Data-driven contact-state estimation of an endoskeleton-reinforced soft pneumatic gripper using sigmoidal pressure–bending response analysis

Soft robotic grippers are uniquely suited for handling fragile objects, yet reliable contact-state awareness remains challenging due to sensor noise, signal drift, and limited interpretability of current approaches. This study presents an interpretable two-stage analytical pipeline for contact estimation of a pneumatic soft gripper using low-cost commercial flex sensors embedded within an endoskeleton-reinforced PneuNet structure. The pipeline first establishes pressure–bending relationships through sigmoidal modelling of single-finger mechanics, delineating free bending, initial contact, and full engagement (blocking). A multi-finger comparative analysis then uses differences in transition pressures and bending trajectories among fingers to infer object geometry and detect abnormal grasp behavior. Evaluated across 10 objects; spherical, cylindrical, asymmetric, delicate, and miniature; symmetrical objects synchronized, while irregular objects showed staggered finger engagement. The sigmoidal model achieved a mean R 2 = 0.94 across blocking positions. The gripper achieved an 80% grasp success rate across 10 diverse objects and a 650 g payload capacity. Comparing bending trajectories further detects yielding (in delicate objects) during grasping. By combining physically interpretable modelling with lightweight signal processing, the proposed approach achieves contact-state estimation using cost-effective sensing hardware without custom tactile arrays, training data, or computationally intensive models. This work offers a practical pathway toward low-cost sensing solutions for soft robotic manipulation in industrial applications.