Simultaneous Shape Reconstruction and Force Estimation of Soft Bending Actuators Using Distributed Inductive Curvature Sensors

Soft robots, with their remarkable advantages in various applications, face the critical challenge of embodied perception, encompassing proprioceptive sensing and perceiving unknown environments (exteroception). In this article, we achieve simultaneous continuous shape reconstruction and external force estimation for soft bending actuators using only a proprioceptive curvature sensor. We introduce a novel distributed inductive curvature sensor designed for capturing continuous shape through electromagnetic induction. In addition, we enhance an analytical static model based on the Euler–Bernoulli curved beam theory to predict the shape under pneumatic actuation and external forces. Furthermore, a model-based optimization algorithm is proposed to estimate external forces based on the measured shape. Extensive experimental validation supports the efficacy of the proposed sensor and algorithms.