Physics-guided residual inverse-transition modeling for continuum robots with simulation and ordered experimental evaluation

This study distinguishes two levels that were conflated in the original submission: a tendon-driven mechanical dynamics model used only in simulation, and an ordered one-step inverse-transition estimator used for the recorded experiment. The experimental estimator does not identify force-level inverse dynamics because the supplied dataset contains no verified sampling interval, velocity, acceleration, tendon tension, actuator torque, pneumatic pressure, or contact-force channel. Instead, it predicts the next measured six-channel length-state increment from the present Cartesian state, desired Cartesian increment, and a structured representation of the measured length state. The first-order prior is a global empirical differential map, J∈ R3× 6 , estimated only from the training block; it has rank 3, condition number 3.49, and singular values 1.425, 1.317, and 0.409. Reviewer-driven ablation further showed that the Clarke-like 3× 3 transform is a full-rank coordinate change rather than a dimensionality reduction, that appending both raw channels and deterministic modes reweights Gaussian-kernel distances, and that the one-step history term does not improve the held-out experimental prediction. The revised experimental instantiation therefore retains only the four bending coordinates (qα ,1,qβ ,1,qα ,2,qβ ,2) in the nonlinear residual learner and excludes both the common mode and duplicated raw/mode features. On the chronologically held-out 39-transition test block, this bending-mode residual KRR obtains a task-space RMSE of 0.365 mm and a cable/length-state RMSE of 0.745 mm, compared with 0.469 mm for a validation-tuned direct KRR, 0.596 mm for ridge regression, 0.654 mm for the NARX-feature model, and 0.795 mm for the global empirical prior. A four-sample moving-block bootstrap gives a within-trajectory 95% interval of approximately 0.282–0.437 mm for the revised task-space RMSE. A paired sign-randomization test against direct KRR gives p≈ 0.060 , so the small test block does not justify a claim of statistically conclusive superiority over that strongest nonlinear baseline. The independently learned forward evaluator has a test component RMSE of 0.139 mm and vector RMSE of 0.240 mm, but its larger validation error also reveals chronological distribution shift. Accordingly, the revised claims are restricted to free-space, one-step inverse-transition prediction on the recorded trajectory family; no cross-speed, cross-platform, force/contact, or closed-loop hardware generalization is claimed.