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Research Papers

Mechanics Modeling of Multisegment Rod-Driven Continuum Robots

[+] Author and Article Information
William S. Rone

Robotics and Mechatronics Lab,
Department of Mechanical and Aerospace
Engineering,
The George Washington University,
801 22nd Street, NW,
Washington, DC 20052

Pinhas Ben-Tzvi

Robotics and Mechatronics Lab,
Department of Mechanical and Aerospace
Engineering,
The George Washington University,
801 22nd Street, NW,
Washington, DC 20052
e-mail: bentzvi@gwu.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 22, 2013; final manuscript received February 20, 2014; published online June 5, 2014. Assoc. Editor: Vijay Kumar.

J. Mechanisms Robotics 6(4), 041006 (Jun 05, 2014) (12 pages) Paper No: JMR-13-1097; doi: 10.1115/1.4027235 History: Received May 22, 2013; Revised February 20, 2014

This paper presents a novel modeling approach for the mechanics of multisegment, rod-driven continuum robots. This modeling approach utilizes a high-fidelity lumped parameter model that captures the variation in curvature along the robot while simultaneously defined by a discrete set of variables and utilizes the principle of virtual power to formulate the statics and dynamics of the continuum robot as a set of algebraic equations for the static model and as a set of coupled ordinary differential equations (ODEs) in time for the dynamic model. The actuation loading on the robot by the actuation rods is formulated based on the calculation of contact forces that result in rod equilibrium. Numerical optimization calculates the magnitudes of these forces, and an iterative solver simultaneously estimates the robot's friction and contact forces. In addition, modeling considerations including variable elastic loading among segments and mutual segment loading due to rods terminating at different disks are presented. The resulting static and dynamic models have been compared to dynamic finite element analyses and experimental results to validate their accuracy.

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Figures

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Fig. 1

Multisegment continuum robotic structure (a) three-dimensional representation of structure with eight disks rigidly mounted along an elastic core, with six actuation rods to control shape. Three rods terminate at the fourth disk, and three rods terminate at the eighth disk. (b) Typical planar mode shape of two-segment manipulator illustrating bending of the proximal and distal segments.

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Fig. 2

Discretization of proximal and distal subsegments accounting for the disk, core, and rods, with mass mi and moment of inertia Ii,lcl

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Fig. 3

(a) Illustration of the x-z plane curvature βi and the y-z plane curvature γi. (b) Illustration of the intermediate coordinates: the in-plane curvature ki, the bending plane angle φi, and the subsegment bending angle θi.

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Fig. 4

Illustration of the radius offset for a case when φ = 0

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Fig. 5

(a) 2D projection of a single-segment rod-driven manipulator with the upper rod in tension and the two lower rods passive (zero axial force). (b) Free-body diagram of the rod under consideration with the applied force from the actuator, the end force from the rod's rigid connection to the end disk, and the contact forces parallel to the disks, normal to the rod and applied at the disk locations.

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Fig. 6

Assignment of tension input variables to actuation transmission rods for a two-segment continuum robot with three rods per segment

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Fig. 7

Convergence of contact force magnitudes for a two segment, eight-disk continuum robot. (a) T1,1 actuated with 30 N (rod connects at disk 4). (b) T2,2 actuated with 30 N (rod connects at disk 8).

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Fig. 8

Zero actuation virtual power dynamic model response β curvatures. These curvature profile correspond to tip oscillations with peak-to-peak amplitude of 9.48 mm around x = −4.74 mm.

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Fig. 9

Rod 1-1 actuation (10 N) dynamic virtual power model β curvature responses

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Fig. 10

Rod 2-2 actuation (10 N) dynamic virtual power model β curvature responses

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Fig. 11

Comparison of the calculated static virtual power model equilibrium to the steady-state component of the dynamic virtual power model response for actuation of 10 N in rod 1-1

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Fig. 12

Comparison of the calculated static virtual power model equilibrium to the steady-state component of the dynamic virtual power model response for actuation of 10 N in rod 2-2

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Fig. 13

Comparisons of the zero actuation dynamic virtual power model response steady-state component to the calculated equilibria using the static virtual power model and the static finite element analysis model

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Fig. 14

Comparison of frequency response of vertical displacements of (a) disk 1 and (b) disk 8 from VP and FEA simulations

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Fig. 15

Rod-driven, two-segment prototype used for validating actuated case studies

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Fig. 16

Comparison of the experimentally measured static equilibrium and the calculated static virtual power model equilibrium for tensions of 10, 20, and 30 N in rod 1-1

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Fig. 17

Comparison of β curvatures for subsegments 1–4 for the experimentally measured static equilibrium and the calculated static virtual power model equilibrium for 30 N tension in rod 1-1

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Fig. 18

Comparison of the experimentally measured static equilibrium and the calculated static virtual power model equilibrium for tensions of 5, 10, and 15 N in rod 2-2

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Fig. 19

Comparison of the experimentally measured static equilibrium and the calculated static virtual power model equilibrium for a tension of 25 N in rod 1-1 and tensions of 5, 10, and 15 N in rod 2-2

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