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

Capabilities of hard and soft robots

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]

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

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 model

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 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 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.

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 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.

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

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.