Recent years show an increasing interest in flexible robots due to their adaptability merits. This paper introduces a novel set of hyper-redundant flexible robots which we call actuated flexible manifold (AFM). The AFM is a two-dimensional hyper-redundant grid surface embedded in 2 or 3. Theoretically, such a mechanism can be manipulated into any continuous smooth function. We introduce the mathematical framework for the kinematics of an AFM. We prove that for a nonsingular configuration, the number of degrees of freedom (DOF) of an AFM is simply the number of its grid segments. We also show that for a planar rectangular grid, every nonsingular configuration that is also energetically stable is isolated. We show how to calculate the forward and inverse kinematics for such a mechanism. Our analysis is also applicable for three-dimensional hyper-redundant structures as well. Finally, we demonstrate our solution on some actuated flexible grid-shaped surfaces.

References

References
1.
Shvalb
,
N.
,
Moshe
,
B. B.
, and
Medina
,
O.
,
2013
, “
A Real-Time Motion Planning Algorithm for a Hyper-Redundant Set of Mechanisms
,”
Robotica
,
31
(
8
), pp.
1327
1335
.
2.
Shapiro
,
A.
,
Greenfield
,
A.
, and
Choset
,
H.
,
2007
, “
Frictional Compliance Model Development and Experiments for Snake Robot Climbing
,”
IEEE International Conference on Robotics and Automation
,
Rome, Italy
, pp.
574
579
.
3.
Ota
,
T.
,
Degani
,
A.
,
Zubiate
,
B.
,
Wolf
,
A.
,
Choset
,
H.
,
Schwartzman
,
D.
, and
Zenati
,
M. A.
,
2006
, “
Epicardial Atrial Ablation Using a Novel Articulated Robotic Medical Probe Via a Percutaneous Subxiphoid Approach
,”
Innovations
,
1
(
6
), pp.
335
340
.
4.
Yamada
,
H.
,
Takaoka
,
S.
, and
Hirose
,
S.
,
2013
, “
A Snake-Like Robot for Real-World Inspection Applications (The Design and Control of a Practical Active Cord Mechanism)
,”
Adv. Rob.
,
27
(
1
), pp.
47
60
.
5.
Chirikjian
,
G. S.
,
1997
, “
Inverse Kinematics of Binary Manipulators Using a Continuum Model
,”
J. Intell. Rob. Syst.
,
19
(
1
), pp.
5
22
.
6.
Hamerly
,
G.
, and
Elkan
,
C.
,
2002
, “
Alternatives to the k-Means Algorithm That Find Better Clusterings
,”
11th International Conference on Information and Knowledge Management
,
ACM
, pp.
600
607
.
7.
Kim
,
S.
,
Laschi
,
C.
, and
Trimmer
,
B.
,
2013
, “
Soft Robotics: A Bioinspired Evolution in Robotics
,”
Trends Biotechnol.
,
31
(
5
), pp.
287
294
.
8.
Onal
,
C. D.
,
Chen
,
X.
,
Whitesides
,
G. M.
, and
Rus
,
D.
,
2011
, “
Soft Mobile Robots With On-Board Chemical Pressure Generation
,”
15th International Symposium on Robotics Research
(ISRR), Flagstaff, AZ, Aug. 28–Sept. 1.
9.
Shepherd
,
R.
,
Ilievski
,
F.
,
Choi
,
W.
,
Morin
,
S.
,
Stokes
,
A.
,
Mazzeo
,
A.
,
Chen
,
X.
,
Wang
,
M.
, and
Whitesides
,
G.
,
2011
, “
Multigait Soft Robot
,”
Proc. Natl. Acad. Sci.
,
108
(
51
), pp.
20400
20403
.
10.
Kim
,
S.
,
Hawkes
,
E.
,
Choy
,
K.
,
Joldaz
,
M.
,
Foleyz
,
J.
, and
Wood
,
R.
,
2009
, “
Micro Artificial Muscle Fiber Using NiTi Spring for Soft Robotics
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS 2009
),
St. Louis, MO
, Oct. 10–15, pp.
2228
2234
.
11.
Laschi
,
C.
,
Cianchetti
,
M.
,
Mazzolai
,
B.
,
Margheri
,
L.
,
Follador
,
M.
, and
Dario
,
P.
,
2012
, “
Soft Robot Arm Inspired by the Octopus
,”
Adv. Rob.
,
26
(
7
), pp.
709
727
.
12.
Calisti
,
M.
,
Giorelli
,
M.
,
Levy
,
G.
,
Mazzolai
,
B.
,
Hochner
,
B.
,
Laschi
,
C.
, and
Dario
,
P.
,
2011
, “
An Octopus-Bioinspired Solution to Movement and Manipulation for Soft Robots
,”
Bioinspiration Biomimetics
,
6
(
3
), p.
036002
.
13.
Zheng
,
T.
,
Branson
,
D. T.
,
Guglielmino
,
E.
,
Kang
,
R.
,
Cerda
,
G. A. M.
,
Cianchetti
,
M.
,
Follador
,
M.
,
Godage
, I
. S.
, and
Caldwell
,
D. G.
,
2013
, “
Model Validation of an Octopus Inspired Continuum Robotic Arm for Use in Underwater Environments
,”
ASME J. Mech. Rob.
,
5
(
2
), p.
021004
.
14.
Trimmer
,
B.
,
2014
, “
A Journal of Soft Robotics: Why Now?
,”
Soft Rob.
,
1
(
1
), pp.
1
4
.
15.
Walker
,
I.
,
Dawson
,
D.
,
Flash
,
T.
,
Grasso
,
F.
,
Hanlon
,
R.
,
Hochner
,
B.
,
Kier
,
W.
,
Pagano
,
C.
,
Rahn
,
C.
, and
Zhang
,
Q.
,
2005
, “
Continuum Robot Arms Inspired by Cephalopods
,”
Proc. SPIE
,
5804
, pp.
303
314
.
16.
Trivedi
,
D.
,
Rahn
,
C. D.
,
Kier
,
W. M.
, and
Walker
,
I. D.
,
2008
, “
Soft Robotics: Biological Inspiration, State of the Art, and Future Research
,”
Appl. Bionics Biomech.
,
5
(
3
), pp.
99
117
.
17.
Reddy
,
J. N.
,
2007
,
Theory and Analysis of Elastic Plates and Shells
,
CRC Press
, Boca Raton, FL.
18.
Ali
,
S.
,
Boyer
,
F.
, and
Porez
,
M.
,
2011
, “
Terrestrial Locomotion Modeling Bio-Inspired by Elongated Animals
,”
Procedia Comput. Sci.
,
7
, pp.
317
319
.
19.
Leyendecker
,
S.
, and
Kanso
,
E.
,
2009
, “
Locomotion of a Submerged Cosserat Beam
,”
ASME
Paper No. DETC2009-87198.
20.
Spillmann
,
J.
, and
Teschner
,
M.
,
2009
, “
Cosserat Nets
,”
IEEE Trans. Visualization Comput. Graph.
,
15
(
2
), pp.
325
338
.
21.
Popov
,
E.
,
2001
, “
Geometrical Modeling of Tent Fabric Structures With the Stretched Grid Method
,”
11th International Conference on Computer Graphics and Vision (GRAPHICON2001), UNN, Nizhny Novgorod
,
Russia
, Sept. 10–17, pp.
138
143
.
22.
Blanc
,
D.
, and
Shvalb
,
N.
,
2012
, “
Generic Singular Configurations of Linkages
,”
Topol. Appl.
,
159
(
3
), pp.
877
890
.
23.
Kelley
,
J. L.
, and
Stone
,
M.
,
1955
,
General Topology
, Vol.
233
,
van Nostrand
,
Princeton, NJ
.
24.
Merlet
,
J.-P.
,
2012
,
Parallel Robots
,
Springer Science & Business Media
,
New York
.
25.
Warner
,
S.
,
1990
,
Modern Algebra
,
Dover Publications
,
New York
.
26.
Blanc
,
D.
, and
Shvalb
,
N.
,
2011
, “
Actuations of Linkages and Their Singularities
,”
Ariel University
. Ariel, Israel, epub.
27.
Murray
,
R. M.
,
Li
,
Z.
,
Sastry
,
S. S.
, and
Sastry
,
S. S.
,
1994
,
A Mathematical Introduction to Robotic Manipulation
,
CRC Press
,
Boca Raton, FL
.
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