Abstract

Flexible continuum manipulators (FCMs) are gaining importance because of their maneuverability and pliability in confined and complex spaces, where rigid link manipulators underperform. However, the dynamic behavior and control of the FCM are quite challenging due to its complex nonlinear behavior. In this study, a finite element-based dynamic model framework is derived that accounts for the geometric nonlinearities and inertial effects. An experimental setup of tendon-driven FCM, consisting of a flexible backbone, is developed to validate the model. The modal analysis of the model is in agreement with the analytical solutions, with less than 10% error. The model is also validated for various loading conditions on the tip-actuated tendon-driven FCM. The steady-state tip position predictions are within 15% of the ground truth.

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References

1.
Mattei
,
T. A.
,
Rodriguez
,
A. H.
,
Sambhara
,
D.
, and
Mendel
,
E.
,
2014
, “
Current State-of-the-Art and Future Perspectives of Robotic Technology in Neurosurgery
,”
Neurosurgical Rev.
,
37
(
3
), pp.
357
366
.
2.
Simaan
,
N.
,
Xu
,
K.
,
Wei
,
W.
,
Kapoor
,
A.
,
Kazanzides
,
P.
,
Taylor
,
R.
, and
Flint
,
P.
,
2009
, “
Design and Integration of a Telerobotic System for Minimally Invasive Surgery of the Throat
,”
Int. J. Rob. Res.
,
28
(
9
), pp.
1134
1153
.
3.
Bajo
,
A.
,
Dharamsi
,
L. M.
,
Netterville
,
J. L.
,
Garrett
,
C. G.
, and
Simaan
,
N.
,
2013
, “
Robotic-Assisted Micro-Surgery of the Throat: The Trans-Nasal Approach
,”
2013 IEEE International Conference on Robotics and Automation
,
Karlsruhe, Germany
,
May 6–10
, pp.
232
238
.
4.
Chen
,
G.
,
Pham
,
M. T.
, and
Redarce
,
T.
,
2008
, “
A Guidance Control Strategy for Semi-Autonomous Colonoscopy Using a Continuum Robot
,”
Recent Progress in Robotics: Viable Robotic Service to Human: An Edition of the Selected Papers from the 13th International Conference on Advanced Robotics
,
Berlin, Heidelberg
,
Dec. 3
, Springer, pp.
63
78
.
5.
Mehling
,
J. S.
,
Diftler
,
M. A.
,
Chu
,
M.
, and
Valvo
,
M.
,
2006
, “
A Minimally Invasive Tendril Robot for In-Space Inspection
,”
The First IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics, BioRob 2006
,
Pisa, Italy
,
Feb. 20–22
, IEEE, pp.
690
695
.
6.
Robinson
,
G.
, and
Davies
,
J. B. C.
,
1999
, “
Continuum Robots-A State of the Art
,” Proceedings 1999 IEEE International Conference on Robotics and Automation,
Vol. 4
, pp.
2849
2854
.
7.
Hannan
,
M. W.
, and
Walker
,
I. D.
,
2003
, “
Kinematics and the Implementation of an Elephant’s Trunk Manipulator and Other Continuum Style Robots
,”
J. Robot. Syst.
,
20
(
2
), pp.
45
63
.
8.
Sears
,
P.
, and
Dupont
,
P.
,
2006
, “
A Steerable Needle Technology Using Curved Concentric Tubes
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Beijing, China
,
Oct. 9–15
, pp.
2850
2856
.
9.
Webster
,
R. J.
,
Okamura
,
A. M.
, and
Cowan
,
N. J.
,
2006
, “
Toward Active Cannulas: Miniature Snake-Like Surgical Robots
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Beijing, China
,
Oct. 9–15
, pp.
2857
2863
.
10.
Wei
,
W.
, and
Simaan
,
N.
,
2012
, “
Modeling, Force Sensing, and Control of Flexible Cannulas for Microstent Delivery
,”
ASME J. Dyn. Syst. Meas. Control
,
134
(
4
), p.
041004
.
11.
Chen
,
G.
,
Pham
,
M. T.
, and
Redarce
,
T.
,
2006
, “
Development and Kinematic Analysis of a Silicone-Rubber Bending Tip for Colonoscopy
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Beijing, China
,
Oct. 9–15
, pp.
168
173
.
12.
Kang
,
R.
,
Branson
,
D. T.
,
Zheng
,
T.
,
Guglielmino
,
E.
, and
Caldwell
,
D. G.
,
2013
, “
Design, Modeling and Control of a Pneumatically Actuated Manipulator Inspired by Biological Continuum Structures
,”
Bioinsp. Biomim.
,
8
(
3
), p.
036008
.
13.
Grassmann
,
R. M.
,
Rao
,
P.
,
Peyron
,
Q.
, and
Burgner-Kahrs
,
J.
,
2022
, “
FAS-A Fully Actuated Segment for Tendon-Driven Continuum Robots
,”
Front. Robot. AI
,
9
, p.
873446
.
14.
Nguyen
,
T.-D.
, and
Burgner-Kahrs
,
J.
,
2015
, “
A Tendon-Driven Continuum Robot With Extensible Sections
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Hamburg, Germany
,
Sept. 28
, pp.
2130
2135
.
15.
Zhong
,
G.
,
Peng
,
B.
, and
Dou
,
W.
,
2022
, “
Kinematics Analysis and Trajectory Planning of a Continuum Manipulator
,”
Int. J. Mech. Sci.
,
222
, p.
107206
.
16.
Huang
,
S.
,
Meng
,
D.
,
She
,
Y.
,
Wang
,
X.
,
Liang
,
B.
, and
Yuan
,
B.
,
2018
, “
Statics of Continuum Space Manipulators With Nonconstant Curvature Via Pseudorigid-Body 3R Model
,”
IEEE Access
,
6
, pp.
70854
70865
.
17.
Feng
,
T.
,
Vadali
,
M.
,
Ma
,
Z.
,
Chen
,
D.
, and
Dykstra
,
J.
,
2017
, “
A Finite Element Method With Full Bit-Force Modeling to Analyze Drillstring Vibration
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
9
), p.
091016
.
18.
Webster III
,
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
.
19.
Jones
,
B. A.
, and
Walker
,
I. D.
,
2006
, “
Kinematics for Multisection Continuum Robots
,”
IEEE Trans. Robot.
,
22
(
1
), pp.
43
55
.
20.
Neppalli
,
S.
,
Csencsits
,
M. A.
,
Jones
,
B. A.
, and
Walker
,
I. D.
,
2009
, “
Closed-Form Inverse Kinematics for Continuum Manipulators
,”
Adv. Robot.
,
23
(
15
), pp.
2077
2091
.
21.
Garriga-Casanovas
,
A.
, and
Rodriguez y Baena
,
F.
,
2018
, “
Kinematics of Continuum Robots With Constant Curvature Bending and Extension Capabilities
,”
ASME J. Mech. Rob.
,
11
(
1
), p.
011010
.
22.
Grazioso
,
S.
,
Sonneville
,
V.
,
Di Gironimo
,
G.
,
Bauchau
,
O.
, and
Siciliano
,
B.
,
2017
, “
A Nonlinear Finite Element Formalism for Modelling Flexible and Soft Manipulators
,”
2016 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR)
,
San Francisco, CA
,
Dec. 13–16
, pp.
185
190
.
23.
Xu
,
K.
, and
Simaan
,
N.
,
2010
, “
Analytic Formulation for Kinematics, Statics, and Shape Restoration of Multibackbone Continuum Robots Via Elliptic Integrals
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
011006
.
24.
Jones
,
B. A.
,
Gray
,
R. L.
, and
Turlapati
,
K.
,
2009
, “
Three Dimensional Statics for Continuum Robotics
,”
2009 IEEE/RSJ International Conference on Intelligent Robots and Systems
,
St. Louis, MO
,
Oct. 11–15
, pp.
2659
2664
.
25.
Grazioso
,
S.
,
Di Gironimo
,
G.
, and
Siciliano
,
B.
,
2019
, “
A Geometrically Exact Model for Soft Continuum Robots: The Finite Element Deformation Space Formulation
,”
Soft Robot.
,
6
(
6
), pp.
790
811
.
26.
Godage
,
I. S.
,
Wirz
,
R.
,
Walker
,
I. D.
, and
Webster
,
R. J.
,
2015
, “
Accurate and Efficient Dynamics for Variable-Length Continuum Arms: A Center of Gravity Approach
,”
Soft Robot.
,
2
(
3
), pp.
96
106
.
27.
Ben-Tzvi
,
W.
,
November 9–15, 2012
, “
Continuum Manipulator Statics Based on the Principle of Virtual Work
,”
Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition
,
Oct. 8
, pp.
321
328
, ASME Paper No. IMECE2012-87675.
28.
Rone
,
W. S.
, and
Ben-Tzvi
,
P.
,
2014
, “
Continuum Robot Dynamics Utilizing the Principle of Virtual Power
,”
IEEE Trans. Robot.
,
30
(
1
), pp.
275
287
.
29.
Xu
,
K.
, and
Simaan
,
N.
,
2010
, “
Analytic Formulation for Kinematics, Statics, and Shape Restoration of Multibackbone Continuum Robots Via Elliptic Integrals
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
011006
.
30.
Ehsani-Seresht
,
A.
, and
Hashemi-Pour Moosavi
,
S.
,
2020
, “
Dynamic Modeling of the Cable-Driven Continuum Robots in Hybrid Position-Force Actuation Mode
,”
ASME J. Mech. Rob.
,
12
(
5
), p.
051002
.
31.
Peksen
,
M.
,
2018
,
Multiphysics Modeling: Materials, Components, and Systems
, 1st ed.,
Academic Press Elsevier Science
,
New York
.
32.
Feng
,
T.
,
2019
,
Modeling and Control of Drillstring Dynamics for Vibration Suppression
,
ProQuest Dissertations Publishing
,
Austin, TX
.
33.
Feng
,
T.
,
Vadali
,
M.
, and
Chen
,
D.
,
2017
, “
Modeling and Analysis of Directional Drilling Dynamics
,”
Dynamic Systems and Control Conference
,
Tysons Corner, VA
,
Oct. 11
,
Vol. 58295
, p. V003T43A006, Paper No. DSCC2017-5358.
34.
Han
,
S. M.
,
Benaroya
,
H.
, and
Wei
,
T.
,
1999
, “
Dynamics of Transversely Vibrating Beams Using Four Engineering Theories
,”
J. Sound. Vib.
,
225
(
5
), pp.
935
988
.
35.
Reddy
,
J.
,
1 November 2020
,
An Introduction to the Finite Element Method
, 4th ed.,
McGraw Hill
,
New Delhi
.
36.
Dai
,
J. S.
,
2015
, “
Euler–Rodrigues Formula Variations, Quaternion Conjugation and Intrinsic Connections
,”
Mech. Mach. Theory
,
92
(
2015
), pp.
144
152
.
37.
Lurie
,
A. I.
,
2010
,
Theory of Elasticity
, 2005th edition ed.,
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
,
Berlin, Germany
.
38.
Site
,
M.
,
2011
, “Overview of Materials for Nylon 66/6.”
39.
Ogata
,
K.
,
2010
,
Modern Control Engineering
, 5th edition ed.,
Pearson
,
London, UK
.
40.
Rao
,
S.
,
2017
,
Mechanical Vibrations
, 5th ed.,
Pearson Education
,
New Delhi
.
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