A screw-based formulation of the kinematics, differential kinematics, and statics of soft manipulators is presented, which introduces the soft robotics counterpart to the fundamental geometric theory of robotics developed since Brockett's original work on the subject. As far as the actuation is concerned, the embedded tendon and fluidic actuation are modeled within the same screw-based framework, and the screw-system to which they belong is shown. Furthermore, the active and passive motion subspaces are clearly differentiated, and guidelines for the manipulable and force-closure conditions are developed. Finally, the model is validated through experiments using the soft manipulator for minimally invasive surgery STIFF-FLOP.

References

1.
Webster
,
R. J.
, and
Jones
,
B. A.
,
2010
, “
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
,”
Int. J. Rob. Res.
,
29
(
13
), pp.
1661
1683
.
2.
Walker
,
I. D.
,
2013
, “
Continuous Backbone ‘Continuum’ Robot Manipulators
,”
ISRN Rob.
,
2013
, pp.
1
19
.
3.
Jones
,
B. A.
, and
Walker
,
I. D.
,
2006
, “
Kinematics for Multisection Continuum Robots
,”
IEEE Trans. Rob.
,
22
(
1
), pp.
43
55
.
4.
Neppalli
,
S.
,
Csencsits
,
M. A.
,
Jones
,
B. A.
, and
Walker
,
I. D.
,
2009
, “
Closed-Form Inverse Kinematics for Continuum Manipulators
,”
Adv. Rob.
,
23
(
15
), pp.
2077
2091
.
5.
Rucker
,
D. C.
, and
Webster
,
R. J.
,
2011
, “
Statics and Dynamics of Continuum Robots With General Tendon Routing and External Loading
,”
IEEE Trans. Rob.
,
27
(
6
), pp.
1033
1044
.
6.
Godage
,
I. S.
,
Medrano-Cerda
,
G. A.
,
Branson
,
D. T.
,
Guglielmino
,
E.
, and
Caldwell
,
D. G.
,
2015
, “
Dynamics for Variable Length Multisection Continuum Arms
,”
Int. J. Rob. Res.
,
35
(6), pp. 695–722.
7.
Camarillo
,
D. B.
,
Milne
,
C. F.
,
Carlson
,
C. R.
,
Zinn
,
M. R.
, and
Salisbury
,
J. K.
,
2008
, “
Mechanics Modeling of Tendon-Driven Continuum Manipulators
,”
IEEE Trans. Rob.
,
24
(
6
), pp.
1262
1273
.
8.
Polygerinos
,
P.
,
Wang
,
Z.
,
Overvelde
,
J. T. B.
,
Galloway
,
K. C.
,
Wood
,
R. J.
,
Bertoldi
,
K.
, and
Walsh
,
C. J.
,
2015
, “
Modeling of Soft Fiber-Reinforced Bending Actuators
,”
IEEE Trans. Rob.
,
31
(
3
), pp.
778
789
.
9.
Marchese
,
A. D.
, and
Rus
,
D.
,
2015
, “
Design, Kinematics, and Control of a Soft Spatial Fluidic Elastomer Manipulator
,”
Int. J. Rob. Res.
,
35
(7), pp. 840–869.
10.
Bajo
,
A.
, and
Simaan
,
N.
,
2016
, “
Hybrid Motion/Force Control of Multi-Backbone Continuum Robots
,”
Int. J. Rob. Res.
,
35
(
4
), pp.
422
434
.
11.
Renda
,
F.
,
Cacucciolo
,
V.
,
Dias
,
J.
, and
Seneviratne
,
L.
,
2016
, “
Discrete Cosserat Approach for Soft Robot Dynamics: A New Piece-Wise Constant Strain Model With Torsion and Shears
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Daejeon, South Korea, Oct. 9–14, pp.
5495
5502
.
12.
Brockett
,
R. W.
,
1984
, “
Robotic Manipulators and the Product of Exponentials Formula
,”
Mathematical Theory of Networks and Systems
,
Springer
,
Berlin
, pp.
120
129
.
13.
Renda
,
F.
,
Giorelli
,
M.
,
Calisti
,
M.
,
Cianchetti
,
M.
, and
Laschi
,
C.
,
2015
, “
Dynamic Model of a Multibending Soft Robot Arm Driven by Cables
,”
IEEE Trans. Rob.
,
30
(
5
), pp.
1109
1122
.
14.
Arezzo
,
A.
,
Mintz
,
Y.
,
Allaix
,
M. E.
,
Gerboni
,
G.
,
Brancadoro
,
M.
,
Cianchetti
,
M.
,
Menciassi
,
A.
,
Wurdemann
,
H.
,
Noh
,
Y.
,
Fras
,
Y.
,
Glowka
,
J.
,
Nawrat
,
Z.
,
Cassidy
,
G.
,
Walker
,
R.
,
Arolfo
,
S.
,
Bonino
,
M.
,
Morino
,
M.
, and
Althoefer
,
K.
, 2017, “
Total Mesorectal Excision Using a Soft and Flexible Robotic Arm: A Feasibility Study in Cadaver Models
,”
Surg. Endoscopy
,
31
(1), pp. 264–273.
15.
Edwards
,
C. H.
, and
Penney
,
D. E.
,
2013
, “
Differential Equations and Linear Algebra
,”
Always Learning
,
Pearson Education Limited
, Harlow, England.
16.
Selig
,
J. M.
,
2007
, “
Geometric Fundamentals of Robotics
,”
Monographs in Computer Science
,
Springer
,
New York
.
17.
Bullo
,
F.
, and
Murray
,
R. M.
,
1995
, “
Proportional Derivative (PD) Control on the Euclidean Group
,”
European Control Conference
(
ECC
), Rome, Italy, Sept. 5–8, pp.
1091
1097
.
18.
Abate
,
M.
, and
Tovena
,
F.
,
2011
, “
Geometria Differenziale
,”
UNITEXT
,
Springer Milan
, Milan, Italy.
19.
Murray
,
R. M.
,
Li
,
Z.
, and
Sastry
,
S. S.
,
1994
,
A Mathematical Introduction to Robotic Manipulation
,
Taylor & Francis
, CRC Press, Boca Raton, FL.
20.
Boyer
,
F.
, and
Renda
,
F.
,
2016
, “
Poincaré's Equations for Cosserat Media: Application to Shells
,”
J. Nonlinear Sci.
,
27
(1), pp. 1–44.
21.
Featherstone
,
R.
,
2008
,
Rigid Body Dynamics Algorithms
,
Springer
, New York.
22.
Gibson
,
C. G.
, and
Hunt
,
K. H.
,
1990
, “
Geometry of Screw Systems—1: Screws: Genesis and Geometry
,”
Mech. Mach. Theory
,
25
(
1
), pp.
1
10
.
23.
Wu
,
Y.
,
Lowe
,
H.
,
Carricato
,
M.
, and
Li
,
Z.
,
2016
, “
Inversion Symmetry of the Euclidean Group: Theory and Application to Robot Kinematics
,”
IEEE Trans. Rob.
,
32
(
2
), pp.
312
326
.
24.
Brockett
,
R. W.
,
1999
, “
Explicitly Solvable Control Problems With Nonholonomic Constraints
,”
38th IEEE Conference on Decision and Control
(
CDC
), Phoenix, AZ, Dec. 7–10, pp.
13
16
.
25.
Selig
,
J. M.
,
2015
, “
A Class of Explicitly Solvable Vehicle Motion Problems
,”
IEEE Trans. Rob.
,
31
(
3
), pp.
766
777
.
You do not currently have access to this content.