  In this paper, we present a novel and generic data-driven method to
servo-control the 3-D shape of continuum and soft robots embedded with fiber
Bragg grating (FBG) sensors. Developments of 3-D shape perception and control
technologies are crucial for continuum robots to perform the tasks autonomously
in surgical interventions. However, owing to the nonlinear properties of
continuum robots, one main difficulty lies in the modeling of them, especially
for soft robots with variable stiffness. To address this problem, we propose a
versatile learning-based adaptive controller by leveraging FBG shape feedback
that can online estimate the unknown model of continuum robot against
unexpected disturbances and exhibit an adaptive behavior to the unmodeled
system without priori data exploration. Based on a new composite adaptation
algorithm, the asymptotic convergences of the closed-loop system with learning
parameters have been proven by Lyapunov theory. To validate the proposed
method, we present a comprehensive experimental study by using two continuum
robots both integrated with multi-core FBGs, including a robotic-assisted
colonoscope and multi-section extensible soft manipulators. The results
demonstrate the feasibility, adaptability, and superiority of our controller in
various unstructured environments as well as phantom experiments.
