Artificial Fishtail

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Description

Todays autonomous underwater vehicles (AUVs) are subject to noise polution and inefficiency due to their propulsion-driven design. The evolution of fish has, on the other hand optimized their underwater efficiency and agility over millenia. The adaption of fish-like drive systems for AUVs is therefore an obvious choice.

Model Description

This model describes the silicon body of an artificial fishtail supported by a central carbon beam. The rear part of the fish-body without the fins is modeled as as a 3d FEM model using linear elasticity. In the current stage of modeling the tail is rigidly mounted in the front, the states in $x$ represent the displacements of the finite element degrees of freedom. The fish-like locomotion is enabled by pumping air between two sets of pressure chambers in the left and right halves of the tail. The single input $u$ of the system is thus the pumping pressure. The outputs are displacements of certain surface points. There are two variants of the model. The first has only three outputs representing the displacements of the point of interest, the rear tip of the carbon beam, in the three spatial directions. For the second variant 6 additional points on the flank are added as outputs. These show two effects. On the one hand, for purely input output related reduction methods they avoid drastic deviations on the interior states. on the other hand they show a smoothing effect for the models transfer function.

Dimensions

System structure:

$\begin{align} M \ddot{x}(t) + E \dot{x}(t) + K x(t) &= B u(t) \\ y(t) &= C x(t) \end{align}$

System dimensions:

$M \in \mathbb{R}^{N \times N}$, $E \in \mathbb{R}^{N \times N}$, $K \in \mathbb{R}^{N \times N}$, $B \in \mathbb{R}^{N \times M}$, $C \in \mathbb{R}^{P \times N}$, with $N=779\,232$ and $M=1$.

System variants:

• $P = 3$: $C=$Cp in the data files,
• $P = 21$: $C=$Cp_ext in the data files.