Gust Estimation and Rejection with a Disturbance Observer for Proprioceptive Underwater Soft Morphing Wings

TL;DR

The paper tackles gust disturbance rejection for underwater soft morphing wings by exploiting proprioceptive deformation sensed through an e-skin. It develops a PCC-based dynamic model of a hydraulically actuated wing, couples Thin Airfoil Theory for lift, and designs an Extended Kalman Filter–based disturbance observer to estimate angle of attack from curvature, enabling a disturbance-aware control law. A PI controller uses the estimated disturbance to track a reference wing curvature that preserves lift, with simulations and experiments showing improved rejection of step changes and gust-like disturbances. The work demonstrates that proprioception integrated with disturbance observers can enable stable, efficient operation of soft underwater vehicles in highly perturbed environments, and suggests extensions to higher-dimensional wing morphologies for richer disturbance estimation.

Abstract

Unmanned underwater vehicles are increasingly employed for maintenance and surveying tasks at sea, but their operation in shallow waters is often hindered by hydrodynamic disturbances such as waves, currents, and turbulence. These unsteady flows can induce rapid changes in direction and speed, compromising vehicle stability and manoeuvrability. Marine organisms contend with such conditions by combining proprioceptive feedback with flexible fins and tails to reject disturbances. Inspired by this strategy, we propose soft morphing wings endowed with proprioceptive sensing to mitigate environmental perturbations. The wing's continuous deformation provides a natural means to infer dynamic disturbances: sudden changes in camber directly reflect variations in the oncoming flow. By interpreting this proprioceptive signal, a disturbance observer can reconstruct flow parameters in real time. To enable this, we develop and experimentally validate a dynamic model of a hydraulically actuated soft wing with controllable camber. We then show that curvature-based sensing allows accurate estimation of disturbances in the angle of attack. Finally, we demonstrate that a controller leveraging these proprioceptive estimates can reject disturbances in the lift response of the soft wing. By combining proprioceptive sensing with a disturbance observer, this technique mirrors biological strategies and provides a pathway for soft underwater vehicles to maintain stability in hazardous environments.

Figures (10)

• Figure 1: The flexible wing under study. Hydraulic actuators along the length of the wing can be pressurised to increase the curvature. The curvature can be measured using a proprioceptive e-skin.
• Figure 2: a) The experimental setup from micklem2024closed. The assembly was placed in a flume. The motor rotated the setup to simulate different angles of attack. The load cell measured lift force. b) The geometry of the wing model. The kinematics of the wing are described in a Cartesian coordinate plane. The parameter $\theta$ describes the curvature of the wing. $s$ describes the normalised distance along the centreline of the wing, with $s=0$ at the base and $s=1$ at the tip. $h(s)$ describes the thickness of the wing.
• Figure 3: The camberline of the wing, used for thin aerofoil theory. $F_l$ and $F_d$ are the forces from lift and drag, $\alpha$ is the angle of attack and $U$ is the speed of the oncoming flow.
• Figure 4: Plot showing the response of the model compared to the real response when subject to the same inputs and initial conditions. The inputs are the internal pressure (manually adjusted), and $\alpha$ stepped from 0 to 0.1745 rad and back.
• Figure 5: Plot showing the response of the model compared to the real response when subject to the same inputs and initial conditions. The inputs are the internal pressure (manually adjusted), and $\alpha$ stepped from 0.2618 to 0 rad and back.