This article proposes a robust command-filtered control method with prescribed performance for flexible-joint robots (FJRs) wherein matched and mismatched disturbances are compensated by designing generalized proportional integral disturbance observers (GPIOs). The contributions are threefold. Firstly, a prescribed performance function (PPF), compared with that of the previous schemes, frees the assumption that the initial value of tracking errors within a predetermined region and thus is global, which brings dynamic response and steady-state precision benefits. Secondly, unlike most existing backstepping controllers that handle only internal uncertainties, the method presented here also considers time-varying external disturbances which may affect the tracking performance of the FJRs. Thirdly, a second-order command filter and a filter error compensation method are designed to avoid the ”complexity explosion” problem encountered in the traditional backstepping scheme. Analysis with the Lyapunov function proves the asymptotical stability of the closed-loop system. Simulation and experiments are performed to validate the feasibility and fine performance of the recommended control strategy.

This paper presents a miniature manipulator under Cartesian control for minimally invasive transluminal endoscopic surgery. The manipulator had four degrees of freedom (DoFs) and a diameter of only 3.5 mm. The compact size of the manipulator allowed it to pass through the instrument channel of the endoscope, and its high dexterity allowed it to perform most of the operations in endoscopic surgery such as marking, grasping, hanging, etc. The implicit function relationship in the kinematics of the continuum manipulator was analyzed. By introducing the regression analysis method, the analytical form of the inverse kinematics was obtained. The distribution of singularities in the manipulator workspace was analyzed with emphasis. The presence of singularities made Cartesian mapping control between the primary side and secondary side impossible. By introducing the smoothing method of the joint trajectory, the discontinuity of the joint velocity at the singularity was avoided and the primary–secondary mapping under Cartesian control was realized. The trajectory-tracking experiment proved that the smoothness of the joint trajectory could make the manipulator smoothly pass through the singularity. The fixed-point marking experiment proved that the Cartesian control could improve the intuition of operation and the efficiency of task completion. Comprehensive performance experiments showed that the manipulator had enough dexterity to execute complex operations.