Closed-loop underwater soft robotic foil shape control using flexible e-skin

TL;DR

The paper tackles the challenge of real-time deformation sensing for underwater soft robotics, where external sensors hinder flexibility. It introduces a liquid-metal capacitive e-skin paired with an MLP-based estimator to map capacitances to foil shape for real-time camber estimation and closed-loop control via a PID controller. The results demonstrate accurate shape tracking with max sensor error < 2.2% and low normalised RMSE (0.03–0.11) across representative trajectories, with a rise time of ~1.7 s. This approach enables untethered, real-time state estimation for underwater soft propulsion and has potential to extend to 3D state estimation and more complex multi-DoF morphologies in future work.

Abstract

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.

Figures (10)

• Figure 1: (a) Schematic of the tunable-stiffness soft foil. The rigid nose houses the internal pressure tubing, and clamps the silicone tail. The soft silicone tail has holes to house the inflatable rubber tubes which can expand and contract with pressure. The e-skin is bonded to the silicone tail using a thin layer of EcoFlex-30. (b) (Left) Soft robotic foil with e-skin attached for deformation measurement. The red tracking markers allow for the position of the foil to be tracked underwater for training and ground truth comparison. (Right) e-skin module for the soft robotic foil before attachment to the robot. 6 wires allow for the reading of 9 signals for training and measurement.
• Figure 2: Outline of the key physical parameters for the control problem. The angle between any oncoming flow and the leading edge $\alpha$ is the angle of attack. The straight line from the leading edge to the trailing edge is the chord line. The line from leading edge to the trailing edge through the centre of the foil is the camber line. The perpendicular distance between the chord and the camber lines defines the camber.
• Figure 3: Fabrication process of the capacitive e-skin. (a) Deployment of copper electrodes on the 3D-printed mould, (b) Eco-flex 00-30 is poured into the 3D printed mould, (c) curing of the top layer at room temperature for 4 hours and release the mould, (d) fabrication of an additional silicone backing layer and bonding with the top layer by means of the uncured silicone mixture as the adhesive, (e) injection of Liquid metal into the hollow channels with a second needle used as an exhaust for the air and finally sealing of the holes created by the needles with additional silicone. (f) The fabricated Liquid metal e-skin.
• Figure 4: Schematic of the static testing set up. The pressurisation of the foil is controlled using a linear actuator connected to a syringe which supplies the pressure. An underwater camera records the motion of the foil for training and ground truth comparison.
• Figure 5: Signals of calibrated capacitance readouts, eq. \ref{['eqn: skin calibration']}, during foil deformation (top) and corresponding foil deformation (bottom) throughout five repetitive cycles of camber actuation.