State Estimation of a Shape-Flexible Multi-Fingered Robotic Hand Leveraging Multiple Proximity Sensors Measuring an Ambient Environment Including the Self-Body and a Constant Curvature Model

This paper studies state estimation for continuum robotic fingers during in-hand manipulation, where accurate pose estimation relative to the environment is required in feature-sparse scenes. To address this requirement, we adopt a SLAM-based formulation that estimates the robot pose and a local map from exteroceptive sensing. Continuum fingers lack encoder-based joint angle measurements, while conventional SLAM assumes feature-rich environments that are rarely avail- able inside the hand. We propose a SLAM-based estimator that fuses exteroceptive proximity sensing with a constant-curvature kinematic prior by replacing encoder angles with virtual joint angles from the model. The key idea is to leverage designed in- hand self-body elements, namely the opposing fingers and the palm, as stable reference geometry to maintain observability in feature-spares environments. We evaluate our method through free motion and grasping simulations, and analyze the effect of presence and shape of the palm on estimation accuracy. The proposed estimator outperforms a kinematics-only baseline by suppressing bias, reducing a position error of an end effector, and improving map quality. We demonstrate that three-dimensional contoured palms enhance observability, and a composite wavy palm yields the smallest errors without temporal drift. These results indicate that designed in-hand geometry enables effective state estimation for continuum fin- gers in feature-sparse grasping scenarios, supporting reliable in-hand manipulation.