Abstract: Tendon-driven continuum manipulators are highly suited for space operations, offering low rotational inertia, high compliance, and hyper-redundant bending capabilities. These characteristics enable lightweight and dexterous manipulation in confined environments, facilitating space tasks such as intravehicular and extravehicular inspection, equipment maintenance, and payload handling. However, nonlinear friction, transmission backlash, and material hysteresis cause actual physical deformations to deviate from predictions of the idealized piecewise constant curvature (PCC) model, thereby degrading end-effector position estimation and closed-loop tracking performance. To address these challenges, this paper presents a physics-informed neural network (PINN)-based model predictive control (MPC) framework designed for tendon-driven continuum manipulators in space operations. Specifically, the PCC model serves as a geometric prior, while a PINN is designed to estimate the end-effector position residuals induced by unmodeled effects. To enforce physical consistency, a backbone-length boundary constraint and a spatial-symmetry constraint motivated by friction mechanics are incorporated into the learning process. The resulting PINN model is then integrated into an MPC framework, wherein tendon stroke and actuator velocity limits are explicitly handled via receding horizon optimization. By leveraging a terminal-constraint framework and Lyapunov stability theory, the recursive feasibility of the control law, the asymptotic convergence of the predicted tracking error, and the ultimate boundedness of the actual tracking error are rigorously proved. Finally, ground experiments on a three-section prototype validate that the proposed scheme improves position estimation accuracy and yields better performance in both point-to-point and continuous trajectory tracking tasks.

Key words: space continuum manipulator, tendon-driven continuum manipulator, physics-informed neural network, model predictive control, piecewise constant curvature model