Images of underwater objects are distorted by refraction at the water-glass-air interfaces and these distortions can lead to substantial errors when reconstructing the objects' position and shape. So far, aquatic locomotion studies have minimized refraction in their experimental setups and used the direct linear transform algorithm (DLT) to reconstruct position information, which does not model refraction explicitly. Here we present a refraction corrected ray-tracing algorithm (RCRT) that reconstructs position information using Snell's law. We validated this reconstruction by calculating 3D reconstruction error-the difference between actual and reconstructed position of a marker. We found that reconstruction error is small (typically less than 1%). Compared with the DLT algorithm, the RCRT has overall lower reconstruction errors, especially outside the calibration volume, and errors are essentially insensitive to camera position and orientation and the number and position of the calibration points. To demonstrate the effectiveness of the RCRT, we tracked an anatomical marker on a seahorse recorded with four cameras to reconstruct the swimming trajectory for six different camera configurations. The RCRT algorithm is accurate and robust and it allows cameras to be oriented at large angles of incidence and facilitates the development of accurate tracking algorithms to quantify aquatic manoeuvers.

Abstract-An autonomous underwater vehicle with a biomechanical propulsion system is a possible answer to the demand for small, silent sensor platforms in many fields. The design of Galatea, a bio-mimetic AUV, involves four aspects: hydrodynamic shape, the propulsion, the motion control systems and payload. The shape of the hull is based on a modified Wortmann FX 71-L-150/20 airfoil. Wind tunnel tests have been conducted to determine the hydrodynamic force coefficients. The propulsion system is based on bio-mimetic undulating fin propulsion. A test set-up is build to get more insight in the fundamentals of this mechanism. The swimming behaviour is currently manually controlled and will be developed into an fully autonomous system. In the future, more research on the undulating fin propulsion system will be carried out and a second, modular prototype robot will be developed.

Autonomous robots are used to inspect, repair and maintain underwater assets. These tasks require energy-efficient robots, including efficient movement to extend available operational time. To examine the suitability of a propulsion system based on undulating fins, we built two robots with one and two fins, respectively, and conducted a parametric study for combinations of frequency, amplitude, wavenumber and fin shapes in free-swimming experiments, measuring steady-state swimming speed, power consumption and cost of transport. The following trends emerged for both robots. Swimming speed was more strongly affected by frequency than amplitude across the examined wavenumbers and fin heights. Power consumption was sensitive to frequency at low wavenumbers, and increasingly sensitive to amplitude at high wavenumbers. This increasing sensitivity of amplitude was more pronounced in tall rather than short fins. Cost of transport showed a complex relation with fin size and kinematics and changed drastically across the mapped parameter space. At equal fin kinematics as the single-finned robot, the double-finned robot swam slightly faster (>10%) with slightly lower power consumption (<20%) and cost of transport (<40%). Overall, the robots perform similarly to finned biological swimmers and other bio-inspired robots, but do not outperform robots with conventional propulsion systems.

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