Anding Xu, Xunwei Wu, Huishen Zhu, and Jin Guo
Manipulators, time-varying boundary, barrier Lyapunov function, adaptive constraint control, RBF neural network
In some application scenarios, to constrain the trajectory tracking error of each joint during the movement of the manipulators, it can always be confined within the time-varying boundary to achieve high precision control of the manipulators. Firstly, a time-varying tangent barrier Lyapunov function is proposed by constructing the time- varying constraint boundary of exponential decay, which can satisfy both constrained and unconstrained cases. Secondly, the controller is designed by using inversion method and time-varying tangential barrier Lyapunov function to ensure that the tracking error of the system does not violate the time-varying constraint. In addition, radial basis function (RBF) neural network adaptive algorithm is used to compensate system uncertainties and external disturbances, and the stability of the control system is proved. Finally, the control algorithms are compared using MATLAB/Simulink. The results show that under external disturbance and system uncertainty, the manipulators can achieve high precision trajectory tracking control by using this control algorithm. Compared with the second-order sliding mode control (SMC) algorithm, the controller designed in this paper can make the root-mean-square (RMS) error of each joint trajectory of the manipulators smaller, in which the joint trajectory tracking error is reduced by about ten times and the joint velocity error is reduced by nearly 20 times. Thus, the control algorithm in this paper can track the motion trajectory quickly and accurately in complex cases.
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