Vision-Based Shape Reconstruction of Soft Continuum Arms Using a Geometric Strain Parametrization

TL;DR

A vision-based shape estimator that utilizes a geometric strain based representation for the soft continuum arm’s shape, which reduces the dimension of the curved shape to a finite set of strain basis functions, thereby allowing for efficient optimization for the shape that best fits the observed image.

Abstract

Interest in soft continuum arms has increased as their inherent material elasticity enables safe and adaptive interactions with the environment. However to achieve full autonomy in these arms, accurate three-dimensional shape sensing is needed. Vision-based solutions have been found to be effective in estimating the shape of soft continuum arms. In this paper, a vision-based shape estimator that utilizes a geometric strain based representation for the soft continuum arm's shape, is proposed. This representation reduces the dimension of the curved shape to a finite set of strain basis functions, thereby allowing for efficient optimization for the shape that best fits the observed image. Experimental results demonstrate the effectiveness of the proposed approach in estimating the end effector with accuracy less than the soft arm's radius. Multiple basis functions are also analyzed and compared for the specific soft continuum arm in use.

Figures (5)

• Figure 1: (above) Images of the $BR^2$ soft continuum arm Uppalapati2021 from different angles showing a configuration that involves simultaneous bending and twist. (bottom) The view from the camera used for estimating the shape.
• Figure 2: An illustration of the SCA and the corresponding position $\mathbf{p}$, orientation $\mathbf{R}$, and tangent $\frac{\partial{\mathbf{p}}}{\partial{s}}$ of a single cross-section.
• Figure 3: Images of the soft robot with various configurations along with the projection of the estimated shape, in green, using (above) 2-segment constant strain basis and (below) quadratic basis functions. The red circles are the detected marker points on the image, and the blue circle is the projection of the magnetic sensor reading onto the image space.
• Figure 4: Estimated shape of the SCA using various basis functions. The blue point is the SCA's tip position obtained from the magnetic sensor.
• Figure 5: 3D position samples from the SCA's workspace with the corresponding error in (a,b) the tip position and (c,d) tip direction using a 2-segment constant strains basis and a quadratic basis.