A High‐Precision and Robust Geometric Relationships‐Inspired Neural Network for the Inverse Kinematic Modeling of the Tendon‐Actuated Continuum Manipulator

Continuum manipulators can operate in complex environments where traditional rigid manipulators fail. However, the modeling of inverse kinematics remains challenging because of its inherent nonlinearities and various external conditions. This work proposes an online learning control framework with a data cache pool utilizing a constant-curvature model inspired neural network (CCMINN) model to obtain the inverse kinematics model of tendon-actuated continuum manipulators. The CCMINN model is a kind of geometric relationships-inspired neural network, which is inspired by the geometric relationships within the constant-curvature model. This model improves the ability of traditional fully connected neural network models on high convergence speed and precision through its constant-curvature inspiration layers. These layers embed geometry insights into the neural network structure rather than loss functions like physics-informed neural networks. The online learning framework enables CCMINN to maintain high control accuracy in a variety of external load scenarios. Experiments show average tracking errors of 1.4 mm, 1.38 mm, and 1.48 mm (0.7%, 0.64%, and 0.74% of the continuum manipulator length) in the free space, under constant and variable loading conditions, respectively. The results show that combining the fast-converging CCMINN with an online learning control framework enables high-precision and robust positioning control of continuum manipulators under various external payloads.