  In this paper, we use the optimal control methodology to control a flexible,
elastic Cosserat rod. An inspiration comes from stereotypical movement patterns
in octopus arms, which are observed in a variety of manipulation tasks, such as
reaching or fetching. To help uncover the mechanisms underlying these observed
morphologies, we outline an optimal control-based framework. A single octopus
arm is modeled as a Hamiltonian control system, where the continuum mechanics
of the arm is modeled after the Cosserat rod theory, and internal, distributed
muscle forces and couples are considered as controls. First order necessary
optimality conditions are derived for an optimal control problem formulated for
this infinite dimensional system. Solutions to this problem are obtained
numerically by an iterative forward-backward algorithm. The state and adjoint
equations are solved in a dynamic simulation environment, setting the stage for
studying a broader class of optimal control problems. Trajectories that
minimize control effort are demonstrated and qualitatively compared with
observed behaviors.
