Abstract

Structures and actuation systems need to be closely integrated together in the future to create faster, more efficient, lightweight dynamic machines. Such actuated structures would be used for morphing aircraft wings, lightweight actuated space structures, or in robotics. This approach requires actuators to be distributed through the structure. A tensegrity structure is a very promising candidate for this future integration due to its potentially excellent stiffness and strength-to-weight ratio, and the inherent advantage of being a multi-element structure into which actuators can be embedded. This paper presents methods for analysis of the structure geometry, for closed-loop motion control, and includes experimental results for a structure actuated by lightweight pneumatic muscles. In a practical morphing tensegrity structure, it cannot be assumed that tension and compression members always meet at a point. Thus, a form-finding method has been developed to find stable geometries and determine stiffness properties for tensegrity structures with nodes of finite dimension. An antagonistic multi-axis control scheme has been developed for the shape position and motion control. In the experimental actuated tensegrity system presented the pneumatic muscles are controlled by on-off valves, for which a dead-band switching controller is designed based on a new stability criterion. The experimental system demonstrates accurate control of shape change while maintaining a desired level of internal preload in a stiff structure, showing considerable promise for future lightweight dynamic machines.

References

References
1.
Barbarino
,
S.
,
Bilgen
,
O.
,
Ajaj
,
R. M.
,
Friswell
,
M. I.
, and
Inman
,
D. J.
,
2011
, “
A Review of Morphing Aircraft
,”
J. Intell. Mater. Syst. Struct.
,
22
(
9
), pp.
823
877
.10.1177/1045389X11414084
2.
Miura
,
K.
,
1984
, “
Design and Operation of a Deployable Truss Structure
,”
18th Aerospace Mechanisms Symposium
,
Goddard Space Flight Center
,
Greenbelt, MD
, May, pp.
49
63
.
3.
Miura
,
K.
,
Furuya
,
H.
, and
Suzuki
,
K.
,
1985
, “
Variable Geometry Truss and Its Application to Deployable Truss and Space Crane Arm
,”
Acta Astronaut.
,
12
(
7–8
), pp.
599
607
.10.1016/0094-5765(85)90131-6
4.
Ramrakhyani
,
D. S.
,
Lesieutre
,
G. A.
,
Frecker
,
M. I.
, and
Bharti
,
S.
,
2005
, “
Aircraft Structural Morphing Using Tendon-Actuated Compliant Cellular Trusses
,”
J. Aircr.
,
42
(
6
), pp.
1614
1620
.10.2514/1.9984
5.
Sofla
,
A. Y. N.
,
Elzey
,
D. M.
, and
Wadley
,
H. N. G.
,
2009
, “
Shape Morphing Hinged Truss Structures
,”
Smart Mater. Struct.
,
18
(
6
), p.
065012
.10.1088/0964-1726/18/6/065012
6.
Sofla
,
A. Y. N.
,
Elzey
,
D. M.
, and
Wadley
,
H. N. G.
,
2007
, “
A Rotational Joint for Shape Morphing Space Truss Structures
,”
Smart Mater. Struct.
,
16
(
4
), pp.
1277
1284
.10.1088/0964-1726/16/4/040
7.
Moosavian
,
A.
,
Xi
,
F. F.
, and
Hashemi
,
S. M.
,
2013
, “
Design and Motion Control of Fully Variable Morphing Wings
,”
J. Aircr.
,
50
(
4
), pp.
1189
1201
.10.2514/1.C032127
8.
Sultan
,
C.
,
2009
, “
Tensegrity: Sixty Years of Art, Science, and Engineering
,”
Adv. Appl. Mech
,
43
, pp.
69
145
.10.1016/S0065-2156(09)43002-3
9.
Fuller
,
R. B.
,
1962
, “
Tensile-Integrity Structures
,” U.S. Patent No. 3 063 521.
10.
Emmerich
,
D. G.
,
1996
, “
Emmerich on Self-Tensioning Structures
,”
Int. J. Space Struct.
,
11
(
1–2
), pp.
29
36
.10.1177/026635119601-205
11.
Zhang
,
J. Y.
,
Guest
,
S. D.
, and
Ohsaki
,
M.
,
2009
, “
Symmetric Prismatic Tensegrity Structures—Part II: Symmetry-Adapted Formulations
,”
Int. J. Solids Struct.
,
46
(
1
), pp.
15
30
.10.1016/j.ijsolstr.2008.07.035
12.
Zhang
,
J. Y.
,
Guest
,
S. D.
,
Connelly
,
R.
, and
Ohsaki
,
M.
,
2010
, “
Dihedral ‘Star’ Tensegrity Structures
,”
Int. J. Solids Struct.
,
47
(
1
), pp.
1
9
.10.1016/j.ijsolstr.2009.05.018
13.
Koohestani
,
K.
, and
Guest
,
S. D.
,
2013
, “
A New Approach to the Analytical and Numerical Form-Finding of Tensegrity Structures
,”
Int. J. Solids Struct.
,
50
(
19
), pp.
2995
3007
.10.1016/j.ijsolstr.2013.05.014
14.
Koohestani
,
K.
,
2013
, “
A Computational Framework for the Form-Finding and Design of Tensegrity Structures
,”
Mech. Res. Commun.
,
54
, pp.
41
49
.10.1016/j.mechrescom.2013.09.010
15.
Tran
,
H. C.
, and
Lee
,
J.
,
2013
, “
Form-Finding of Tensegrity Structures Using Double Singular Value Decomposition
,”
Eng. Comput.
,
29
(
1
), pp.
71
86
.10.1007/s00366-011-0245-7
16.
Zhang
,
L. Y.
,
Li
,
Y.
,
Cao
,
Y. P.
, and
Feng
,
X. Q.
,
2014
, “
Stiffness Matrix Based Form-Finding Method of Tensegrity Structures
,”
Eng. Struct.
,
58
, pp.
36
48
.10.1016/j.engstruct.2013.10.014
17.
Tibert
,
G.
, and
Pellegrino
,
S.
,
2003
, “
Review of Form-Finding Methods for Tensegrity Structures
,”
Int. J. Space Struct.
,
18
(
4
), pp.
209
223
.10.1260/026635103322987940
18.
Skelton
,
R. E.
, and
Oliveira
,
M. C.
,
2009
,
Tensegrity Systems
, 1st ed.,
Springer US
,
Boston, MA
.
19.
Plummer
,
A.
, and
Lai
,
G.
,
2015
, “
New Concepts for Parallel Kinematic Mechanisms Using Fluid Actuation
,”
Seventh International Conference on Fluid Power and Mechatronics
, Harbin, China, Aug., Keynote Paper.
20.
Djouadi
,
S.
,
Motro
,
R.
,
Pons
,
J. C.
, and
Crosnier
,
B.
,
1998
, “
Active Control of Tensegrity Systems
,”
ASCE J. Aerosp. Eng.
,
11
(
2
), pp.
37
44
.10.1061/(ASCE)0893-1321(1998)11:2(37)
21.
Aldrich
,
J. B.
,
Skelton
,
R. E.
, and
Kreutz-Delgado
,
K.
,
2003
, “
Control Synthesis for a Class of Light and Agile Robotic Tensegrity Structures
,”
Proceedings of the 2003 American Control Conference
, Vol.
1–6
,
New York
, June 4–6, pp.
5245
5251
.10.1109/ACC.2003.1242560
22.
Sultan
,
C.
,
Corless
,
M.
, and
Skelton
,
R. E.
,
2000
, “
Tensegrity Flight Simulator
,”
J. Guid., Control, Dyn.
,
23
(
6
), pp.
1055
1064
.10.2514/2.4647
23.
Bel Hadj Ali
,
N.
, and
Smith
,
I. F. C.
,
2010
, “
Dynamic Behavior and Vibration Control of a Tensegrity Structure
,”
Int. J. Solids Struct.
,
47
(
9
), pp.
1285
1296
.10.1016/j.ijsolstr.2010.01.012
24.
Beck
,
H.
, and
Cooper
,
J.
,
2012
,
Kurilpa Bridge
,
Images Publishing Group
,
Melbourne, Australia
.
25.
Benaroya
,
H.
,
1993
, “
Tensile-Integrity Structures for the Moon
,”
ASME Appl. Mech. Rev.
,
46
(
6
), pp.
326
335
.10.1115/1.3120361
26.
Tibert
,
A. G.
, and
Pellegrino
,
S.
,
2002
, “
Deployable Tensegrity Reflectors for Small Satellites
,”
J. Spacecr. Rockets
,
39
(
5
), pp.
701
709
.10.2514/2.3867
27.
Caluwaerts
,
K.
,
Despraz
,
J.
,
Işçen
,
A.
,
Sabelhaus
,
A. P.
,
Bruce
,
J.
,
Schrauwen
,
B.
, and
SunSpiral
,
V.
,
2014
, “
Design and Control of Compliant Tensegrity Robots Through Simulation and Hardware Validation
,”
J. R. Soc. Interface
,
11
(
98
), p.
20140520
.10.1098/rsif.2014.0520
28.
Toklu
,
Y. C.
,
Temur
,
R.
,
Bekdas
,
G.
, and
Uzun
,
F.
,
2013
, “
Space Applications of Tensegric Structures
,”
Proceedings of Sixth International Conference on Recent Advances in Space Technologies
, Istanbul, Turkey, June 12–14, pp.
29
32
.
29.
Moored
,
K. W.
, and
Bart-Smith
,
H.
,
2007
, “
The Analysis of Tensegrity Structures for the Design of a Morphing Wing
,”
ASME J. Appl. Mech.
,
74
(
4
), pp.
668
676
.10.1115/1.2424718
30.
Moored
,
K. W.
, and
Bart-Smith
,
H.
,
2009
, “
Investigation of Clustered Actuation in Tensegrity Structures
,”
Int. J. Solids Struct.
,
46
(
17
), pp.
3272
3281
.10.1016/j.ijsolstr.2009.04.026
31.
Salisbury
,
K.
,
Townsend
,
W.
,
Ebrman
,
B.
, and
DiPietro
,
D.
,
1988
, “
Preliminary Design of a Whole-Arm Manipulation System (WAMS)
,”
IEEE International Conference on Robotics and Automation
, Vol.
1
, Philadelphia, PA, Apr. 24–29, pp.
254
260
.10.1109/ROBOT.1988.12057
32.
Bicchi
,
A.
, and
Tonietti
,
G.
,
2004
, “
Fast and ‘Soft-Arm’ Tactics
,”
IEEE Rob. Autom. Mag.
,
11
, pp.
22
33
.10.1109/MRA.2004.1310939
33.
He
,
J.
,
Liu
,
R.
,
Wang
,
K.
, and
Shen
,
H.
,
2012
, “
The Mechanical Design of Snake-Arm Robot
,”
IEEE Tenth International Conference on Industrial Informatics
, Beijing, China, July 25–27, pp.
758
761
.10.1109/INDIN.2012.6301169
34.
Buckingham
,
R.
, and
Graham
,
A.
,
2005
, “
Snaking Around in a Nuclear Jungle
,”
Ind. Robot Int. J.
,
32
(
2
), pp.
120
127
.10.1108/01439910510582246
35.
Bloss
,
R.
,
2011
, “
Robotic Snake Arm Reaches Into Radioactive Regions
,”
Ind. Robot Int. J.
,
38
, pp.
200
201
.10.1108/ir.2011.04938baf.004
36.
Sultan
,
C.
,
2013
, “
Stiffness Formulations and Necessary and Sufficient Conditions for Exponential Stability of Prestressable Structures
,”
Int. J. Solids Struct.
,
50
(
14–15
), pp.
2180
2195
.10.1016/j.ijsolstr.2013.03.005
37.
Craig
,
J. J.
,
2018
,
Introduction to Robotics: Mechanics and Control
, 4th ed.,
Pearson
,
London, UK
.
38.
Guest
,
S.
,
2006
, “
The Stiffness of Prestressed Frameworks: A Unifying Approach
,”
Int. J. Solids Struct
,
43
(
3–4
), pp.
842
854
.10.1016/j.ijsolstr.2005.03.008
39.
Lai
,
G.
,
Plummer
,
A. R.
,
Cleaver
,
D. J.
, and
Zhou
,
H.
,
2016
, “
Parallel Kinematic Mechanisms for Distributed Actuation of Future Structures
,”
J. Phys.: Conf. Ser.
,
744
, p.
012169
.10.1088/1742-6596/744/1/012169
40.
Lai
,
G.
,
2017
, “
Distributed Actuation and Control for Morphing Structures
,” Ph.D. thesis,
University of Bath
,
Bath, UK
.
41.
Plummer
,
A.
,
2010
, “
A General Co-Ordinate Transformation Framework for Multi-Axis Motion Control With Applications in the Testing Industry
,”
Control Eng. Pract.
,
18
(
6
), pp.
598
607
.10.1016/j.conengprac.2010.02.015
42.
Lai
,
G.
, and
Plummer
,
A.
,
2017
, “
Relay Control of a Morphing Tensegrity Structure With Distributed Pneumatic Actuation
,”
The Nineth International Conference on Fluid Power Transmission and Control
, Hangzhou, China, Apr. 11–13, Paper No. PB7.
43.
Dougherty
,
T.
,
1995
,
Systems and Control: An Introduction to Linear, Sampled an Non-Linear Systems
,
World Scientific
,
Singapore
.
44.
Lai
,
G.
,
Plummer
,
A.
, and
Cleaver
,
D.
, “
The Development and Validation of a Dynamic Model for a Tensegrity Structure With Distributed Actuation
,”
Proc. Inst. Mech. Eng. Part I
, In press.
45.
Tondu
,
B.
,
2012
, “
Modelling of the McKibben Artificial Muscle: A Review
,”
J. Intell. Mater. Syst. Struct.
,
23
(
3
), pp.
225
253
.10.1177/1045389X11435435
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