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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
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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.
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References

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Figures

Grahic Jump Location
Fig. 1

Capabilities of hard and soft robots

+Capabilities of hard and soft robots
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Capabilities of hard and soft robots
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]
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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. 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. 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).
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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. 5

Soft robotic manipulator model

+Soft robotic manipulator model
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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.
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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.
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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
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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.

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