  This paper introduces a Cosserat rod based mathematical model for modeling a
self-controllable variable curvature soft continuum robot. This soft continuum
robot has a hollow inner channel and was developed with the ability to perform
variable curvature utilizing a growing spine. The growing spine is able to grow
and retract while modifies its stiffness through milli-size particle (glass
bubble) granular jamming. This soft continuum robot can then perform continuous
curvature variation, unlike previous approaches whose curvature variation is
discrete and depends on the number of locking mechanisms or manual
configurations. The robot poses an emergent modeling problem due to the
variable stiffness growing spine which is addressed in this paper. We
investigate the property of growing spine stiffness and incorporate it into the
Cosserat rod model by implementing a combined stiffness approach. We conduct
experiments with the soft continuum robot in various configurations and
compared the results with our developed mathematical model. The results show
that the mathematical model based on the adapted Cosserat rod matches the
experimental results with only a 3.3\% error with respect to the length of the
soft continuum robot.
