  Continuum robots with variable stiffness have gained wide popularity in the
last decade. Layer jamming (LJ) has emerged as a simple and efficient technique
to achieve tunable stiffness for continuum robots. Despite its merits, the
development of a control-oriented dynamical model tailored for this specific
class of robots remains an open problem in the literature. This paper aims to
present the first solution, to the best of our knowledge, to close the gap. We
propose an energy-based model that is integrated with the LuGre frictional
model for LJ-based continuum robots. Then, we take a comprehensive theoretical
analysis for this model, focusing on two fundamental characteristics of
LJ-based continuum robots: shape locking and adjustable stiffness. To validate
the modeling approach and theoretical results, a series of experiments using
our \textit{OctRobot-I} continuum robotic platform was conducted. The results
show that the proposed model is capable of interpreting and predicting the
dynamical behaviors in LJ-based continuum robots.
