  The use of soft robotics for real-world underwater applications is limited,
even more than in terrestrial applications, by the ability to accurately
measure and control the deformation of the soft materials in real time without
the need for feedback from an external sensor. Real-time underwater shape
estimation would allow for accurate closed-loop control of soft propulsors,
enabling high-performance swimming and manoeuvring. We propose and demonstrate
a method for closed-loop underwater soft robotic foil control based on a
flexible capacitive e-skin and machine learning which does not necessitate
feedback from an external sensor. The underwater e-skin is applied to a highly
flexible foil undergoing deformations from 2% to 9% of its camber by means of
soft hydraulic actuators. Accurate set point regulation of the camber is
successfully tracked during sinusoidal and triangle actuation routines with an
amplitude of 5% peak-to-peak and 10-second period with a normalised RMS error
of 0.11, and 2% peak-to-peak amplitude with a period of 5 seconds with a
normalised RMS error of 0.03. The tail tip deflection can be measured across a
30 mm (0.15 chords) range. These results pave the way for using e-skin
technology for underwater soft robotic closed-loop control applications.
