  This paper presents a novel vision-based proprioception approach for a soft
robotic finger that can estimate and reconstruct tactile interactions in both
terrestrial and aquatic environments. The key to this system lies in the
finger's unique metamaterial structure, which facilitates omni-directional
passive adaptation during grasping, protecting delicate objects across diverse
scenarios. A compact in-finger camera captures high-framerate images of the
finger's deformation during contact, extracting crucial tactile data in
real-time. We present a volumetric discretized model of the soft finger and use
the geometry constraints captured by the camera to find the optimal estimation
of the deformed shape. The approach is benchmarked using a motion capture
system with sparse markers and a haptic device with dense measurements. Both
results show state-of-the-art accuracies, with a median error of 1.96 mm for
overall body deformation, corresponding to 2.1% of the finger's length. More
importantly, the state estimation is robust in both on-land and underwater
environments as we demonstrate its usage for underwater object shape sensing.
This combination of passive adaptation and real-time tactile sensing paves the
way for amphibious robotic grasping applications.
