We present a unified formulation for describing the dynamics of a new class of aquatic multi-body soft robots. This formulation accounts for the continuum hyperelastic nature of the vehicles and for the interaction with the dense fluid across which they dwell. We start by introducing the highly unconventional design concept of a soft underwater vehicle inspired by the octopus capable of swimming, manipulating and crawling. The dynamics of the robot, which consists of a multi-limbed continuum of elastomeric materials, is extremely complex to account for with conventional modelling tools. Hence a Cosserat based formalism where a Reissner shell model and a finite-strain beam formulation are joined is conceived which lends itself to the description of the highly non linear dynamics of this new family of vehicles in a dense fluid.
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