Recurrent neural network robust curvature tracking control of tendon-driven continuum manipulators with simultaneous joint stiffness regulation

Continuum manipulators, despite their prominent flexibility and compliance, possess relatively low inherent stiffness and weak load capacity. Realizing simultaneous curvature tracking control and joint stiffness regulation for continuum manipulators would further broaden their application possibilities. In this paper, we propose a concurrent robot shape and stiffness control framework for a class of tendon-driven continuum manipulators (TDCMs). Firstly, by employing an efficient lumped-parameter dynamics model, the feedforward control term is computed offline along the desired reference trajectory. Integrating this term with our designed nonsmooth proportional-derivative robust controller leads to rapid convergence of the curvature tracking errors. Secondly, to further enhance the robustness of the control scheme, a lightweight recurrent neural network observer is designed to estimate the disturbances. Finally, the joint stiffness model of the TDCMs is derived. Based on the redundant-driven characteristics of the flexible segments and considering tendon tension constraints, we achieve simultaneous adjustment of joint stiffness and positions through tendon tension redistribution using the null-space control term. Global uniform asymptotic stability is established by the designed Lyapunov function. Simulation experiments validate the effectiveness of the proposed control scheme.