PSO-based nonlinear model predictive planning and discrete-time sliding tracking control for uncertain planar underactuated manipulators

Control of planar underactuated manipulators (PUM) with unknown parameter perturbations and external disturbances is still a challenging task due to their complex and peculiar characteristics. The research on it is significant in the view of wide applications in practice. In this paper, taking an uncertain 3-degree of freedom PUM with a free first joint as a benchmark example, we discuss its position control issue. Specifically, an integrated control method is developed, including the nonlinear model prediction control (NMPC) based on an improved particle swarm optimisation (PSO) algorithm and the discrete-time fast terminal sliding mode (FTSM) control. The PSO-based NMPC is proposed for planning discrete trajectories of the active joint angles in real time, along which the manipulator end-point can reach the desired position. Then the discrete-time FTSM controllers are designed to keep the active joints tracking the discrete trajectories, where the uncertainties related to the active links/joints are estimated by time delay estimation method. Besides, the influence of the uncertainties related to the free link/joint on the system can be made up by the NMPC in real time. It is confirmed via simulations that the above method can achieve the accurate positioning of such an uncertain manipulator.