Recently, a new concept for continuum robots capable of producing macro-scale and micro-scale motion has been presented. These robots achieve their multi-scale motion capabilities by coupling direct actuation of push-pull backbones for macro-motion with indirect actuation whereby the equilibrium pose is altered to achieve micro-scale motion. This paper presents a first attempt at explaining the micro-motion capabilities of these robots from a modeling perspective. This paper presents the macro- and micro-motion kinematics of a single-segment continuum robot by using statics coupling effects among its subsegments. Experimental observations of the micro-scale motion demonstrate a turning point behavior which could not be explained well using the current modeling methods. We present a simplistic modeling approach that introduces two calibration parameters to calibrate the moment coupling effects among the subsegments of the robot. It is shown that these two parameters can reproduce the turning point behavior at the micro-scale. The instantaneous macro- and micro-scale kinematics Jacobians and the calibration parameters identification Jacobian are derived. The modeling approach is verified against experimental data showing that our simplistic modeling approach can capture the experimental motion data with the RMS position error of 5.82 μm if one wishes to fit the entire motion profile with the turning point. If one chooses to exclude motions past the turning point, our model can fit the experimental data with an accuracy of 4.76 μm.

References

References
1.
Kwartowitz
,
D. M.
,
Herrell
,
S. D.
, and
Galloway
,
R. L.
,
2006
, “
Toward Image-Guided Robotic Surgery: Determining Intrinsic Accuracy of the Da Vinci Robot
,”
Int. J. Comput. Assisted Radiol. Surgery
,
1
(
3
), pp.
157
165
.
2.
Kwartowitz
,
D. M.
,
Herrell
,
S. D.
, and
Galloway
,
R. L.
,
2007
, “
Update: Toward Image-Guided Robotic Surgery: Determining the Intrinsic Accuracy of the DaVinci-S Robot
,”
Int. J. Comput. Assisted Radiol. Surgery
,
1
(
5
), pp.
301
304
.
3.
Kanazawa
,
T.
,
Sarukawa
,
S.
,
Fukushima
,
H.
,
Takeoda
,
S.
,
Kusaka
,
G.
, and
Ichimura
,
K.
,
2011
, “
Current Reconstructive Techniques Following Head and Neck Cancer Resection Using Microvascular Surgery
,”
Ann. Vas. Dis.
,
4
(
3
), pp.
189
195
.
4.
Slutsky
,
D. J.
,
2014
, “
The Management of Digital Nerve Injuries
,”
J. Hand Surgery
,
39
(
6
), pp.
1208
1215
.
5.
Chen
,
C.
,
Tang
,
P.
,
Zhang
,
L.
, and
Wang
,
B.
,
2014
, “
Treatment of Fingertip Degloving Injury Using the Bilaterally Innervated Sensory Cross-Finger Flap
,”
Ann. Plast. Surg.
,
73
(
6
), pp.
645
651
.
6.
Lohmeyer
,
J. A.
,
Kern
,
Y.
,
Schmauss
,
D.
,
Paprottka
,
F.
,
Stang
,
F.
,
Siemers
,
F.
,
Mailaender
,
P.
, and
Machens
,
H.-G.
,
2014
, “
Prospective Clinical Study on Digital Nerve Repair With Collagen Nerve Conduits and Review of Literature
,”
J. Reconstr. Microsur.
,
30
(
4
), pp.
227
234
.
7.
Yu
,
H.
,
Shen
,
J.-H.
,
Joos
,
K. M.
, and
Simaan
,
N.
,
2016
, “
Calibration and Integration of B-mode Optical Coherence Tomography for Assistive Control in Robotic Microsurgery
,”
IEEE/ASME Trans. Mechatron.
,
21
(
6
), pp.
2613
2623
.
8.
Zuo
,
S.
,
Hughes
,
M.
, and
Yang
,
G.-Z.
,
2017
, “
Flexible Robotic Scanning Device for IntraOperative Endomicroscopy in Mis
,”
IEEE/ASME Trans. Mechatron.
,
22
(
4
), pp.
1728
1735
.
9.
Fujimoto
,
J. G.
,
2003
, “
Optical Coherence Tomography for Ultrahigh Resolution in Vivo Imaging
,”
Nat. Biotechnol.
,
21
(
11
), pp.
1361
1367
.
10.
Luo
,
W.
,
Nguyen
,
F. T.
,
Zysk
,
A. M.
,
Ralston
,
T. S.
,
Brockenbrough
,
J.
,
Marks
,
D. L.
,
Oldenburg
,
A. L.
, and
Boppart
,
S. A.
,
2005
, “
Optical Biopsy of Lymph Node Morphology Using Optical Coherence Tomography
,”
Technol. Cancer Res. Treat.
,
4
(
5
), pp.
539
547
.
11.
Del Giudice
,
G.
,
Wang
,
L.
,
Shen
,
J.-H.
,
Joos
,
K.
, and
Simaan
,
N.
,
2017
, “
Continuum Robots For Multi-Scale Motion: Micro-Scale Motion Through Equilibrium Modulation
,”
2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IRoS)
,
Vancouver, BC, Canada
,
Sept. 24–28
, New York, pp.
2537
2542
.
12.
Robinson
,
G.
, and
Davies
,
J.
,
1999
, “
Continuum Robots-A State of The Art
,”
Proceedings of the 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), Vol. 4.
,
Detroit, MI
,
May 10–15
.
13.
Simaan
,
N.
,
Taylor
,
R.
, and
Flint
,
P.
,
2004
, “
A Dexterous System for Laryngeal Surgery
,”
IEEE International Conference on Robotics and Automation, Proceedings of the ICRA’04, Vol. 1
,
New Orleans, LA
,
Apr. 26–May 1
.
14.
Egeland
,
O.
,
1987
, “
Task-space Tracking With Redundant Manipulators
,”
IEEE J. Rob. Autom.
,
3
(
5
), pp.
471
475
.
15.
Comparetti
,
M. D.
,
Vaccarella
,
A.
,
Dyagilev
,
I.
,
Shoham
,
M.
,
Ferrigno
,
G.
, and
De Momi
,
E.
,
2012
, “
Accurate Multi-Robot Targeting for Keyhole Neurosurgery Based on External Sensor Monitoring
,”
Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
,
226
(
5
), pp.
347
359
.
16.
Hodac
,
A.
, and
Siegwart
,
R. Y.
,
1999
, “
Decoupled Macro/Micro-Manipulator for Fast and Precise Assembly Operations: Design and Experiments
,”
Proceedings of the SPIE 3834, Microrobotics and Microassembly
,
Boston, MA
,
Aug. 18
,
B. J.
Nelson
and
J.-M.
Breguet
, eds., pp.
122
130
.
17.
Entsfellner
,
K.
,
Strauss
,
G.
,
Berger
,
T.
,
Dietz
,
A.
, and
Lueth
,
T. C.
,
2012
, “
Micro-Macro Telemanipulator for Middle-Ear Microsurgery
,”
Proceedings of ROBOTIK 2012, 7th German Conference on Robotics, VDE
,
Munich, Germany
,
May 21–22
, pp.
1
4
.
18.
Abiko
,
S.
, and
Yoshida
,
K.
,
2004
, “
On-line Parameter Identification of A Payload Handled By Flexible Based Manipulator
,”
2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566), Vol. 3
,
Sendai, Japan
,
Sept. 28–Oct. 2
, IEEE, New York, pp.
2930
2935
.
19.
Cho
,
C.
,
Kang
,
S.
,
Kim
,
M.
, and
Song
,
J.-B.
,
2005
, “
Macro-Micro Manipulation With Visual Tracking and Its Application to Wheel Assembly
,”
Int. J. Control, Autom., Syst.
,
3
(
3
), pp.
461
468
.
20.
Kim
,
J.
,
Janabi-Sharifi
,
F.
, and
Kim
,
J.
,
2008
, “
A Physically-Based Haptic Rendering for Telemanipulation With Visual Information: Macro and Micro Applications
,”
2008 IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Nice, France
,
Sept. 22–26
, IEEE, pp.
3489
3494
.
21.
Nagatsu
,
Y.
, and
Katsura
,
S.
,
2013
, “
Macro-Micro Bilateral Control Using Kalman Filter Based State Observer for Noise Reduction and Decoupling of Modal Space
,”
IECON 2013 – 39th Annual Conference of the IEEE Industrial Electronics Society
,
Vienna, Austria
,
Nov. 10-13
, IEEE, pp.
3489
3494
.
22.
Portman
,
V. T.
,
Sandler
,
B.-Z.
, and
Zahavi
,
E.
,
2001
, “
Rigid 6-DOF Parallel Platform for Precision 3-D Micromanipulation
,”
Int. J. Mach. Tools. Manuf.
,
41
(
9
), pp.
1229
1250
.
23.
Shoham
,
M.
,
2005
, “
Twisting Wire Actuator
,”
ASME J. Mech. Des.
,
127
(
3
), pp.
441
445
.
24.
Rul
,
C.
,
Wang
,
X.
, and
Guo
,
S.
,
2007
, “
A Novel Tool Using SMA Actuator for Cell Puncturing
,”
SICE Annual Conference 2007
,
Takamatsu, Japan
,
Sept. 18–20
, IEEE, New York, pp.
254
258
.
25.
Yun
,
Y.
, and
Li
,
Y.
,
2008
, “
A Novel Design and Analysis of a 3-DOF Parallel Manipulator for Micro/Nano Manipulation
,”
2008 IEEE Workshop on Advanced Robotics and Its Social Impacts
,
Hsinchu, Taiwan
,
Dec. 9–11
, IEEE, New York, pp.
1
6
.
26.
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
.
27.
Rone
,
W. S.
, and
Ben-Tzvi
,
P.
,
2014
, “
Continuum Robot Dynamics Utilizing the Principle of Virtual Power
,”
IEEE Trans. Rob.
,
30
(
1
), pp.
275
287
.
28.
Rucker
,
D. C.
, and
Webster III
,
R. J.
,
2011
, “
Statics and Dynamics of Continuum Robots with General Tendon Routing and External Loading
,”
IEEE Trans. Rob.
,
27
(
6
), pp.
1033
1044
.
29.
Li
,
Z.
,
Ren
,
H.
,
Chiu
,
P. W. Y.
,
Du
,
R.
, and
Yu
,
H.
,
2016
, “
A Novel Constrained Wire-driven Flexible Mechanism and Its Kinematic Analysis
,”
Mech. Mach. Theory
,
95
(
Jan.
), pp.
59
75
.
30.
Dupont
,
P. E.
,
Lock
,
J.
,
Itkowitz
,
B.
, and
Butler
,
E.
,
2010
, “
Design and Control of Concentric-tube Robots
,”
IEEE Trans. Rob.
,
26
(
2
), pp.
209
225
.
31.
Webster III
,
R. J.
,
Romano
,
J. M.
, and
Cowan
,
N. J.
,
2009
, “
Mechanics of Precurved-Tube Continuum Robots
,”
IEEE Trans. Rob.
,
25
(
1
), pp.
67
78
.
32.
Xu
,
K.
, and
Simaan
,
N.
,
2008
, “
An Investigation of the Intrinsic Force Sensing Capabilities of Continuum Robots
,”
IEEE Trans. Rob.
,
24
(
3
), pp.
576
587
.
33.
Simaan
,
Nabil
,
2005
, “
Snake-Like Units Using Flexible Backbones and Actuation Redundancy for Enhanced Miniaturization
,”
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
,
Barcelona, Spain
,
Apr. 18–22
, IEEE, New York, pp.
3012
3017
.
34.
Goldman
,
R. E.
,
Bajo
,
A.
, and
Simaan
,
N.
,
2014
, “
Compliant Motion Control for Multisegment Continuum Robots With Actuation Force Sensing
,”
IEEE Trans. Rob.
,
30
(
4
), pp.
890
902
.
35.
Roy
,
R.
,
Wang
,
L.
, and
Simaan
,
N.
,
2017
, “
Modeling and Estimation of Friction, Extension, and Coupling Effects in Multisegment Continuum Robots
,”
IEEE/ASME Trans. Mechatron.
,
22
(
2
), pp.
909
920
.
36.
Wang
,
L.
, and
Simaan
,
N.
,
2014
, “Investigation of Error Propagation in Multi-Backbone Continuum Robots,”
Advances in Robot Kinematics
,
Springer
,
New York
, pp.
385
394
.
37.
Xu
,
K.
, and
Simaan
,
N.
,
2010
, “
Intrinsic Wrench Estimation and Its Performance Index for Multisegment Continuum Robots
,”
IEEE Trans. Rob.
,
26
(
3
), pp.
555
561
.
38.
Siciliano
,
B.
, and
Khatib
,
O.
,
2008
,
Springer Handbook of Robotics
,
Springer Science & Business Media
,
Berlin Heidelberg
.
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