Concentric Tube Robots: Stability Analysis, Optimal Design, and Shape Sensing : 컨센트릭 튜브 로봇: 안정성 분석, 최적 디자인, 자세 측정

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Junhyoung Ha

공과대학 기계항공공학부
Issue Date
서울대학교 대학원
Concentric tube robotcontinuum robotelastic stabilityshape sensing
학위논문 (박사)-- 서울대학교 대학원 : 기계항공공학부, 2015. 8. 박종우.
Minimally invasive surgery can involve navigating
inside small cavities or reaching around sensitive tissues. Robotic
instruments based on concentric tube technology are well suited
to these tasks since they are slender and can be designed to take
on shapes of high and varying curvature along their length. One
limitation of these robots, however, is that elastic instabilities
can arise when manipulating the robots by rotating or translating the bases
of the tubes. As the tubes rotate and translate with respect to
each other, elastic potential energy associated with tube bending
and twisting can accumulate
if a configuration is not locally
elastically stable, then a dangerous snapping motion may occur
as energy is suddenly released.

To enhance the elastic stability of the concentric tube robots,
this paper presents two researches: i) optimal design of tube pair,
ii) local stability test to avoid unstable configurations.
While prior work has considered tubes of piecewise-constant pre-curvature,
the first research in this paper proposes varying tube pre-curvature as a
function of arc length as a means to enhance stability. Stability
conditions for a planar tube pair are derived and used to define
an optimal design problem. This framework enables solving for
pre-curvature functions that achieve a desired tip orientation
range while maximizing stability and respecting bending strain
limits. Analytical and numerical examples of the approach are
provided. The second research provide a local stability condition
and test to determine if a configuration is a stable equilibrium or not.
This condition applies to arbitrary robot designs with any external
loads. The local stability test based on this condition is validated by comparison
with known stability results, and its utility is demonstrated by
application to stable path planning.

Though those two researches address the elastic instability issue of
concentric tube robots, they both are based on the theoretical
kinematics of the robots. Robot control requires the rapid computation of
this kinematics, which involves solving complex mechanics-based models.
Furthermore, shape computation based on kinematic input variables can
be inaccurate due to parameter errors and model simplification. An
alternate approach is to compute the shape in real time from a
set of sensors positioned along the length the robot that provide
measurements of local curvature, e.g., optical fiber Bragg gratings.
In this point of view, the third research in this paper proposes
a general framework for selecting the
number and placement of such sensors with respect to arc length
so as to compute the forward kinematic solution accurately
and quickly. The approach is based on defining numerically
efficient shape reconstruction models parameterized by sensor
number and location. Optimization techniques are used to
solve for the sensor locations that minimize shape and tip
error between a reconstruction model and a mechanics-based
model. As a specific example, several reconstruction models
are proposed and compared for concentric tube robots. These
results indicate that the choice of reconstruction model as well
as sensor placement can have a substantial effect on shape
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Mechanical Aerospace Engineering (기계항공공학부)Theses (Ph.D. / Sc.D._기계항공공학부)
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