Non-linear Finite-Time Tracking Control of Uncertain Robotic Manipulators Using Time-Varying Disturbance Observer-Based Sliding Mode Method

Abstract

In this paper, a time-varying chattering-free disturbance observer-based position tracking control law of serial robotic manipulators is presented to track a reference signal in a finite time. The key idea is to employ a positive-increasing function associated with the control/observer objectives to improve the control performance. First, the model of an uncertain robotic manipulator is presented as the case study of the proposed strategy. Then, the time-varying form of the robotic manipulator model is obtained to provide finite-time boundedness using the first-order sliding mode method. Moreover, without any knowledge about the upper bounds of the uncertainties, a reduced-order observer is presented to estimate the uncertainties in a finite time. Subsequently, a disturbance observer-based finite-time position tracking control law is designed. The time-varying gains are provided to converge the position tracking error to a neighborhood of zero in a finite time. Finally, comparative simulations are presented to show the effectiveness of the proposed scheme compared to other existing strategies.

A Modified Robotic Manipulator Controller Based on Bernstein-Kantorovich-Stancu Operator

“…In order to verify the advantages of the robotic manipulator control method proposed in this paper, we compared it with the new method in the same field in [ 14 ] and used the disturbance of Case 2 in Figure 4 carried out under the condition that the disturbance has no background noise and there is background noise in the disturbance–to illustrate the effectiveness of the method in this paper.…”

“…As shown in the position estimation and velocity estimation in Figure 10 , the method in [ 14 ] can observe the position and velocity during the operation of the manipulator servo system, and as shown in the disturbance estimation in Figure 10 , it can better control the manipulator joints. However, in the initial stage of the servo system operation, that is, during the start-up process, it can be seen that there are obvious observation distortions.…”

“…Compared with the disturbance imposed in Figure 6 , Figure 7 and Figure 8 , the influence on the stability of the system is not obvious. This shows that the method proposed in [ 14 ] is not timely enough to update the model after the system state changes, and it is not suitable for manipulators that require high-precision positioning accuracy and trajectory accuracy.…”

“…In recent years, some disturbance observers designed based on sliding mode observers have also achieved good results in the application of manipulator controllers, and the design of initial parameters is low in difficulty and easy to achieve. However, with the change of external disturbance characteristics, these parameters are difficult to evolve quickly and accurately, resulting in weak adaptability of the controller and difficulty applying in the presence of complex disturbances [ 14 , 15 ]. Therefore, a novel Bernstein–Kantorovich (BK) operator is added to the disturbance observer in this paper.…”

Adaptive Fractional-Order Non-Singular Fast Terminal Sliding Mode Control Based on Fixed Time Disturbance Observer for Manipulators

“…For the presence of matching disturbance in the system, a fractional disturbance observer is introduced in [28] to compensate for the system, which improved the positioning performance of the double pendulum offshore crane. In [29], a reduced-order observer is raised to gauge the uncertainty in the system, and realizes the tracking of the position of the manipulator in a limited time. In [30], the extended state observer is improved, and a fixed-time extended state disturbance observer is proposed, which ensures the high accuracy tracking control of the two-link manipulator.…”