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Rapidly Deployed and Assembled Tensegrity System An Augmented Design Approach



The Rapidly Deployable and Assembled Tensegrity (RDAT) project enables the efficient automated design and deployment of differential-geometry tensegrity structures through computation-driven design-to-installation workflow. RDAT employs the integration of parametric and solid-modeling methods with production by streamlining computer numerically controlled manufacturing through novel detailing and production techniques to develop an efficient manufacturing and assembly system. The RDAT project emerges from the Authors' research in academia and professional practice focusing on computationally produced full-scale performative building systems and their innovative uses in the building and construction industry.
Rapidly Deployed and Assembled
Tensegrity System
Phillip Anzalone
New York City College of
Technology, CUNY
Stephanie Bayard
Pra Instute
Ralph S. Steenblik
New York City College of
Technology, CUNY
An Augmented Design Approach
The Rapidly Deployable and Assembled Tensegrity (RDAT) project enables the ecient automated
design and deployment of dierenal-geometry tensegrity structures through computaon-driven
design-to-installaon workow. RDAT employs the integraon of parametric and solid-modeling
methods with producon by streamlining computer numerically controlled manufacturing through
novel detailing and producon techniques to develop an ecient manufacturing and assembly
system. The RDAT project emerges from the Authors' research in academia and professional
pracce focusing on computaonally produced full-scale performave building systems and their
innovave uses in the building and construcon industry.
The Rapidly Deployable and Assembled Tensegrity (RDAT) system
developed from the authors' research focusing on the invenon
of computaonally produced performave full-scale building
systems and how they can have innovave uses in the building
and construcon industry (Anzalone 2014; Anzalone 2016).
Currently, RDAT research is at a stage of full-scale producon
of tensegrity masts and plates with variable geometric congu-
raons, including the necessary design, analysis and producon
workow (Clarke and Anzalone 2006). The goal of the RDAT
program is to enable rapid design and deployment of a wide
variety of dierenal-geometry tensegrity structures through an
augmented design process, engaging machine learning, auto-
maon and mixed-reality interfaces to produce a manufacturing
and installaon workow at the scale of architectural building
systems. The project incorporates the integraon of parametric
and solid-modeling methods to enable computer numerically
controlled (CNC) manufacturing of components and ecient
complex system assembly in the eld through innovave design
detailing and producon methods.
The RDAT Program leverages the advantages of tensegrity
structures, coupling advances in science and technology
produced since their incepon. In 1975, Buckminster Fuller
coined the term tensegrity as a conjuncon of tension and
integrity (Fuller 1975). The term describes a structural system
of compressive and tension members that yield mechanical
equilibrium. More recently, Pinaud, Masic and Skelton precisely
state that tensegrity structures are a set of disconnuous
compressive components interacng with a set of connuous
tensile components to dene a stable volume in space (2003).
Contemporary research in tensegrity has expanded to include
biological systems such as bone and tendon conguraons,
as the study of forces and indeterminate structures through
computaonal analysis has expanded the science considerably.
Although contemporary architects and designers now have
access to computaonal tools with potenal to solve the
indeterminate forces associated with tensegrity structures, very
few tensegrity systems are developed within the architecture
profession due to some of the inherent features of the struc-
tures. The systems tend to be dicult to precisely form, have
exibility under load beyond normave architectural structures,
and require materials and detailing beyond normal possibility in
building condions. Renewed interest in deployable structural
systems, cable façade systems, and fabric tensile structures
demonstrates the need for an interface architects can use
to eciently develop tensegrity designs prior to compleng
the cumbersome calculaons tradionally associated with
indeterminate form-nding. For example, Kenneth Snelson’s
tensegrity sculptures are the embodiment of the Fuller and
Pinaud denions of tensegrity (Zhang, Oshaki, and Kanno
2006). His methodology is based upon physical model building,
numerous measurements, and iterave renement of tension
cable lengths on the nal unique piece. Research completed
at the Max Planck Instute for Intelligent Systems in Stugart
states an analycal form-nding method exists requiring the
designer to predene the cable length but then calculates the
rao directly without involving the iterave process (Bugartz
2007). Contemporary computaonal tools can be harnessed to
bring about a more ecient integraon of digital and physical
producon in the creaon of indeterminate structures.
Tensegrity structures have numerous advantageous properes.
As three-dimensional self-stressing cable systems, they have a
relavely small number of disjoint compression members (Figure
1). They are self-erecng, as tensioning the nal cable trans-
forms them from a compact loose network of members into a
large three-dimensional volume. As such, tensegrity systems
are extremely lightweight, materially ecient, embody resilient
properes, allow system exibility, and are composed of primarily
standardized linear elements. In addion, through the RDAT
System, they are now calculable, easy to assemble and recon-
gurable, oering potenal uses as structural reinforcement,
infrastructural elements, reusable or le-in-place formwork,
scaolding, and other building construcon elements as well as
1 Tensegrity structures - disjoint compression members systems.
the well-understood use as exible building components such as
roofs, curtain-walls and other similar systems (Oppenheim and
Williams 1997).
Contemporary computaonal tools can be harnessed to bring
about a more ecient integraon of digital and physical produc-
on in the creaon of indeterminate structures. If parametric
design (and it's associated byproduct Building Integrated
Modeling) dened digital producon in Architecture the rst two
decades of the twenty-rst century, augmented design intelli-
gence will dene the designer's way of working for at least the
next two. The second machine age is upon us, ushering in “the
automaon of knowledge work" (Brynjolfsson and McAfee 2016),
which will again transform the designer's process akin to the
transformaons brought on by the personal computer at the end
of the last millennium.
Inspired by Vannevar Bush's "As We Make" (1945), outlining a
way of working collaboravely with computers, Doug Engelbart
published "Augmenng Human Intellect: A Conceptual
Framework" (1962). This history is important for spelling out
a method and the idea of co-authoring, or collaboraon, with
computaonal systems in the process of creaon. Jumping ahead,
more specically: "To design is to generate and to choose" (Mitra
et al. 2016). Parametric design is based in using algorithms to
generate versions. In early 2010 David Ruen gave an intro-
ductory lecture at the Architectural Associaon in London on
his Galapagos solver for Grasshopper, taking algorithmic design
to an intelligent next level, allowing designers to construct an
algorithm and set tness parameters for which the computer can
test soluons to nd the best t.
Where parametric modeling allows for a streamlined workow
for version matrices, the use of an augmented design intelligent
solver allows for an intelligent version matrix where all possible
outcomes are considered for tness. This creates a much more
robust process that supplements the intuion of the designer
with soluons which may have been overlooked or not consid-
ered otherwise.1 As stated by David Copps at MIT's EmTech,
augmented intelligence requires three components: a machine
learning environment, a user experience, and human curaon
Using recent developments in machine learning as a part of the
design process opens extensive opportunies for developing
prototype versioning, so the designer may realiscally tease out
and analyze innumerable possible conguraons. This allows for
comprehensive near real-me analysis of a greater set of possible
parametric examples. The research team believes that this
technique will aid in the discovery of unrealized conguraons
potenally with unforeseen benets or applicaons. Addionally,
incorporang sensors into the assembly allows for an automa-
cally actuated or responsive system that can be deployed as part
of the structure. This will lead to analycal feedback into the
machine learning parameters for applicaon to future cong-
uraons, and opmal techniques for real-me environmental
Rapidly Deployed and Assembled Tensegrity System Anzalone, Bayard, Steenblik
2 CATIA and Grasshopper soluons inform the RDAT System.
There is an opportunity to use new and novel tools such as the
OpenAI Gym project, used to develop and test reinforcement
learning (RL) algorithms or agents. Some of the environments
lend themselves to use with the development of dynamic
structures; in essence, they allow an RL agent to explore cong-
uraons without preconcepon. This method is similar to current
computaonal geometry tools in that it allows the designer to
evaluate more iteraons, but it takes the logic one step further
because the RL agent uses four values to inform the iterave
learning process, observaon, reward, info, and done (used to
reset the environment for another iterave experiment)
This logic is based on a tried and tested "agent-environment
loop". Each me step, the agent chooses an acon, and the
environment returns an observaon and a reward. The RL
agents start with random acons and then, through the feed-
back provided by the iterave learning process, the RL agent is
encouraged to make increasingly informed decisions over me.
Current experiments have not been directed toward spaal
or architectural problems, but the preliminary exercises show
promise for their applicaon toward dynamic structural systems.
Another recent development which feeds the augmented design
approach is "Deep Reinforcement Learning for Tensegrity Robot
Locomoon" (Zhang 2017). This project uses mirror descent
guided policy search (MDGPS) as a means of accomplishing
tensegrity locomoon. The replicaon and adaptaon of both of
these learning systems will enhance the RDAT’s augmented deci-
sion-making process through the use of computaonal learning
As a design methodology, the RDAT System integrates these
properes into digital design tools, a detailed and customized set
of physical components, and digital fabricaon technologies to
create a cohesive system, migang the interoperability issues
associated with exisng cross-plaorm design, analysis, fabri-
caon and project delivery methods. The goal is to develop an
opmized, project-dependent workow, coupled with intelligent
building components, to resolve interoperability conicts by
adapng exisng soluons and proposing innovave alternaves.
Since the late 1980s, architects and engineers have used
computer-aided design and manufacturing (CAD/CAM) tools
to develop building projects while narrowing the gap between
representaon and fabricaon. Researchers have argued that
advances in digital design and fabricaon have led to a triumph
of appearance over substance and that few truly new materials,
features and processes have resulted from the proliferaon of
digital design techniques. Furthermore, the reliance of architects
on crasmen and fabricators to carry out their designs suggests
that architects are disconnected from the skill of making.
Research on the use of digital design tools (CAD/CAM, BIM,
scripng and computaonal analysis), project delivery methods,
and fabricaon technologies in order to synthesize full-scale case
study projects, lead to new proposals to develop the use of inno-
vave materials, novel processes and ulmately to reintroduce
making to architects as an integral component of digital design
and fabricaon (Atelier Architecture 64 n.d.).
Prototyping done within the framework of exisng soware
is a crical method for rapidly developing a set of processes
for tesng while simultaneously developing the criteria for the
eventual custom design and analysis tools that the authors
are currently programming. Using CATIA Generave Shape
Design and CATIA Knowledge Paerns combined with Rhino
and Grasshopper studies, the RDAT System concludes with the
fabricaon of a tensegrity tower derived from designs param-
eterized in the computaonal system through a customized
program interface (Figure 2). The digital and associated physical
fabricated components address pre-stressing or post-stretching
of the tension elements during the assembly process as well
as assembly tolerances, while also tracking each category of
element for opmizing strength, assembly sequence and inven-
tory (Figure 3).
The RDAT node detail was developed to allow for variable
parametric assembly processing with the ability to be quickly
deployed, demounted and reassembled for numerous tension
line conguraons. Addionally, the node is simple to construct,
as strong as tradional tensegrity connecon methods, ecient
3 RDAT node detail.
and elegant (Figure 4). The fundamental process relies on the
inherent compressive forces on the strut at the node detail from
the combina on of three acute angle tension wires and one
obtuse angle wire. At each node, the three-dimensional vectors
combine to a resultant vector which is always directed into the
node, thus preven ng the separa on of node and strut. This
allows for rota on to relieve internal stresses from system  exing,
and struts easily engage and disengage during assembly and
demoun ng of the structure.
The RDAT system node is fundamentally composed of a cylinder
of material that is machined to  t within the strut. In the case
study, fabricated high-density polyurethane foam was used
to prototype the cylinders to  t snugly within the anodized
aluminum tubes. CNC equipment was used to tap a thread into
the center of the cylinder for the a achment of the connec on
disk. The connec on disk is a disk of plasma-cut steel that can be
bolted to the cylinder as well as connected to the four tension
lines at the node. The cu ng of the disk is detailed to allow for
tolerance at the tension connec ons; the load is transferred
to the disk and strut simultaneously for seamless force- ow
through the system.
Once all elements are produced using extracted computer
model data, the process for assembling a completed tensegrity
prism is 1) construc on of nodes, 2) assembly of an end-prism,
and 3) a achment of the remaining prism elements linearly to
the end-prism (Figure 5). Once constructed horizontally, the
Rapidly Deployed and Assembled Tensegrity System Anzalone, Bayard, Steenblik
4 Parametric assembly with rapid, demounted and reassembled.
5 Tensegrity prism assembling is node construc on, end-prism assembly, and linear a achment of end-prisms.
6 Lightweight structure can be re-posi oned by one or two people.
Case Study 1: Urban Forest, Montpelier, France, 2010
The Urban Forest installaon was constructed for the Seventh
Annual Fesval des Architectures Vives exhibion in Montpelier
France in 2012. It served as a test for rapid deployment of a
full-scale system due to the requirements of erecon within one
night. The structures are three six-meter-tall conical tensegrity
towers of anodized aluminum compression members and stain-
less-steel tension members (Figure 8). Installed in the Hotel de
Griy courtyard in Montpelier, the towers suspend a network of
metallic mylar dichroic “leaves, reecng and colorizing sunlight
to the inhabited space below (Figure 9). The modied 5-prism
tower structure features an innovave nodal design allowing
rapid deployment and compact storage measuring 2 m long and
50 cm in diameter.
structure is lightweight enough to be posioned vercally by
one or two people, depending on the height of the complete
structure (Figure 6). If the structure is to be demounted and
transported, the procedure is reversed; place the assembly in a
horizontal posion and 1) remove the primary tensioning cable
at one end-prism, 2) collapse the end-prism, 3) remove one
cable from the adjacent prism, collapsing the prism, repeang
step three unl all prisms are collapsed, and then bind and fold
each set of rods on the others unl a single package of rods
and cables is collected and bound together (Figure 7). While
assembly is longer in duraon than disassembly, a ve-prism
structure such as the case-study has been assembled in as lile
as one hour.
Producon of a tensegrity structure, fabricaon, assembly
and installaon, has historically been the site of trial-and-error
methods as described above. The RDAT system integrates
the design, analysis, fabricaon and assembly of the system
through developments based on the authors' previous work in
advanced networked structural systems. A crical aspect of the
development of a seamless workow is the step between the
computaonal form-nding and analysis and the manufacturing
of the components for physical construcon. The creaon of a
detail that is designed from its incepon to conform to the algo-
rithms and parameters that are incorporated into the soware
including geometry, material properes, degrees of freedom
and other aspects of the system is essenal to assure that the
produced components have the capacity to perform as designed.
Simultaneously, a feedback loop is put in place to allow develop-
ments during prototyping, case studies and physical tesng to
integrate results into the programming of the CAD/CAE system,
ensuring that the computaonal component conforms to the
producon component. Through a series of case studies where
building scale producon is realized, the system can be tested
against performave and producon criteria.
Urban Forest is a prototype for digitally fabricated tensegrity
structures in the form of self-supporng towers and a means to
demonstrate and test the structural strength as well as its formal
capacies. Urban Forest is an inial prototype driven by ideas in
the greater context of potenal architectural applicaons, such
as eciency in materials, structural strength, and other technical
benets. Tensegrity presents a system that is easily transportable,
collapsible, and has the potenal to create large walls, enclosures,
structures with minimal amount of materials.
The Urban Forest case study was used to test the ability to
prefabricate the components in place within the structural
conguraon, collapse the structure for shipping, and redeploy
with a minimal of me and labor required. This project was
erected in France by one person over the course of an evening,
proving that the design concept was sound while revealing
potenals for improvement in the design and detailing that were
added to later iteraons.
Case Study 2: Salford Meadows Tensegrity Bridge
The Tensegrity Bridge entry for the Salford Meadows Bridge
Compeon seeks to provide a needed link between Salford
Meadows and the surrounding community, while simultaneously
promong an ecient and funconal structure and celebrang
the future potenal of Manchester (Figure 10). With a nod to
the rich industrial past of the local community, the innovave
tensegrity structure proposed reinforces the dynamic nature of
the nearby Engineering Faculty of the University of Salford and
develops a catalyst for encouraging future growth (Figure 11).
The importance of the local community demands a world-class
structure as a response to the development of the city.
Tensegrity Bridge was developed through an in-house computa-
onal program to streamline the design, analysis and producon
of a tensegrity system through parametric solid-modeling and
computaonal physics simulaons, allowing for the formulaon
of a sinuous shape that weaves the cable supports around a
direct linear pathway (Figure 12). The design strategy develops
the potenal of Salford Meadows by creang a link and aracng
new visitors, while expressing the bridge as a landmark through
the highly visible conguraons at the landings of the bridge. The
system is engineered to take advantage of the forces developed
in a pedestrian bridge of this scale through computaonal sizing
and conguraon of the elements and the tensegrity form.
The structure is naturally resilient and self-tunes to develop
counter-vibraon, dampening movement due to passage of
pedestrians. Suspension supports for the footbridge, connected
with an isolang detail, reduce vibraons by dispersing the forces
in the naturally resilient tensegrity system. The lightness of the
structure reduces the need for extensive foundaons at the
embankment so that support can be focused primarily on two
point loads above the river, providing a less invasive grounding
condion and simultaneously expressing the gracefulness of the
10 Salford Meadows Bridge Compeon entry.
13 Parametric physics simulaons, enable the sinuous shape.
12 Parametric physics simulaons, enable the sinuous shape.
Rapidly Deployed and Assembled Tensegrity System Anzalone, Bayard, Steenblik
11 A nod to the community’s industrial past and academic connecon.
This compeng entry allowed for the study of a full-scale
applicaon with the collaboraon of an engineer with extensive
specialty structures experse, including tensegrity structures,
Dr. Will Laufs. The authors were able to test the form-nding
and analysis of their computaonal format in response to the
program and the Engineer’s advice (Figure 13). Further rene-
ments in the algorithms used resulted from the applicaon of the
system at bridge scale.
The Towards a New Industry installaon quietly explores the
ambient possibilies of new industry, tensegrity systems, and
new media with an exhibion of projects and content related
to AECOM’s 2014 student compeon Urban SOS: Towards
a New Industry. Featuring video integrated in three tensegrity
sculptures, the exhibion curates the four nalist projects as well
as schemes from other program parcipants. The system is a
triad of self-supporng tensegrity towers where the placement
of the structures allows individuals to freely circulate around
each respecve tower, experiencing the layering of materials and
video projecon mul-topicly (Figure 14). The self-supporng
nature of tensegrity towers introduced a unique design and
fabricaon challenge. The formal quality of the sculptures along
with an intelligent use of materials required the collaboraon and
experse of various designers—this integrated design approach
is one which denes the success and spirit of the Urban SOS
The Towards a New Industry installaon allowed the authors to
further rene the system to include adjustable detailing for eld
modicaons (Figure 15). The addion of relavely high-weight
projectors to the system on-site posed a challenge to the form-
nding algorithms that needed to have adjustment capabilies
once installed (Figure 16). A novel adjustable node and strut
system was added to accommodate on-site changes to the
system and loading condions, bringing the RDAT system closer
to the goal of an automacally actuated system.
Inial research parally addresses digital design and fabricaon
issues with tensegrity systems, but more importantly, exposes
the disconnect between ease of digital design and the reali-
es of construcng complex geometric systems. In parcular,
the tensegrity tool provides the designer with a workow that
adjusts the tensegrity structural system based upon user-inputs
while also generang the necessary fabricaon specicaons.
However, successful deployment of a tensegrity structure
remains in the execuon of the assembly methods used outside
of the digital design and digital fabricaon toolbox. Furthermore,
synthec biology research arms the need for physical tesng of
prototype composite materials in order to validate the compu-
taonal analysis. With the existence of an opmized digital
workow, eorts should be focused on developing an interface
for transioning digital design content into manufacturable
objects by adapng exisng fabricaon technologies or designing
new fabricaon soluons.
14 Integrated approach - input from various experse.
16 New challenges driver further innovaons. 17 Future developments.
15 Each installaon allows for addional renements.
100 Rapidly Deployed and Assembled Tensegrity System Anzalone, Bayard, Steenblik
The goal of future work is to contribute to the design, produc-
on and realizaon of innovave projects through connued
research in digital design and fabricaon technologies (Figure
17). Using recent developments in machine learning in the design
process opens extensive opportunies for development of proto-
type versioning in order for the designer to realiscally tease out
and analyze innumerable possible conguraons. This allows
for comprehensive real-me analysis of a greater set of possible
parametric soluons. The research team believes that this
technique will aid in the discovery of unrealized conguraons
potenally with unforeseen benets or applicaons. Addionally,
incorporang sensors into the assembly allows for an automa-
cally actuated or responsive system. Eventually, this may lead to
analycal feedback into the machine learning parameters applied
to future conguraons, and opmal techniques for interacon.
Current developments include generalizing the prism geometry
beyond three struts, expanding the mast structure into a planar
surface and incorporang actuated sensing and programmed
systems into the structure. Currently, the team has been
expanded to include interdisciplinary experse beyond architec-
ture to innovate in the computaonal algorithms and interface,
developing a recongurable MEMS joint and strut system that
will allow tuning and topology adapon (with the Mechanical
Engineering & Industrial Design Department) and a system to
research modes of automated assembly in on-site construc-
on condions (with the Civil Engineering & Construcon
Management Department). Future interdisciplinary research
trajectories include the incorporaon of energy generang and
storage strategies with a robocs industry partner as part of a
building integrated system.
Research Assistants at GSAPP: Brigee Borders, Shaun Salisbury, Sissily
Harrell and Rebecca Riss
Research Assistants at aa64: Vida Chang, Brian Vallario and Ardavan
Collaborave Enes: LaufsED (Dr. Will Laufs), AECOM (Aidan Flaherty
(Project Manager), Travis Frankel, Tyler McMarn, Daniel Lee (Video
Producer) and Peter Zellner.), NYC AIA Center for Architecture, Mio
Guberinic, Costumer.
Fabricaon Team at GSAPP: Nathan Carter, Diego Rodriguez, Vahe
Markosian, Andrew Maier, Jacob Esoco, Michael Schissel, Maya Porath,
Eileen Chen, Michelle Mortensen, Michelle Ku, Arkadiusz Piegdon and
Zachary Maurer, Wade Coon, Taylor Burch
1. IBM has recently released its quantum experience allowing research
iniaves to use it's quantum computer. The introducon of quantum
compung into the mix as we move toward more intelligent machines
creates expansive possibilies yet unknown to humanity. Concevibly
opening the door to soluon sets beyond the current comprehension
of humanity.
Atelier Architecture 64. n.d. hp://
Anzalone, Phillip. 2013. “RDAT: Rapidly Deployable and Assembled
Tensegrity System.” Presentaon at TxA Emerging Design and Technology
Conference, 74th Texas Society of Architects Annual Convenon and
Design Expo. Houston: TxA.
Anzalone, Phillip, and Stephanie Bayard. 2016. “Intelligent Tensegrity
System.” In Facade Tectonics World Congress Proceedings, vol. 2, edited by
Douglas Noble, Karen Kensek, and Shreya Das, 469–76. Los Angeles:
Facade Tectonics Instute.
Brynjolfsson, Erik, and Andrew McAfee. 2016. The Second Machine Age:
Work, Progress, and Prosperity in a Time of Brilliant Technologies. New York:
W. W. Norton & Company.
Bugartz, H.J. 2007. "Analyc and Numeric Invesgaons of Form-Finding
Methods for Tensegrity Structures." Ph.D. diss., Max Planck Instute for
Metals Research.
Bush, Vannevar. 1945. “As We May Think." The Atlanc, July 1945.
Clarke, Cory, and Phillip Anzalone. 2006. “Systems and Methods
for Construcon of Space-truss Structures.” US Patent Applicaon
20060254200 A1, led November 18, 2005.
Copps, David. 2016. “Augmented Intelligence at Work: Presented by
Brainspace.” Filmed 23 May 2016 at MIT Technology Review Events,
MIT, Cambridge, MA. Video. hps://
Engelbart, Douglas C. 1962. “Augmenng Human Intellect: A Conceptual
Framework” Report for Air Force Oce of Scienc Research, AFOSR-
3223. Reproduced at Doug Engelbart Instute website, hp://www.
Fuller, R. Buckminster. 1975. Synergecs: Exploraons in the Geometry of
Thinking. London: Collier-Macmillan.
Oppenheim, Irving J., and William O. Williams. 1997. "Mechanics of
Tensegrity Prisms." In Proceedings of the 14th Internaonal Symposium on
Automaon and Robocs in Construcon, 473–79. Pisburgh, PA: ISARC.
Pinaud, Jean-Paul, Milenko Masic, and Robert E. Skelton. 2003. "Path
Planning for the Deployment of Tensegrity Structures." Proceedings of
SPIE: Smart Structures and Materials 5049: 436–47.
Schumacher, Patrik. 2016. “Design Parameters to Parametric Design.” In
The Routledge Companion for Architecture Design and Pracce: Established
and Emerging Trends, edited by Mitra Kanaani and Dak Kopec. New York:
Zhang, J. Y., M. Oshaki, and Y. Kanno. 2006. "A Direct Approach to Design
of Geometry and Forces of Tensegrity Systems." Internaonal Journal of
Solids and Structures 43 (7-8): 2260–78.
Zhang, Marvin, Xinyang Geng, Jonathan Bruce, Ken Caluwaerts,
Massimo Vespignani, Vytas SunSpiral, Pieter Abbeel, Sergey Levine.
2017. "Deep Reinforcement Learning for Tensegrity Robot Locomoon."
arXiv:1609.09049v3 [cs.RO] 8 Mar 2017
All drawings and images by the authors.
Phillip Anzalone is a Professor of Architectural Technology at NYC
College of Technology as well as a praccing Architect as Principal at
Atelier Architecture 64. Phillip’s research includes the applicaon of
science and technology to architectural design problems. Phillip is the
lead research and development faculty for the NYCCT Architecture
department’s Computer Numerically Controlled and Roboc Fabricaon
Laboratory. Phillip has a BPA Architecture from SUNY Bualo and a
MArch from Columbia University.
Stephanie Bayard is an Adjunct Associate Professor of Architecture
at Pra Instute, and a Principal at Atelier Architecture 64. Stephanie
previously worked for Bernard Tschumi Architects and internaon-
ally in Milan, Paris and New York. She has taught at Parsons The New
School for Design, Ohio State University and Rensselaer Polytechnic
Instute. Stephanie teaches design studios and housing seminars at Pra
Instutes's Graduate Architecture + Urban Design Program. Stephanie
received her Architecture Diploma with disncon from Paris La Villee,
France, and her MsAAD from Columbia University.
Ralph S. Steenblik is an adjunct professor at CUNY, has taught at Pra
Instute and NJIT, and has made signicant contribuons at mulple
renowned architecture oces, including Asymptote Architecture and Pelli
Clarke Pelli. Most recently his work was published in "Project Ancipaon"
2016, and he spoke at AIANY Design Conference 2016, and at an
UNESCO sponsored symposium on Ancipaon held in Trento, Italy. He
holds a masters from SCI-Arc.
Full-text available
Robustness, compactness, and portability of tensegrity robots make them suitable candidates for locomotion on unknown terrains. Despite these advantages, challenges remain relating to ease of fabrication, shape morphing (packing-unpacking), and locomotion capabilities. The paper introduces a design methodology for fabricating tensegrity robots of varying morphologies with modular components. The design methodology utilizes perforated links, coplanar (2D) alignment of components and individual cable tensioning to achieve a 3D tensegrity structure. These techniques are utilized to fabricate prism (three-link) tensegrity structures, followed by tensegrity robots in icosahedron (six-link), and shpericon (curved two-link) formation. The methodology is used to explore different robot morphologies that attempt to minimize structural complexity (number of elements) while facilitating smooth locomotion (impact between robot and surface). Locomotion strategies for such robots involve altering the position of center-of-mass (referred to as internal mass shifting) to induce “tip-over.” As an example, a sphericon formation comprising of two orthogonally placed circular arcs with conincident center illustrates smooth locomotion along a line (one degree of freedom). The design of curved links of tensegrity mechanisms facilitates continuous change of the point of contact (along the curve) that results from the tip-over. This contrasts to the sudden and piece-wise continuous change for the case of robots with traditional straight links which generate impulse reaction forces during locomotion. The two resulting robots—the Icosahedron and the Sphericon Tensegrity Robots—display shape morphing (packing-unpacking) capabilities and achieve locomotion through internal mass-shifting. The presented static equilibrium analysis of sphericon with mass is the first step in the direction of dynamic locomotion control of these curved link robots.
Full-text available
Tensegrity structures consist of tendons (in tension) and bars (in compression). Tendons are strong, light, and foldable, so tensegrity structures have the potential to be light but strong and deployable. Pulleys, NiTi wire, or other actuators to selectively tighten some strings on a tensegrity structure can be used to control its shape. This article describes the problem of asymmetric reconfiguration of tensegrity structures and poses one method of finding the open loop control law for tendon lengths to accomplish the desired geometric reconfiguration. In addition, a practical hardware experiment displays the readiness and feasibility of the method to accomplish shape control of the structure.
Tensegrity robots, composed of rigid rods connected by elastic cables, have a number of unique properties that make them appealing for use as planetary exploration rovers. However, control of tensegrity robots remains a difficult problem due to their unusual structures and complex dynamics. In this work, we show how locomotion gaits can be learned automatically using a novel extension of mirror descent guided policy search (MDGPS) applied to periodic locomotion movements, and we demonstrate the effectiveness of our approach on tensegrity robot locomotion. We evaluate our method with real-world and simulated experiments on the SUPERball tensegrity robot, showing that the learned policies generalize to changes in system parameters, unreliable sensor measurements, and variation in environmental conditions, including varied terrains and a range of different gravities. Our experiments demonstrate that our method not only learns fast, power-efficient feedback policies for rolling gaits, but that these policies can succeed with only the limited onboard sensing provided by SUPERball's accelerometers. We compare the learned feedback policies to learned open-loop policies and hand-engineered controllers, and demonstrate that the learned policy enables the first continuous, reliable locomotion gait for the real SUPERball robot.
In the process of designing a tensegrity system, some constraints are usually introduced for geometry and/or forces to ensure uniqueness of the solution, because the tensegrity systems are underdetermined in most cases. In this paper, a new approach is presented to enable designers to specify independent sets of axial forces and nodal coordinates consecutively, under the equilibrium conditions and the given constraints, to satisfy the distinctly different requirements of architects and structural engineers. The proposed method can be used very efficiently for practical applications because only linear algebraic equations are to be solved, and no equation of kinematics or material property is needed. Some numerical examples are given to show not only efficiency of the proposed method but also its ability of searching new configurations.
Presentation at TxA Emerging Design and Technology Conference, 74th Texas Society of Architects Annual Convention and Design Expo
  • Phillip Anzalone
Anzalone, Phillip. 2013. "RDAT: Rapidly Deployable and Assembled Tensegrity System." Presentation at TxA Emerging Design and Technology Conference, 74th Texas Society of Architects Annual Convention and Design Expo. Houston: TxA.
Intelligent Tensegrity System
  • Phillip Anzalone
  • Stephanie Bayard
Anzalone, Phillip, and Stephanie Bayard. 2016. "Intelligent Tensegrity System." In Facade Tectonics World Congress Proceedings, vol. 2, edited by Douglas Noble, Karen Kensek, and Shreya Das, 469-76. Los Angeles: Facade Tectonics Institute.
The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies
  • Erik Brynjolfsson
  • Andrew Mcafee
Brynjolfsson, Erik, and Andrew McAfee. 2016. The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies. New York: W. W. Norton & Company.
Analytic and Numeric Investigations of Form-Finding Methods for Tensegrity Structures
  • H J Bugartz
Bugartz, H.J. 2007. "Analytic and Numeric Investigations of Form-Finding Methods for Tensegrity Structures." Ph.D. diss., Max Planck Institute for Metals Research.