  In this paper, we propose a novel variable-length estimation approach for
shape sensing of extensible soft robots utilizing fiber Bragg gratings (FBGs).
Shape reconstruction from FBG sensors has been increasingly developed for soft
robots, while the narrow stretching range of FBG fiber makes it difficult to
acquire accurate sensing results for extensible robots. Towards this
limitation, we newly introduce an FBG-based length sensor by leveraging a rigid
curved channel, through which FBGs are allowed to slide within the robot
following its body extension/compression, hence we can search and match the
FBGs with specific constant curvature in the fiber to determine the effective
length. From the fusion with the above measurements, a model-free filtering
technique is accordingly presented for simultaneous calibration of a
variable-length model and temporally continuous length estimation of the robot,
enabling its accurate shape sensing using solely FBGs. The performances of the
proposed method have been experimentally evaluated on an extensible soft robot
equipped with an FBG fiber in both free and unstructured environments. The
results concerning dynamic accuracy and robustness of length estimation and
shape sensing demonstrate the effectiveness of our approach.
