  Proprioception is the "sixth sense" that detects limb postures with motor
neurons. It requires a natural integration between the musculoskeletal systems
and sensory receptors, which is challenging among modern robots that aim for
lightweight, adaptive, and sensitive designs at a low cost. Here, we present
the Soft Polyhedral Network with an embedded vision for physical interactions,
capable of adaptive kinesthesia and viscoelastic proprioception by learning
kinetic features. This design enables passive adaptations to omni-directional
interactions, visually captured by a miniature high-speed motion tracking
system embedded inside for proprioceptive learning. The results show that the
soft network can infer real-time 6D forces and torques with accuracies of
0.25/0.24/0.35 N and 0.025/0.034/0.006 Nm in dynamic interactions. We also
incorporate viscoelasticity in proprioception during static adaptation by
adding a creep and relaxation modifier to refine the predicted results. The
proposed soft network combines simplicity in design, omni-adaptation, and
proprioceptive sensing with high accuracy, making it a versatile solution for
robotics at a low cost with more than 1 million use cycles for tasks such as
sensitive and competitive grasping, and touch-based geometry reconstruction.
This study offers new insights into vision-based proprioception for soft robots
in adaptive grasping, soft manipulation, and human-robot interaction.
