Soft continuum robots provide a compelling solution for safe interactions with unknown and unstructured environments, owing to their compliance and infinite degrees of freedom. However, the non-linear deformation and inherent underactuation pose a persistent challenge for real-time control and state estimation. To date, continuum structures are typically discretized using a fixed-parameter kinematic model, introducing a trade-off between model accuracy and computational efficiency.

This letter presents an adaptive kinematic modeling framework to address the challenge of underactuation in a different way - not by increasing model resolution or complexity - but by making the model parametric with respect to a set of parameters that are dynamically adapted using a novel inverse kinematic adaptive controller.

We formally prove stability of the adaptive controller and validate its performance through simulations and experiments, considering setpoint reaching tasks with variable end-effector payloads. Even though the approach introduces additional challenges, in comparison to the conventional fixed-parameter models presented in literature, the proposed solution enhances shape representation, redundancy resolution, and state inference while mitigating model complexity.