Abstract: To overcome the influence of uncertain factors such as mechanical friction,unknown loads,and model errors on the control accuracy of manipulator,a nonsingular fast integrating terminal sliding mode finite time robust control law was designed using exponential obstacle Lyapunov function.Firstly,a mathematical model of the manipulator with uncertain factors was established,and the interference value was accurately estimated by designing an observer. Then,the terminal sliding surface of nonsingular fast integration was designed by using the angle error of the manipulator,and the finite time robust control law was designed based on the exponential obstacle Lyapunov function. Finally,the stability analysis also verified that the designed finite time robust control law could converge within the effective time. The simulation results of a 3-DOF manipulator show that the proposed finite time robust control law can effectively overcome the influence of uncertainties factors on the control accuracy of the manipulator,the maximum estimation error of the observer is 0.1 (°)/s²,and the maximum tracking error of each joint angle of the manipulator is 0.1°,which verifies the effectiveness of the design method.In the 3-D space fixed coordinate positioning experiment,under the proposed finite time robust control law,the maximum positioning error of the manipulator is 0.22 cm,and the maximum running time is 2.2 s,which verifies that higher control accuracy and running efficiency can be achieved in practical engineering applications.

Key words: manipulator, observer, exponential barrier Lyapunov function, nonsingular fast integral terminal sliding mode, finite time robust control law