Real-time shape estimation of a wire-driven soft snake-like robot based on micro-inertial sensors

Due to the lack of accurate theoretical deformation models, real-time shape perception and closed-loop shape control of soft snake-like robots severely restrict their deployment in unstructured scenarios including narrow-space inspection, minimally invasive medical operation and post-disaster debris reconnaissance. This work develops a modular cable-driven soft snake robot and proposes a novel shape estimation framework relying on distributed micro-inertial sensors. Kalman filtering and complementary PI filtering are adopted to convert raw key-point measurements into module attitude data, which are fused with a parabolic geometric model to reconstruct the robot's 3D central line morphology in real time. Comparative experiments on single modules and the full robot are carried out to validate the precision and anti-disturbance robustness of the proposed method against conventional constant-curvature modeling. Experimental results demonstrate obvious accuracy advantages over constant-curvature schemes under multiple interference conditions. For a standalone flexible module without external payload, the maximum endpoint positioning error is below 3.5 %; under static 500 g end loading, the maximum positioning error rises to 11.38 mm. Stable motion without morphological bifurcation is maintained during dynamic loading tests. For full-robot winding gait tests under ideal planar conditions, the average root-mean-square shape estimation error is 7.67 mm, dropping to approximately 5.3 mm for small-amplitude undulating gaits, while the maximum RMSE reaches 15.7 mm under large bending amplitudes; additional obstacle-crossing experiments with contact disturbances yield an average RMSE of 10.86 mm and a peak RMSE of 19.4 mm. Future work will extend full-robot shape estimation tests to unstructured outdoor terrain to further validate the method's engineering adaptability in complex field environments.