T. Baaij et al., “Learning 3D shape proprioception for continuum soft robots with multiple magnetic sensors,” Soft Matter, vol. 19, no. 1, pp. 44–56, 2023, DOI: 10.1039/D2SM00914E.

Sensing the shape of continuum soft robots without obstructing their movements and modifying their natural softness requires innovative solutions. This letter proposes to use magnetic sensors fully integrated into the robot to achieve proprioception. Magnetic sensors are compact, sensitive, and easy to integrate into a soft robot. We also propose a neural architecture to make sense of the highly nonlinear relationship between the perceived intensity of the magnetic field and the shape of the robot. By injecting a priori knowledge from the kinematic  model, we obtain an effective yet data-efficient learning strategy. We first demonstrate in simulation the value of this kinematic prior by investigating the proprioception behavior when varying the sensor configuration, which does not require us to re-train the neural network. We validate our approach in experiments involving one soft segment  containing a cylindrical magnet and three magnetoresistive sensors. During the experiments, we achieve mean relative errors of 4.5%.