This paper presents a kinetostatic modeling framework for flexible cannulas (concentric tubing robots) subject to tip loads. Unlike existing methods that allow fast computation of the beam tip position, this modeling framework provides fast computation of both the tip position and the entire shape of the deflected robot. A method for online force sensing based on inverse kinetostatic solution is also proposed and assistive telemanipulation control methods for microstent delivery are presented. The modeling framework uses polynomial approximation and linear interpolation based on elliptic integral solutions to the deflection of lightweight beams. To date, there are no systems capable of stent delivery in retinal vasculature. The modeling and control frameworks of this paper are validated experimentally on pilot studies for microstent delivery. We believe that the methods presented in this paper open the way for robot-assisted retinal microvascular stenting that may potentially revolutionize the treatment of blinding retinal vasculature diseases.

References

1.
Webster
,
R. J.
,
Kim
,
J. S.
,
Cowan
,
N. J.
,
Chirikjian
,
G. S.
, and
Okamura
,
A. M.
, 2006, “
Nonholonomic Modeling of Needle Steering
,”
Int. J. Robot. Res.
,
25
(
5–6
), pp.
509
525
.
2.
Minhas
,
D.
,
Engh
,
J.
,
Fenske
,
M.
, and
Riviere
,
C. N.
, 2007, “
Modeling of Needle Steering Via Duty-Cycled Spinning
,”
28th Annual International Conference of IEEE Engineering in Medicine and Biology Society
,
Lyon
,
France
, pp.
2756
2759
.
3.
Glozman
,
D.
, and
Shoham
,
M.
, 2007, “
Image-Guided Robotic Flexible Needle Steering
,”
IEEE Trans. Robot.
,
23
(
3
), pp.
459
467
.
4.
Okazawa
,
S.
,
Ebrahimi
,
R.
,
Chuang
,
J.
,
Salcudean
,
S. E.
, and
Rohling
,
R.
, 2005, “
Hand-Held Steerable Needle Device
,”
IEEE/ASME Trans. Mechatron.
,
10
(
3
), pp.
285
296
.
5.
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
, pp.
2850
2856
.
6.
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
, pp.
2857
2863
.
7.
Jones
,
B. A.
,
Gray
,
R. L.
, and
Turlapati
,
K.
, 2009, “
Three Dimensional Statics for Continuum Robotics
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, St. Louis, pp.
2659
2664
.
8.
Webster
,
R. J.
,
Romano
,
J. M.
, and
Cowan
,
N. J.
, 2009, “
Mechanics of Precurved-Tube Continuum Robots
,”
IEEE Trans. Rob.
,
25
(
1
), pp.
67
78
.
9.
Rubin
,
M. B.
, and
Tufekci
,
E.
, 2005, “
Three-Dimensional Free Vibrations of a Circular Arch Using the Theory of a Cosserat Point
,”
J. Sound Vib.
,
286
, pp.
799
816
.
10.
Sears
,
P.
, and
Dupont
,
P.
, 2007, “
Inverse Kinematics of Concentric Tube Steerable Needles
,”
IEEE International Conference on Robotics and Automation
, Rome, Italy, pp. 1887–1892.
11.
Alterovitz
,
R.
,
Branicky
,
M.
, and
Goldberg
,
K.
, 2008, “
Motion Planning Under Uncertainty for Image-Guided Medical Needle Steering
,”
Int. J. Robot. Res.
,
27
(
11–12
), pp.
1361
1374
.
12.
Park
,
W.
,
Liu
,
Y.
,
Zhou
,
Y.
,
Moses
,
M.
, and
Chirikjian
,
G. S.
, 2008, “
Kinematic State Estimation and Motion Planning for stochastic Nonholonomic Systems Using the Exponential Map
,”
Robotica
,
26
(
4
), pp.
419
434
.
13.
Kallem
,
V.
, and
Cowan
,
N. J.
, 2009, “
Image Guidance of Flexible Tip-Steerable Needles
,”
IEEE Trans. Robot.
,
25
(
1
), pp.
191
196
.
14.
Mahvash
,
M.
, and
Dupont
,
P.
, 2008, “
Bilateral Teleoperation of Flexible Surgical Robots
,”
IEEE International Conference on Robotics and Automation, Workshop on New Vistas and Challenges in Telerobotics
,
Pasadena
,
CA
, pp.
58
64
.
15.
Xu
,
K.
, and
Simaan
,
N.
, 2010, “
Analytic Formulation for Kinematics, Statics and Shape Restoration of Multi-Backbone Continuum Robots via Elliptic Integrals
,”
ASME J. Mech. Robot.
,
2
(
1
), pp.
011006
(1–13).
16.
Kimball
,
C.
, and
Tsai
,
L.-W.
, 2002, “
Modeling of Flexural Beams Subjected to Arbitrary End Loads
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
223
234
.
17.
Goksel
,
O.
,
Dehghan
,
E.
, and
Salcudean
,
S. E.
, 2009, “
Modeling and Simulation of Flexible Needles
,”
Med. Eng. Phys.
,
31
, pp.
1069
1078
.
18.
Wang
,
X.
, and
Mills
,
J. K.
, 2005, “
Dynamic Modeling of a Flexible-Link Planar Parallel Platform Using a Substructuring Approach
,”
Mech. Mach. Theory
,
41
(
6
), pp.
671
687
.
19.
Wakamatsu
,
H.
, and
Hirai
,
S.
, 2004, “
Static Modeling of Linear Object Deformation Based on Differential Geometry
,”
Int. J. Robot. Res.
,
23
(
3
), pp.
293
311
.
20.
Wang
,
J.
,
Chen
,
J.-K.
, and
Liao
,
S.
, 2008, “
An Explicit Solution of the Large Deformation of a Cantilever Beam Under Point Load at the Free Tip
,”
J. Comput. Appl. Math.
,
212
, pp.
320
330
.
21.
Shvartsman
,
B. S.
, 1999, “
Direct Method for Analysis of Flexible Beam Under a Follower Load
,”
Proceedings of Computational of Mechanics for the Next Millennium
, Singapore, pp. 155–160.
22.
Howell
,
L. L.
, 2001,
Compliant Mechanisms
,
Wiley
,
New York
.
23.
Su
,
H.-J.
, 2009, “
A Pseudo-rigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads
,”
ASME J. Mech. Robot.
,
1
(
2
),p.
021008
.
24.
Fertis
,
D. G.
, 1999,
Nonlinear Mechanics
,
CRC
,
Boca Raton
.
25.
Wei
,
W.
,
Goldman
,
R. E.
,
Fine
,
H. F.
,
Chang
,
S.
, and
Simaan
,
N.
, 2009, “
Performance Evaluation for Multi-Arm Manipulation of Hollow Suspended Organs
,”
IEEE Trans. Rob.
,
25
(
1
), pp.
147
157
.
26.
Stewart
,
D.
, 1965, “
A Platform With 6 Degrees of Freedom
,”
Proceedings of the Institution of Mechanical Engineers
.
27.
Bynoe
,
L. A.
, and
Weiss
,
J. N.
, 2003, “
Retinal Endovascular Surgery and Intravitreal Triamcinolone Acetonide for Central Vein Occlusion in Young Adults
,”
Am. J. Ophthalmol.
,
135
(
3
), pp.
382
384
.
28.
Weiss
,
J. N.
, 1998, “
Treatment of Central Retinal Vein Occlusion by Injection of Tissue Plasminogen Activator into A Retinal Vein
,”
Am. J. Ophthalmol.
,
126
(
1
), pp.
142
144
.
29.
Weiss
,
J. N.
, 2000, “
Retinal Surgery for Treatment of Central Retinal Vein Occlusion
,”
Ophthalmic Surgery Lasers
,
31
(
2
), pp.
162
165
.
30.
Weiss
,
J. N.
, and
Bynoe
,
L. A.
, 2001, “
Injection of Tissue Plasminogen Activator into A Branch Retinal Vein in Eyes With Central Retinal Vein Occlusion
,”
Ophthalmology
,
108
(
12
), pp.
2249
2257
.
31.
Dewan
,
M.
,
Marayong
,
P.
,
Okamura
,
A. M.
, and
Hager
,
G. D.
, 2004, “
Vision-Based Assistance for Ophthalmic Micro-Surgery
,”
7th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI)
,
Springer, Rennes
,
Saint-Malo, France
, pp.
49
57
.
32.
Paul
,
R. P.
, 1981,
Robot Manipulators: Mathematics, Programming, and Control
,
The MIT Press
,
Cambridge, MA.
33.
Jagtap
,
A.
, and
Riviere
,
C. N.
, 2004, “
Applied Force during Vitreoretinal Microsurgery With Handheld Instruments
,”
26th Annual International Conference of the Engineering in Medicine and Biology Society
,
San Francisco, CA
, pp.
2771
2773
.
34.
Leng
,
T.
,
Miller
,
J. M.
,
Bilbao
,
K. V.
,
Palanker
,
D. V.
,
Huie
,
P.
, and
Blumenkranz
,
M. S.
, 2004, “
The Chick Chorioallantoic Membrane as a Model Tissue for Surgical Retinal Research and Simulation
,”
Retina
,
24
(
3
), pp.
427
434
.
35.
LoRusso
,
F. J.
, and
Font
,
R. L.
, 1999, “
Use of Agar in Ophthalmic Pathology: A Technique to Improve the Handling and Diagnosis of Temporal Artery Biopsies, Subfoveal Membranes, Lens Capsules, and Other Ocular Tissues
,”
Ophthalmology
,
106
(
11
), pp.
2106
2108
.
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