This paper presents an application of the energy shaping methodology to
control a flexible, elastic Cosserat rod model of a single octopus arm. The
novel contributions of this work are two-fold: (i) a control-oriented modeling
of the anatomically realistic internal muscular architecture of an octopus arm;
and (ii) the integration of these muscle models into the energy shaping control
methodology. The control-oriented modeling takes inspiration in equal parts
from theories of nonlinear elasticity and energy shaping control. By
introducing a stored energy function for muscles, the difficulties associated
with explicitly solving the matching conditions of the energy shaping
methodology are avoided. The overall control design problem is posed as a
bilevel optimization problem. Its solution is obtained through iterative
algorithms. The methodology is numerically implemented and demonstrated in a
full-scale dynamic simulation environment Elastica. Two bio-inspired numerical
experiments involving the control of octopus arms are reported