0
Journal of Mechanisms and Robotics | Volume 6 | Issue 2 | research-article
Research Papers

Model-Based Shape Estimation for Soft Robotic Manipulators: The Planar Case

[+] Author and Article Information
Deepak Trivedi

General Electric Global Research Center,
One Research Circle,
Niskayuna, NY 12309
e-mail: trivedid@ge.com

Christopher D. Rahn

Department of Mechanical Engineering,
The Pennsylvania State University,
State College, PA 16802
e-mail: cdrahn@psu.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 29, 2012; final manuscript received October 26, 2013; published online March 4, 2014. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 6(2), 021005 (Mar 04, 2014) (11 pages) Paper No: JMR-12-1154; doi: 10.1115/1.4026338 History: Received September 29, 2012; Revised October 26, 2013
Article
References
Figures
Tables
Citing Articles

Soft robotic manipulators are continuum robots made of soft materials that undergo continuous elastic deformation and produce motion with a smooth backbone curve. In many applications, these manipulators offer significant advantages over traditional manipulators due to their ability to conform to their surroundings, and manipulate objects of widely varying size using whole arm manipulation. Theoretically, soft robots have infinite degrees of freedom (DOF), but the number of sensors and actuators are limited. Many DOFs of soft robots are not directly observable and/or controllable, complicating shape estimation and control. In this paper, we present three methods of shape sensing for soft robotic manipulators based on a geometrically exact mechanical model. The first method uses load cells mounted at the base of the manipulator, the second method makes use of cable encoders running through the length of the manipulator, and the third method uses inclinometers mounted at the end of each section of the manipulator. Simulation results show an endpoint localization error of less than 3% of manipulator length with typical sensors. The methods are validated experimentally on the OctArm VI manipulator.
FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

1
Trivedi, D., Rahn, C. D., Kier, W. M., and Walker, I. D., 2008, “Soft Robotics: Biological Inspiration, State of the Art, and Future Research,” Appl. Bionics Biomech., 5(3), pp. 99–117. [CrossRef]
2
Robinson, G., and Davies, J. B. C., 1999, “Continuum Robots—a State of the Art,” IEEE International Conference on Robotics and Automation, Detroit, Michigan, May 1999, Vol. 4, pp. 2849–2854.
3
Webster, R. J., and Jones, B. A., 2010, “Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review,” Int. J. Robot. Res., 29(13), pp. 1661–1683. [CrossRef]
4
Leleu, S., Abou-Kandil, H., and Bonnassieux, Y., 2001, “Piezoelectric Actuators and Sensors Location for Active Control of Flexible Structures,” IEEE Trans. Instrum. Meas., 50(6), pp. 1577–1582. [CrossRef]
5
Lyshevski, S., 2003, “Data-Intensive Analysis and Control of Flexible Pointing Systems With PZT Actuators,” Frequency Control Symposium and PDA Exhibition Jointly With the 17th European Frequency and Time Forum, 2003, Proceedings of the 2003 IEEE International, May, pp. 948–956.
6
Camarillo, D., Loewke, K., Carlson, C., and Salisbury, J., 2008, “Vision Based 3-D Shape Sensing of Flexible Manipulators,” Robotics and Automation, 2008, ICRA 2008. IEEE International Conference on, May, pp. 2940–2947.
7
Yi, X., Qian, J., Shen, L., Zhang, Y., and Zhang, Z., 2007, “An Innovative 3D Colonoscope Shape Sensing Sensor Based on FBG Sensor Array,” Information Acquisition, 2007, ICIA’07, International Conference on, July, pp. 227–232.
8
Miller, G. A., Askins, C. G., and Friebele, E. J., 2004, “Shape Sensing Using Distributed Fiber Optic Strain Measurements,” Proc. SPIE, 5502, pp. 528–531. [CrossRef]
9
Duncan, R. G., Froggatt, M. E., Kreger, S. T., Seeley, R. J., Gifford, D. K., Sang, A. K., and Wolfe, M. S., 2007, “High-Accuracy Fiber-Optic Shape Sensing,” Proc. SPIE, 6530, pp. 576–587.
10
Sayeh, M. R., Gupta, L., Kagaris, D., Viswanathan, R., and Chung, B., 2001, “Multiplexed Fiber-Optic Strain Sensors for Distributed Sensing,” Proc. SPIE, 4357, pp. 125–129. [CrossRef]
11
Davis, M. A., Kersey, A. D., Sirkis, J., and Friebele, E. J., 1996, “Shape and Vibration Mode Sensing Using a Fiber Optic Bragg Grating Array,” Smart Mater. Struct., 5(6), pp. 759–765. [CrossRef]
12
Marcuse, D., 1976, “Curvature Loss Formula for Optical Fibers,” J. Opt. Soc. Am., 66(1), pp. 216–220. [CrossRef]
13
Hannan, M., and Walker, I. D., 2005, “Real-Time Shape Estimation for Continuum Robots Using Vision,” Robotica, 23, pp. 645–651. [CrossRef]
14
Trivedi, D., Lotfi, A., and Rahn, C., 2008, “Geometrically Exact Models for Soft Robotic Manipulators,” IEEE Trans. Robot., 24(4), pp. 773–780. [CrossRef]
15
Chitrakaran, V. K., Behal, A., Dawson, D. M., and Walker, I. D., 2007, “Setpoint Regulation of Continuum Robots Using a Fixed Camera,” Robotica, 25, pp. 581–586. [CrossRef]
16
Matsuno, T., Fukuda, T., Arai, F., and Hasegawa, Y., 2004, “Flexible Rope Manipulation Using Elastic Deformation Modeling by Dual Manipulator System With Vision Sensor,” J. Robot. Mechatronics, 16(1), pp. 31–38.
17
Croom, J. M., Rucker, D. C., Romano, J. M., and Webster, R. J., 2010, “Visual Sensing of Continuum Robot Shape Using Self-Organizing Maps,” IEEE International Conference on Robotics and Automation, pp. 4591–4596.
18
Reiter, A., Goldman, R. E., Bajo, A., Iliopoulos, K., Simaan, N., and Allen, P. K., 2011. “A Learning Algorithm for Visual Pose Estimation of Continuum Robots,” Intelligent Robots and Systems (IROS), 2011 IEEE/RSJ International Conference on, IEEE, pp. 2390–2396.
19
Reiter, A., Bajo, A., Iliopoulos, K., Simaan, N., and Allen, P. K., 2012, “Learning-Based Configuration Estimation of a Multi-Segment Continuum Robot,” Biomedical Robotics and Biomechatronics (BioRob), 2012 4th IEEE RAS & EMBS International Conference on, IEEE, pp. 829–834.
20
Bajo, A., Goldman, R. E., and Simaan, N., 2011, “Configuration and Joint Feedback for Enhanced Performance of Multi-Segment Continuum Robots,” IEEE International Conference on Robotics and Automation, pp. 2905–2912.
21
Lock, J., Laing, G., Mahvash, M., and Dupont, P. E., 2010, “Quasistatic Modeling of Concentric Tube Robots With External Loads,” Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, IEEE, pp. 2325–2332.
22
Rucker, D., Jones, B. A., and Webster, R. J., 2010, “A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots,” IEEE Trans. Robot., 26(5), pp. 769–780. [CrossRef] [PubMed]
23
Mahvash, M., and Dupont, P. E., 2011, “Stiffness Control of Surgical Continuum Manipulators,” IEEE Trans. Robot., 27(2), pp. 334–345. [CrossRef]
24
Rucker, D., and Webster, R. J., 2011, “Statics and Dynamics of Continuum Robots With General Tendon Routing and External Loading,” IEEE Trans. Robot., 27(6), pp. 1033–1044. [CrossRef]
25
Dienno, D. V., 2006, “Design and Analysis of a Soft Robotic Manipulator With Base Rotation,” Master's thesis, The Pennsylvania State University, University Park, PA.
26
Trivedi, D., Dienno, D., and Rahn, C. D., 2008, “Optimal, Model-Based Design of Soft Robotic Manipulators,” J. Mech. Des., 130(9), p. 091402. [CrossRef]
27
Liu, W., and Rahn, C. D., 2003, “Fiber-Reinforced Membrane Models of McKibben Actuators,” ASME J. Appl. Mech., 70, pp. 853–859. [CrossRef]
28
Antman, S. S., 2004, Nonlinear Problems of Elasticity, Springer-Verlag, New York.
29
Gravagne, I. A., and Walker, I. D., 2000, “Kinematic Transformations for Remotely Actuated Planar Continuum Robots,” IEEE International Conference on Intelligent Robots and Systems, San Francisco, CA, pp. 19–26.
30
Kumar, A., and Healey, T., 2010, “A Generalized Computational Approach to Stability of Static Equilibria of Nonlinearly Elastic Rods in the Presence of Constraints,” Comput. Methods Appl. Mech. Eng., 199(25), pp. 1805–1815. [CrossRef]

Figures

Grahic Jump Location
Fig. 4

Soft robotic manipulator modeled using the Cosserat rod approach, with the backbone position (r) and orientation (d1, d2, d3) parameterized by a single variable s. The manipulator is acted upon by distributed force (f) and discrete forces (F) and moments (M).

+Soft robotic manipulator modeled using the Cosserat rod approach, with the backbone position (r) and orientation (d1, d2, d3) parameterized by a single variable s. The manipulator is acted upon by distributed force (f) and discrete forces (F) and moments (M).
View Large  |  Save Figure  |  Download Slide (.ppt)
Soft robotic manipulator modeled using the Cosserat rod approach, with the backbone position (r) and orientation (d1, d2, d3) parameterized by a single variable s. The manipulator is acted upon by distributed force (f) and discrete forces (F) and moments (M).
Grahic Jump Location
Fig. 3

Cross-sectional view of six and three extensor manipulator sections showing three independent control channels (I, II, and III). d1, d2, and d3 are director vectors and δ3 and δ6 are the distances between tube centers and the centroid of the cross-section for the 3- and 6- extensor manipulator sections, respectively

+Cross-sectional view of six and three extensor manipulator sections showing three independent control channels (I, II, and III). d1, d2, and d3 are director vectors and δ3 and δ6 are the distances between tube centers and the centroid of the cross-section for the 3- and 6- extensor manipulator sections, respectively
View Large  |  Save Figure  |  Download Slide (.ppt)
Cross-sectional view of six and three extensor manipulator sections showing three independent control channels (I, II, and III). d1, d2, and d3 are director vectors and δ3 and δ6 are the distances between tube centers and the centroid of the cross-section for the 3- and 6- extensor manipulator sections, respectively
Grahic Jump Location
Fig. 2

OctArm VI: (a) semitransparent 3D view of arm, (b) close-up photograph of base, (c) close-up, semitransparent view of first section, and (d) photograph of complete arm [25]

+OctArm VI: (a) semitransparent 3D view of arm, (b) close-up photograph of base, (c) close-up, semitransparent view of first section, and (d) photograph of complete arm [25]
View Large  |  Save Figure  |  Download Slide (.ppt)
OctArm VI: (a) semitransparent 3D view of arm, (b) close-up photograph of base, (c) close-up, semitransparent view of first section, and (d) photograph of complete arm [25]
Grahic Jump Location
Fig. 1

Capabilities of hard and soft robots

+Capabilities of hard and soft robots
View Large  |  Save Figure  |  Download Slide (.ppt)
Capabilities of hard and soft robots
Grahic Jump Location
Fig. 5

Soft robotic manipulator model

+Soft robotic manipulator model
View Large  |  Save Figure  |  Download Slide (.ppt)
Soft robotic manipulator model
Grahic Jump Location
Fig. 6

Schematic showing the use of a base-mounted load cell for shape sensing of a three section soft robotic manipulator in planar operation. An inclinometer is also mounted on the base.

+Schematic showing the use of a base-mounted load cell for shape sensing of a three section soft robotic manipulator in planar operation. An inclinometer is also mounted on the base.
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic showing the use of a base-mounted load cell for shape sensing of a three section soft robotic manipulator in planar operation. An inclinometer is also mounted on the base.
Grahic Jump Location
Fig. 7

Schematic showing the use of cable encoders (–) for shape sensing of a three section soft robotic manipulator in planar operation. An inclinometer is also mounted on the base.

+Schematic showing the use of cable encoders (–) for shape sensing of a three section soft robotic manipulator in planar operation. An inclinometer is also mounted on the base.
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic showing the use of cable encoders (–) for shape sensing of a three section soft robotic manipulator in planar operation. An inclinometer is also mounted on the base.
Grahic Jump Location
Fig. 8

Schematic showing the use inclinometers for shape sensing of a three section soft robotic manipulator in planar operation. If the weight of the tip payload is known, an inclinometer at the tip is not required.

+Schematic showing the use inclinometers for shape sensing of a three section soft robotic manipulator in planar operation. If the weight of the tip payload is known, an inclinometer at the tip is not required.
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic showing the use inclinometers for shape sensing of a three section soft robotic manipulator in planar operation. If the weight of the tip payload is known, an inclinometer at the tip is not required.
Grahic Jump Location
Fig. 9

Simulated error in manipulator tip position estimation averaged (RMS) over 64 configurations in the horizontal base orientation using cable encoders with a constant curvature model (dash-dotted), cable encoders with the full model (solid), inclinometer method (dotted) and the load cell method (dashed). The inset shows details of the tip position estimation error for the cable encoder method with full model (solid) and the load cell method (dashed). The area representing one standard deviation around the average error is shaded.

+Simulated error in manipulator tip position estimation averaged (RMS) over 64 configurations in the horizontal base orientation using cable encoders with a constant curvature model (dash-dotted), cable encoders with the full model (solid), inclinometer method (dotted) and the load cell method (dashed). The inset shows details of the tip position estimation error for the cable encoder method with full model (solid) and the load cell method (dashed). The area representing one standard deviation around the average error is shaded.
View Large  |  Save Figure  |  Download Slide (.ppt)
Simulated error in manipulator tip position estimation averaged (RMS) over 64 configurations in the horizontal base orientation using cable encoders with a constant curvature model (dash-dotted), cable encoders with the full model (solid), inclinometer method (dotted) and the load cell method (dashed). The inset shows details of the tip position estimation error for the cable encoder method with full model (solid) and the load cell method (dashed). The area representing one standard deviation around the average error is shaded.
Grahic Jump Location
Fig. 10

Simulated error in manipulator tip position estimation averaged (RMS) over 64 configurations in the vertical base orientation using cable encoders with a constant curvature model (dash-dotted), cable encoders with the full model (solid), inclinometer method (dotted), and the load cell method (dashed). The inset shows details of the tip position estimation error for the cable encoder method with full model (solid) and the load cell method (dashed). The area representing one standard deviation around the average error is shaded.

+Simulated error in manipulator tip position estimation averaged (RMS) over 64 configurations in the vertical base orientation using cable encoders with a constant curvature model (dash-dotted), cable encoders with the full model (solid), inclinometer method (dotted), and the load cell method (dashed). The inset shows details of the tip position estimation error for the cable encoder method with full model (solid) and the load cell method (dashed). The area representing one standard deviation around the average error is shaded.
View Large  |  Save Figure  |  Download Slide (.ppt)
Simulated error in manipulator tip position estimation averaged (RMS) over 64 configurations in the vertical base orientation using cable encoders with a constant curvature model (dash-dotted), cable encoders with the full model (solid), inclinometer method (dotted), and the load cell method (dashed). The inset shows details of the tip position estimation error for the cable encoder method with full model (solid) and the load cell method (dashed). The area representing one standard deviation around the average error is shaded.
Grahic Jump Location
Fig. 11

Estimation of cable encoder measurements (left) from edge and marker detection (right) for 100101 configuration at p = 35 psi

+Estimation of cable encoder measurements (left) from edge and marker detection (right) for 100101 configuration at p = 35 psi
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimation of cable encoder measurements (left) from edge and marker detection (right) for 100101 configuration at p = 35 psi
Grahic Jump Location
Fig. 12

Experimental average error in tip position estimation for the inclinometer method (circles), cable encoder method (asterisks) and the load cell method (triangles) without payload (a) and with a payload of 10 N (b). For the hinged boundary condition in absence of payload, shape estimation without sensing coincides with the load cell method. In presence of a payload, shape estimation without sensing (dashed) shows high error if the payload weight is unknown.

+Experimental average error in tip position estimation for the inclinometer method (circles), cable encoder method (asterisks) and the load cell method (triangles) without payload (a) and with a payload of 10 N (b). For the hinged boundary condition in absence of payload, shape estimation without sensing coincides with the load cell method. In presence of a payload, shape estimation without sensing (dashed) shows high error if the payload weight is unknown.
View Large  |  Save Figure  |  Download Slide (.ppt)
Experimental average error in tip position estimation for the inclinometer method (circles), cable encoder method (asterisks) and the load cell method (triangles) without payload (a) and with a payload of 10 N (b). For the hinged boundary condition in absence of payload, shape estimation without sensing coincides with the load cell method. In presence of a payload, shape estimation without sensing (dashed) shows high error if the payload weight is unknown.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Applicability of the HRA Methods for External Event PSA Based on Simulator Training (PSAM-0337)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
Tooth Forms
Design and Application of the Worm Gear> Chapter 3
Introduction and Definitions
Handbook on Stiffness & Damping in Mechanical Design> Chapter 1
Supporting Systems/Foundations
Handbook on Stiffness & Damping in Mechanical Design> Chapter 5
Openings
Guidebook for the Design of ASME Section VIII Pressure Vessels> Chapter 5
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
This site uses cookies. By continuing to use our website, you are agreeing to our privacy policy. | Accept
Sign In