Double-loop frame-based adaptive neural sliding-mode control of single-input 3-DOF flexible-joint manipulator

Flexible-joint manipulators (FJMs) have been attracting much attention in recent decades. However, position control and vibration suppression of single-input (SI) multi-degrees-of-freedom (multi( $ {\geqslant }3 $ ⩾3)-DOF) FJM is still a high mountain to climb due to the characteristic that some states of such FJMs cannot be directly controlled by the SI. This paper aims to carry out this challenging research. We present a double-loop frame-based adaptive neural sliding-mode control method for an uncertain horizontal SI 3-DOF FJM, i.e. a two-link FJM with only one actuator at the first joint. Since only the actuator angle can be directly controlled, in the inner loop, we design a torque controller so that the actuator angle tracks a time-varying reference actuator angle, designed in real-time by the outer loop. In the outer loop, we consider the reference actuator angle as a virtual control signal and design it based on the dynamic coupling relationships, aiming to indirectly control the first link to its target position and suppress the vibration of both links. Furthermore, to enhance the transient system performance, we plan the input signal of the outer loop (i.e. the target angle) as a smooth reference-trajectory signal. The validity and superiority of this method are demonstrated in simulations.