3-Axis Angular Strain Estimation With Hall Effect Sensors for Proprioception of Soft Robotic Manipulators

Slender soft robots offer significant advantages for real-life applications, particularly in areas that require delicate and adaptable interaction with complex environments. However, their effectiveness and safety can be greatly limited in the absence of sensing capabilities. Hall effect sensors, known for their excellent sensitivity and compact design, offer an innovative solution for equipping soft manipulators with perceptive abilities. In this letter, we propose an optimized sensor-magnet arrangement that can estimate all 3 angular strains of a slender rod, including torsion and bending along orthogonal axes, using a single sensor-magnet pair. With optimized design and experimental data, we trained a neural network to accurately predict angular strains from the measured magnetic fields. Using the predicted strains at different points along the body, we reconstruct the 3D shape of the sensorized manipulator using a Piece-wise Constant Angular Strain (PCAS) model. Two manipulator designs were considered in this work: single-segment and three-segment. Experimental results indicate tip position errors of less than 2% of the total manipulator length for the single-segment soft robot and less than 5% for the three-segment soft robot. The inherent simplicity of our design enables easy scaling and replication while ensuring reliable strain measurements critical for accurate robot shape reconstruction.