An Adaptive Terminal Sliding Mode Control for Robot Manipulators With Non-Singular Terminal Sliding Surface Variables

Abstract

This paper presents an adaptive terminal sliding mode control (TSMC) algorithm for robot manipulators. The contribution of our control method is that the suggested controller can enable the advantages of non-singular TSMC such as non-singularity, high robustness, small transient error, and finite time convergence. To develop the suggested system, a non-singular terminal sliding variable is selected and does not have any complex-value or constraints of the exponent in conventional TSMC. Therefore, it prevents the singularity that occurs in the conventional TSMC and eliminates the reaching phase glitch. Accordingly, the suggested system can ensure that the controlled variables reach the desired values within a randomly known finite time using an efficiently smooth and chattering-free definite control input. In addition, sliding motion in finite time can be achieved by employing the adaptive self-tuning rules with no prior information regarding the upper bounds of undefined parameters (e.g., friction, disturbances, and uncertainties). Furthermore, the finite-time convergence and global stability of the proposed algorithm are proved by the Lyapunov stability theory. Finally, the proposed control algorithm is applied to the joint position tracking control simulation for a 3-DOF PUMA560 robot. The trajectory tracking performance of the proposed method is compared with those of the conventional terminal sliding mode control and the conventional continuous sliding mode control. This comparison shows the efficiency and superiority of the proposed algorithm. INDEX TERMS Non-singular terminal sliding mode control, robotic manipulator, adaptive self-tuning rules, uncertainty, disturbance, chattering behavior.

Robust Finite-Time Convergence Control Mechanism for High-Precision Tracking in a Hybrid Fluid Power Actuator

“…The basis of Lemma 3 is proven by Fridman, Levant, and several other studies, such as [42], [43], [45], [46]. This lemma has also been successfully applied in numerous studies, such as in [45], [50], [52], [53].…”

A Non-Singular Fast Terminal Sliding Mode Control Based on Third-Order Sliding Mode Observer for a Class of Second-Order Uncertain Nonlinear Systems and its Application to Robot Manipulators

“…In order to obtain the control signal for the uncertain nonlinear system (1), an NFTSMC based on TOSM observer as described in Fig.1 is proposed. The control law is proposed as below u = −g(x, t) −1 u eq + u sw (16) In (16), the equivalent control law, u eq , holds the trajectory of the error state on the sliding surface, is designed as…”

“…Theorem 1: Consider the class of second-order uncertain nonlinear systems given by (1), if the NFTSM control input is designed as (16)(17)(18), then the origin of the sliding function (15) is globally finite-time stable equilibrium point and the sliding function (15) will converge to zero in finite time defined by T r = ŝ(0) µ .…”

Synchronization Full-Order Terminal Sliding Mode Control for an Uncertain 3-DOF Planar Parallel Robotic Manipulator

“…NFTSMC well handles the disadvantages of both conventional SMC and conventional terminal sliding mode control (TSMC), such as singularity, undefined time convergence, chattering, and slow convergence. NFTSMC has been successfully applied to serial manipulators and parallel manipulators [18,[33][34][35][36][37][38][39][40]. With NFTSMC, the system states not only achieve fast convergence but also avoids the singularity problem.…”