surface.21,90
Varying the frequency of their driving motors (two21 or
three90) led to some ability to change the robot’s locomotion
speed and direction, with Riefell and Mouret reporting an
impressive maximum speed of 69 BL/min for theirdecimeter-scale robot (rod length of 9.4 cm21). Notably, since
the vibrating class of tensegrity does not require large
structural deformations to locomote, some modeling inaccuracies can be avoided, such as those arising when modeling large deformations and calculating strut collisions. The
vibrating tensegrity thus boasts the resilience characteristicof tensegrity robots and simplifies modeling efforts.
Other locomotion modes

Other locomotion modes achieved by tensegrities include
peristaltic pipe crawling,91,92 hopping,18,93 and flying.20,94
These locomotion modes could potentially allow robots toaccess difficult-to-reach locations or achieve rapid locomotion.
Friesen et al. built a duct climbing robot composed of two
tetragonal sections, made of six linear servos each, andwinches and cables connecting the two sections.91,92 The
tetragonal section would expand to jam in the duct, while thewinches and cables would advance the unjammed section.
This approach could have applications in pipe inspection,
disaster response, or other highly-constrained environments.
Hopping and flying locomotion modes are promising forswitching between rapid, long-distance travel and controlled
local motions, allowing the robot to adjust to mission demands. Garanger et al. showcased a hopping 12-bar rhombicuboctahedron actuated with winch and cables.93 To
achieve hop and roll locomotion, Kim et al. simulated a six-

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bar icosahedron tensegrity with a single thruster in the center,18 whereas Mintchev et al. built a six-bar icosahedrontensegrity with two propellers inside.20 A similar robot by
Zha et al. situates a quadcopter inside a six-bar icosahedrontensegrity. The quadcopter enables flying, while the tensegrity permits the robot to reorient itself after a crash.94
Although no terrestrial mobile robots based on bending
tensegrities have been shown to date, Bliss, Iwasaki, andBart-Smith introduced a class-II tensegrity tower composedof two-bar planar modules that are capable of oscillating a fin
for generating thrust underwater.95 Bending motion primitives have been used by free-swimming fish-inspired robots
as well.38,96 Similarly, Sabelhaus et al. described a fivevertebrae spine tensegrity called ULTRAspine97 and Zappetti et al. demonstrated a variable stiffness vertebrae spine
tensegrity,28 both of which were capable of executing controlled bending motions.
Sensing

Although many tensegrity robots showcased in the literature operate in a sensor-free, open-loop manner,21,67,98 state

SHAH ET AL.

estimation25 and contact sensing23 facilitate closed-loop gait
control and will potentially enable tensegrity robots to execute controlled dynamic locomotion in unstructured environments. A high degree of control over system dynamics
will, in turn, facilitate the transfer of advanced control policies from simulation to physical hardware. Numerous sensing
methods for tensegrities have been proposed (Fig. 5), yet only
a subset of these have been evaluated in dynamic situations.
Since each member of a class 1 tensegrity is axially loaded,
the full state of a tensegrity robot comprises the spatial positions and velocities of its endcaps, ground contact information, tension in the cables, compression of the struts, andorientation of the overall structure (although orientation
could be inferred from the spatial positions in a global reference frame). Often, only partial state information is necessary for successful locomotion. For example, the Modular
Tensegrity Kit introduced by Kimber et al. only requires a
six-axis accelerometer to record its vibrations.19
One logical method to estimate spatial positions is tomeasure the distance between nodes. For cable-actuatedtensegrities, measuring the amount the actuator has contracted (or extended) does not account for stretch in the cables

FIG. 5. Sensors allow tensegrities to estimate their 3D shape (state) and detect environmental interactions.25 (A) Top:
contact measurement using force sensors within the struts’ endcaps. Bottom: numerous sensors were integrated into
REcTeR’s struts.63 (B) State estimation using surface-based strain sensors.26 (C) State estimation using external ranging
sensors. ROS, Robot Operating System; UKF, Unscented Kalman Filter. Color images are available online.

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TENSEGRITY ROBOTICS

themselves or deformation of the struts. Stretch sensors99–101
could potentially be used, but they have only begun to beinvestigated in the context of tensegrity robotics to measurecable length83 or strut extension.91 For cable-driven robots,
quadrature encoders91 or Hall-effect sensors92 attached to themotors that spool the cables have been utilized to estimate
cable length.
Other robots have integrated multiple sensors into the canonical six-bar icosahedron to aid in locomotion. For example, ReCTeR had 24 tension sensors (uncalibrated strain
gauges), six ground-reaction force sensors, and three inertial
measurement units (IMUs) on the endcaps of several of thesix-bar tensegrity’s struts (Fig. 5A).23,63 The tension sensors
were input into linear feedback controllers to drive cable
lengths to set points determined by an embodied reservoir
computer. As a result, the system could recover stable locomotion—even after being physically restrained. Later workby Burms et al. used the force sensors to classify terrain.66
SUPERball was designed to overcome some of the mechanical limitations of ReCTeR, one of those being restrictedsensing capabilities.63 Tension sensors were integrated into
SUPERball’s 12 passive cables, torque sensors were added tothe active cables, and IMUs measured accelerations on theendcaps. Zhang et al. used the accelerometers on SUPERball
to directly transfer policies from NTRT to hardware, addressing part of the simulation-to-reality (sim2real) gap
which prevented open-loop policies from transferring.57
SUPERball v2 featured accelerometers to detect which of its
faces was pointing downward, enabling the robot to determine feasible actions for intuitive real-time teleoperation by ahuman operator.102
Algorithms have also been proposed to intrinsically estimate the shape of tensegrity robots. Caluwaerts et al. proposed an Unscented Kalman Filter-based sensor fusion
algorithm to estimate the 3D state of a tensegrity using
ranging sensors (Fig. 5C).25 Fusing time-of-flight ranging
sensors, IMU, and actuator states, Caluwaerts et al. could
localize a meter-scale tensegrity within a large testing area
(91 m2) with ~10-cm accuracy. Stretch sensors99 and
McKibben muscles103 were integrated into robotic skins to

9create a reconfigurable tensegrity that could roll and achieve
simultaneous estimation of the spatial positions of all nodes
on a six-bar tensegrity (Fig. 5B).26,72
Control

Tensegrities can be actuated to achieve a wide range ofgoals, from attaining a desired structural shape trajectoryin place104 to locomotion,57 to accomplishing a mission
in the field.102 Pose or task-level controllers can use open
loop or closed loop strategies to determine a desiredsequence of actuator commands and associated forces.
The appropriate controller formulation strongly depends
on the types of actuators and sensors on a tensegrity andthe application intent. This section highlights the essential role that control theory has played in developing thefield of tensegrity robotics, while conveying how controls can be applied to achieve more effective in-field
deployment.
Controllers can operate over different time horizons and at
various levels of abstraction (Fig. 6). At a low level, controllers act upon a single strut or cable in a larger network,
modulating tension based on the equations of dynamics.
Alternatively, controllers can operate at a global level andcan be formulated to choose a set of actuation patterns thatsteer a tensegrity toward a goal. As a hybrid approach, local
dynamics controllers can be placed in sequence or hierarchically with controllers of increasing levels of abstraction, toachieve robust global movement policies.
Numerous tensegrity controllers have emerged toachieve closed-loop control objectives, often following
several common development models (as summarized inFig. 7). Classical control strategies rely upon analyticalmodels and convex optimization to regulate intended behaviors.104 More recently, data-driven57 and bioinspired
techniques81 have allowed the control of more complex
systems that analytical methods cannot handle. However,
it is often infeasible to predict the conditions underwhich data-driven and bioinspired approaches can safely
operate.

FIG. 6. Tensegrity robots can be controlled at various levels of abstraction, ranging from low-level motion primitives
generated from manual experimentation or physical models to high-level motion planning to move the robot through a seriesof waypoints. Color images are available online.

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SHAH ET AL.

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FIG. 7. Information flow in tensegrity control policy development.
Top: experiments and biomimicry canbe used to develop open-loop behaviors and/or feedback policies. Bottom:
physics models and equations of motion can generate optimal trajectories,
analytic solutions, and feedback policies that are useful for improving
data-driven behaviors or even generating closed-loop capabilities on theirown. This diagram shows enoughconnections to capture most of theprocesses used by tensegrity robots,although other development frameworks are conceivable, including bidirectional information flows. Color
images are available online.

Analytical approaches

Tensegrity research based on analytical methods has focused on modeling the statics13,105 and dynamics12 of astructure to provide effective equations of motion.14 Given a
dynamic model, it is possible to control a tensegrity structure
along static equilibrium manifolds.104 Changing the rest
lengths of cables in planar tensegrity structures was the goalof the majority of reported controllers. Dynamic models forsuch networks are attainable using minimal coordinates andordinary differential equations of motion (Fig. 6, green
shading).106 Skelton and Oliveira showed that the dynamics
of 3D tensegrities cannot be represented by ordinary differential equations, but rather become systems of differential
algebraic equations.14 Alternatively, feedback linearization
control laws107 and Lyapunov-based controllers for 3D dynamic models106 have also been applied for tensegrity control. Structural control of tensegrities can be coupled with
global planning algorithms to move nodes along a desired
trajectory.108–110 The cables connecting the nodes of tensegrity systems are often assumed to behave like linear
springs. Sabelhaus et al. exploited this feature to designmodel predictive controllers for moving spine-like tensegrities along a desired configuration trajectory.111
The complex dynamics of tensegrity structures makes
controlling them for locomotion a challenge, prompting
several researchers to develop simpler heuristic controllers(Fig. 6, blue shading). For example, Shibata et al. used intuition to design a two-actuator policy to tip a shape-memory
alloy driven icosahedron tensegrity between various faces
and locomote.37 Similarly, hand-picked rolling policies were
demonstrated for icosahedron tensegrities using pneumatic
Mckibben actuators as the tensile elements.26,71 Despite
having 24 candidate edges for actuating, typically only one or
two actuators were necessary to tip the tensegrity from face toface in a predictable manner.
Despite their intuitive appeal, hand-coded policies havenumerous disadvantages. First, they are highly system dependent and do not abstract to other structures beyond theones that the policy was developed for. Second, hand-coded
policies are not conducive to dynamic rolling, but rather
quasi-static locomotion modes, such as tipping face-to-face.
Hand-coded policies do not lend themselves to quickly
generating actuation sequences to attain many successive

face transitions along arbitrary paths. Furthermore, traditional control approaches generally have not accounted for
self-collisions or environmental contact dynamics, limiting
their real-world applicability. Hardware experiments havenot utilized analytical control approaches, because they frequently depend on accurate state information, which is nontrivial to acquire.
Data-driven and bioinspired frameworks

Seeking to expand beyond hand-coded policies, researchers have begun to develop data-driven machine learning, as
well as bioinspired approaches (Fig. 6, blue shading and
Fig. 7, top). When paired with simulators, data-driven approaches are quite appealing, allowing thousands of control
policies to be quickly evaluated. Since an exhaustive searchof control possibilities is impractical, EAs are frequently
applied to achieve locomotive gaits for tensegrities,29,112
potentially through multiagent descriptions of the modular
system.113,114 In addition, forward kinematics of tensegrity
robots have been solved using feature extraction through supervised learning algorithm115 and energy-based local nodemodels for changeable edge lengths116 and strut lengths.117 The
search space can also be reduced by imposing biologicallyinspired a priori couplings of control inputs through CPGs,
which have been applied frequently to soft robots and recently
to tensegrities.58,95 In practice, these approaches that are lessdependent on accurate models can make efficient use of sensor
data and computing resources by exploiting body dynamics andmorphological computation.112
In particular, Paul et al. introduced a simulation pipeline
for developing controllers for three- and four-strut tensegrities with both static and dynamic gaits.29 In this pipeline, an
EA operated upon a population of 200 tensegrity robots in an
ODE simulator to implicitly account for the nonlinear dynamics of the tensegrities and maximize a simulated robot’s
fitness (distance travelled), by modulating the robot’s actuator firing patterns. Since Paul’s pioneering work, many
subsequent articles have utilized learning and simulation to
generate dynamic rolling policies for tensegrities. In subsequent research on six-bar tensegrity robots by Iscen et al.,113
the length of each cable was controlled by a sine wave patternwith an independent phase, duration, and amplitude, driven
by a centralized synchronization signal, as governed by:

TENSEGRITY ROBOTICS

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y(t) ¼ C þ Asin(x t þ /)

11

(1)

Here, y(t) is the length of a cable, C is an offset, A is theactuation amplitude, x is the angular frequency, and / is aphase offset. This formulation resulted in 96 independent
parameters, which were calibrated automatically using EA
that evaluated several thousand controllers in simulation.
Researchers have also proposed phase coupled oscillators
inspired by the salamander nervous system,118,119 applied tospine-like tensegrity robots.58 To generate policies for spine
tensegrities with extremely high DOF, Mirletz et al. used a
Monte Carlo algorithm to generate initial guesses, followedby iteratively sampling a Gaussian distribution around thebest policy parameters.58
Another vein of work relates to deep reinforcement
learning (RL) and holds promise of generating successful
feedback control policies that map directly from sensory data
to task-oriented actions.120 A crucial consideration for extending RL to tensegrities is whether a learned model can bemade to generalize over a large part of the state space. Thisconsideration can be addressed, in part, using model-based
RL tools, such as Guided Policy Search,121 that combine
several locally valid controllers into a single, more broadly
applicable learned policy. RL has successfully facilitated thedevelopment of rolling controller policies for SUPERball.57
Motion planning

If a robot is able to discern its global position, it can engage
in higher level motion planning, exploiting the welldeveloped literature on robot path planning (Fig. 6, red
shading).122 Motion planning is needed to perform complex
tasks with long time horizons, such as goal-directed obstacleavoiding locomotion or purposeful deformation of a tensegrity structure. Numerous planning algorithms have been
proposed for tensegrity robots, ranging from quasi-static
approaches to more complex asymptotically-optimal kinodynamic planners.
Early planning methods for tensegrities planned deployment and shape change by applying optimization to generatea sequence of statically stable configurations.108,123 Further
work accounted for self-collision avoidance in this process.124,125 More recent approaches plan paths for tensegrity
mobility, but still assume a control process slow enough toeliminate any dynamic effects.109,124 This quasi-static assumption is often applicable to tensegrity-based civil structures,126 but is not amenable to robotic applications.
Other planning strategies chain together several motion
primitives using a global planner. This approach decouples
planning from dynamics, often yielding relatively simple yet
intuitive solutions. For example, Vespignani et al. introduced asteerable teleoperation-based controller for icosahedron tensegrities that operated on top of arbitrary tipping control
primitives.102 Seeking to automate the path generation, another group proposed A* for generating actuation sequences
for a rolling and hopping icosahedron in simulation.18 The costfunction for weighing the value of possible trajectories wasdependent on topographic information (height of adjacent tiles
in the search), whether or not hopping or rolling was chosen(equivalent to energy expended), and the travelled distance.
Another study proposed a geometric planning algorithm thatgeneralizes to any n-sided polyhedral.74 The approach com-bines a weighted A* search with geometric constraints of agiven polyhedron and uses an optimization routine to keep
track of orientation and generate collision-free paths throughthe plane. Chaining together motion primitives with a global
planner can be effective for some nonlinear systems. However,
it is best suited to scenarios in which a feasible trajectory canbe generated on a known environmental map a priori.
Although the previously discussed planning approaches
were shown to generate feasible paths, they did not consider
energetic optimality under dynamic conditions. To be efficient during long-term use, a tensegrity planner should be
able to select configurations that take advantage of nonlinear
dynamics. For example, energetically complex behaviors
such as rolling, jumping, and climbing all involve nonlinear
dynamics and may enable highly efficient traversal. As well
as monitoring energy, a planner should accommodate a highdimensional state space, avoid self-collisions, and consider
the topography of the current terrain. These needs can individually be met by strictly geometric methods, but addressing
all of them with a single tool is presently infeasible.
In attempts to converge on physically-realistic, dynamicplanners for tensegrities that tackle the aforementioned
concerns, researchers have begun to look toward kinodynamic motion planning. Kinodynamic motion planning isoften framed as a nonconvex trajectory optimization problem
in which costs are minimized under certain constraints. Sequential convex optimization can be used to iteratively correct a trajectory toward a local minimum.127 An alternative,
probabilistically complete methodology is sampling-based
motion planning. Unlike global roadmap-based approaches
in this planning family, the popular incremental RapidlyExploring Random Trees (RRT) algorithm can directly accommodate dynamics.128 RRT samples control inputs, rather
than states, and grow the tree by propagating inputs’ effects
forward from states that have already been reached, eventually building broad coverage. Littlefield et al. introduced thefirst kinodynamic planning approach for an icosahedron robot.129 They used an informed asymptotically optimal
sampling-based approach to generate collision-free sequences of kinematic rolling primitives to navigate along adesired path through cluttered environments. Doney et al.
used a quality diversity algorithm running a model-freephysical tensegrity to autonomously generate a collection of
motion primitives.130
Grand Challenges

Tensegrity robots have many advantages compared to
traditional autonomous ground vehicles: robustness to impacts, low weight, novel locomotion modes, and modularity.
However, no work to date has demonstrated a fully autonomous, untethered tensegrity robot navigating through unstructured terrain. Many roadblocks to this goal remain
unsolved across the domains of design, locomotion, sensing,and control. In this study, we discuss key challenges andpotential solutions, providing a roadmap for future research.
Automated system design

Building a tensegrity currently requires significant domain
knowledge to balance trade-offs between competing performance objectives. Various authors have emphasized different
objectives in the form of quantitative metrics, as we discussDownloaded by YALE UNIVERSITY from www.liebertpub.com at 11/07/21. For personal use only.

12

later in this section. As an initial example, the performance
objectives for a locomoting tensegrity could include highlocomotion speed, low mass, and minimized cost of transport. Even when a tensegrity robot is designed for one
specific task—locomotion, manipulation, or load bearing—understanding the interplay of topology, materials, andfunction is crucial to realizing an effective system. Across all
tensegrity applications, future research must prioritize a codesign of materials and topology, rather than treating them as
independent of one another. An emerging example of such
codesign is incorporation of variable stiffness material struts,
which have been shown to enhance deployability and modulate the mechanics of a tensegrity in situ.131 Another example are interconnections in a tensegrity robot arm that canbe adjusted to change the tensegrity’s topology and adjust
stiffness during operation.28
Simulators can serve as a practical tool to evaluate thousands of different topology-material arrangements in thecontext of a prescribed function. Yet, finding an appropriatecompromise between design parameters while ensuring thatthe corresponding robot is physically realizable is challenging. There is not currently an established rigorous way toprescreen designs for their feasibility as physical hardware.
Complicating this issue is the fact that simulators containmany parameters that contribute to a gap between simulated
and actual performance. The parameters describing systemgeometry—such as the length, radius, mass, and system topology—are easy to obtain. These parameters could bemeasured on a physical robot and hard coded into the simulation. However, the parameters for the actuation dynamics
and contact forces—such as restitution, friction coefficient,and actuator speed—are more difficult to measure and model.
Simplifying cable mechanics and soft material contacts insimulation reduces the number of parameters to tune, but
simultaneously enlarges the sim2real gap. For example, thesimplification of non-Coulombic friction in cable elements
leads to design outputs that would only be possible withmotors with torques and angular velocities beyond what iscommercially available. Reducing the sim2real gap, or atleast estimating this gap to allow informed prototyping andhypothesis testing, would allow faster transfer from simulation to physical hardware. Possible solutions include injecting noise into the simulator132 and generating a function toestimate the reality gap.33,133 As other promising options,sensor feedback57 and a pretrained classifier from sensors134
have been used to improve sim2real for tensegrity robots. In
contrast to manually measuring the robot parameters, datadriven methods such as these may reduce the human labor
requirements in the iterative identification process.
Other ways to decrease the sim2real gap include improving
and expanding the tools available for manufacturing tensegrity
robots. Ideal designs would boast strong lightweight materials,
low power consumption, lightweight, rapid, and strong actuators, high-density power packs, and high-resolution sensors
for state reconstruction and environmental sensing. Numerous
hardware challenges remain, precluding a simple scaleinvariant design and manufacturing strategy.
One significant challenge is the ‘‘curse of dimensionality,’’whereby the complexity of both design and assembly increases exponentially with increased numbers of struts andcables, in addition to the complexities of designing robots at
various length scales. For example, the power density of

SHAH ET AL.

various actuator choices varies significantly at different
scales. Winch and cable actuators have an excellent power
density in large (e.g., meter-scale) tensegrities, but are obstructive in centimeter scale tensegrities. Conversely, shapememory alloy actuators have excellent power density at all
scales, but are inefficient relative to rotary motors and slower
at large size scales due to slower heat transfer between theactuator and the environment. Another important factor canbe that material properties do not scale with system mass,affecting the level of engineering required. For example, insmall, low-mass tensegrities, the material choice for the
endcaps of the struts is trivial. In contrast, for heavier meterscale tensegrities, the endcaps experience higher impact
loads and abrasive wear.
Furthermore, tensegrities are notoriously difficult to assemble and poorly disposed to automated assembly due totheir complex spatial connections. Recently proposed modular lattices31,41 and vibration-driven struts with integrated
motors19 reduce assembly times, but much remains toward
developing a streamlined tensegrity robot manufacturing
process with integrated sensing and actuation. For example,
the number of struts in a given design has a profound impact
on assembly complexity, which is one of the reasons it is rare
to see rolling tensegrities with more struts than the canonicalsix-bar arrangement or crawling tensegrities with more than
three or four bars in their arrangements. There are several
ways that this challenge may be addressed in the future. One
important step toward reducing the complexity of design andassembly is the reduction of custom designs for each tensegrity robot or making a greater number of the components
digitally manufactured and/or assembled.
State estimation and environmental sensing

In addition to mechanical design challenges, current tensegrity robots are limited by state estimation inaccuracies on
the order of several percent of the tensegrities’ strut length.25,26
Such noisy sensing resolution makes closed-loop control difficult, driving a need for improved sensor fusion algorithms
and more stable onboard sensors. For example, low-noise
strain sensors135 could be integrated into the sensor cables or a
3D camera136 or ranging sensors25 could be attached to strategic locations for tracking node positions. Furthermore, estimating the state of modular tensegrities has been unexplored.
Once improved sensor suites are developed, there are likely
optimal ways to fuse sensor data to obtain a full state estimate
and then use that to produce and control efficient locomotion
gaits. Finally, environmental perception is a largely unexplored domain of tensegrity robotics research, yet presents
immense scientific potential for exploring extraterrestrial environments. While the compliant structure of a tensegrity
provides a safe internal space for placing environmental sensors, scant work has dedicated that space to house scientificpayloads. Many open questions thus remain, including how tomaintain sensor orientation during rolling and how to mitigate
the occlusions caused by the tensegrity struts.
Autonomous navigation

To date, tensegrity locomotion has largely been confined tolaboratories—simplified environments that are but approximations of real-world scenarios. However, navigating unstructured environments autonomously will be essential forDownloaded by YALE UNIVERSITY from www.liebertpub.com at 11/07/21. For personal use only.

TENSEGRITY ROBOTICS

future robotic missions. Improved state estimation could
potentially be used in a closed-loop control policy and integrated into higher level task planning. For example, one
possible hierarchical control scheme would combine advances in polyhedral path planning, real-time adjustment offound paths, and machine learning-based dynamic control
frameworks to create a robust tiered autonomous controller.
Tensegrity planning algorithms could take advantage ofmany environmental features that prove catastrophic toconventional wheeled or legged robots. Discontinuities, suchas cliffs and ridges, require traditional robots to search for a
new safer path. In contrast, a tensegrity robot could take ashortcut—simply rolling off the edge. Such an unconventional planning framework could save mission-critical resources like time and fuel. Recent work has begun to explore
ways to efficiently locomote between arbitrary waypoints
using symmetry-reduced RL on the rough terrain and steep
slope,64,134 but further research is needed to minimize power
consumption. Overall, with appropriately dense and accurate
state information and planning algorithms that embrace discontinuities rather than avoid them, the next generation oftensegrities could complete missions rapidly at lower risk.
Standardized reporting of performance metrics

In the course of preparing this review article, we found that
few articles reported the same sets of system-wide performance
metrics beyond locomotion speed (in addition to measurements
like rod length and robot mass), with many instead only presenting measurements directly related to the study’s novel
claims. Without standardized metrics for tensegrity robotics, itwill be difficult for the field to measure progress in an objective
manner. While adoption of metrics is ultimately up to the research community and warrants further debate and standardization, here we outline a few that we believe are particularly
relevant to tensegrity robots. This list is not exhaustive and ismeant as a concise starting point for the field to build and improve upon. Some metrics can be obtained on a static robot,
while for others the robot must be dynamic during measurement.
For example, potential ‘‘static’’ hardware metrics include: Robot density (kg=m3 )—the mass of the tensegrity ro-

bot divided by its volume, where the volume is definedas the convex hull of the robot when the robot occupies
its maximum volume.
 Characteristic rod length (m)—the length of a tensegrity
strut. Since compressive elements in tensegrities can vary
widely, we define the characteristic length based on oneof several cases as: the minimum or rest length of actuatedrods, the average distance between the geometric centerand the element’s multiple ends for compressive elementswith more than two end nodes (e.g., a tetrahedral element
in a tensegrity spine), or the average strut length in tensegrities that have struts of different lengths. Having
characteristic rod length as a reported metric is especially
important for comparing the costs of transport of tensegrity robots at very different scales.
 Maximum bending, buckling, and crushing loads (N)—the load at which a rod experiences plastic deformationin any of these three load configurations, typically inimpact scenarios.
These metrics seek to provide a quantitative depiction of
how lightweight, large, and strong the robot is, while en-

13

abling comparison between robots as different as the six-bar
icosahedron and spine-like robots. Beyond these static,
structurally-oriented metrics, we present potential locomotion performance metrics, including: Costof transport (unitless)—typically defined as
CoT ¼ mgv=Pin , where m is the system mass, g is thegravitational constant, v is the average velocity, and Pinis the average power input to the robot. Alternatively, it
can be defined as CoT ¼ mgx=Ein , where x is the distance traveled and Ein the energy input. Cost of transport gives the ratio of energy used in productive motion
to that input to the system. Here, we propose measuring
the cost of transport while traveling over flat groundwithout obstacles at standard atmospheric conditions.
Since it is unitless, cost of transport is an effective way
to make comparisons between disparate tensegrity designs, as well as other robots.
 Characteristic velocity (BL=s)—the robot’s velocity
divided by longest length of the robot body. In manycases, the longest length of the body will be approximately the characteristic rod length.
 Maximum climbable incline (degrees)—the maximum
angle a locomoting robot can climb in its intended
environment.
Conclusions

Leveraging their lightweight resilient bodies, tensegrity
robots have shown great potential to explore extreme environments. Tensegrities can engage in numerous locomotion
modes, including crawling, rolling, and hopping. Such operational flexibility enables them to adapt to changing demands, navigate novel terrain, and operate even after
experiencing significant damage. Continued development oftensegrities could one day allow us to explore locations inaccessible with existing technology, such as lava tubes on
extraterrestrial environments.
Beyond the field of robotics, tensegrity structures haveprovided simplified models to test biomechanical theories.
Progressing the field of tensegrity robotics presents a unique
opportunity to build controllable analogs for testing theories
of legged locomotion, the spine’s role in animals’ dynamic
stability, the role of passive stabilization mechanisms incellular behavior, and the stresses experienced throughout thehuman body’s bone-muscle system.4 Illuminating these dynamics will lead to more targeted physical therapy, ergonomic exosuits, and informed biological models. Indeed, bystudying the tensegrity, roboticists have the chance to increase our knowledge of ourselves and improve human life.
Acknowledgments

The United States Government retains, and by accepting
the article for publication, the publisher acknowledges that
the United States Government retains, a nonexclusive, paidup, irrevocable, worldwide license to publish or reproduce
the published form of this work, or allow others to do so, for
United States Government purposes.
Author Disclosure Statement

No competing financial interests exist.

14
Funding Information

D.S.S. was supported by a NASA Space Technology Research Fellowship (Grant 80NSSC17K0164). R.L.B. was
supported by an NSF Graduate Research Fellowship (DGE1333468). M.V. was supported by NASA contracts
NNA16BD14C (Universities Space Research Association)and 80ARC020D0010 (KBR Wyle Services, Llc) with theNASA Ames Research Center. J.W.B., K.B., and R.K.-B.
acknowledge support from the NSF Robust Intelligenceprogram (CISE-1955225 and 1956027).

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