  The precise control of soft and continuum robots requires knowledge of their
shape. The shape of these robots has, in contrast to classical rigid robots,
infinite degrees of freedom. To partially reconstruct the shape, proprioceptive
techniques use built-in sensors resulting in inaccurate results and increased
fabrication complexity. Exteroceptive methods so far rely on placing reflective
markers on all tracked components and triangulating their position using
multiple motion-tracking cameras. Tracking systems are expensive and infeasible
for deformable robots interacting with the environment due to marker occlusion
and damage. Here, we present a regression approach for 3D shape estimation
using a convolutional neural network. The proposed approach takes advantage of
data-driven supervised learning and is capable of real-time marker-less shape
estimation during inference. Two images of a robotic system are taken
simultaneously at 25 Hz from two different perspectives, and are fed to the
network, which returns for each pair the parameterized shape. The proposed
approach outperforms marker-less state-of-the-art methods by a maximum of 4.4%
in estimation accuracy while at the same time being more robust and requiring
no prior knowledge of the shape. The approach can be easily implemented due to
only requiring two color cameras without depth and not needing an explicit
calibration of the extrinsic parameters. Evaluations on two types of soft
robotic arms and a soft robotic fish demonstrate our method's accuracy and
versatility on highly deformable systems in real-time. The robust performance
of the approach against different scene modifications (camera alignment and
brightness) suggests its generalizability to a wider range of experimental
setups, which will benefit downstream tasks such as robotic grasping and
manipulation.
