Forward and Inverse Kinematics of Cable-Driven Continuum Robots

Abstract

This paper deals with the forward and inverse kinematics of continuum robots consisting of a flexible backbone with attached disks and actuated by straight and generally routed cables. For forward kinematics, an efficient geometry-based optimization approach is presented with linear complexity in the number of disks. A feed-forward neural network, trained using the data generated from the forward kinematics, is employed for inverse kinematics. In case of straight cable routing, where the inverse kinematics solutions are unique, a standard mean-squared error loss function is used. For general cable routing, with multiple possible solutions, a modified reconstruction-based loss function is introduced, incorporating a separate network to predict forward kinematics. Both models yield accurate predictions, highlighting the effectiveness of the training and the robustness of the proposed approach. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2026.