  Soft robotic shape estimation and proprioception are challenging because of
soft robot's complex deformation behaviors and infinite degrees of freedom. A
soft robot's continuously deforming body makes it difficult to integrate rigid
sensors and to reliably estimate its shape. In this work, we present
Proprioceptive Omnidirectional End-effector (POE), which has six embedded
microphones across the tendon-driven soft robot's surface. We first introduce
novel applications of previously proposed 3D reconstruction methods to acoustic
signals from the microphones for soft robot shape proprioception. To improve
the proprioception pipeline's training efficiency and model prediction
consistency, we present POE-M. POE-M first predicts key point positions from
the acoustic signal observations with the embedded microphone array. Then we
utilize an energy-minimization method to reconstruct a physically admissible
high-resolution mesh of POE given the estimated key points. We evaluate the
mesh reconstruction module with simulated data and the full POE-M pipeline with
real-world experiments. We demonstrate that POE-M's explicit guidance of the
key points during the mesh reconstruction process provides robustness and
stability to the pipeline with ablation studies. POE-M reduced the maximum
Chamfer distance error by 23.10 % compared to the state-of-the-art end-to-end
soft robot proprioception models and achieved 4.91 mm average Chamfer distance
error during evaluation.
