Predefined-time global sliding mode control design for a 3D pendulum

This paper concentrates on the predefined-time trajectory tracking for an uncertain robotic manipulator system. First, a modified predefined-time control (PTC) algorithm is proposed. Subsequently, with the help of proposed modified PTC algorithm and the nonsingular design method of terminal sliding mode, a novel nonsingular terminal sliding-mode control (NTSMC) scheme is proposed for ensuring the predefined-time convergence of tracking errors. The advantages of the newly proposed control scheme are as follows. (i) Unlike the conventional predefined-time sliding-mode control (SMC) which only guarantees the predefined-time convergence of sliding-mode surface, the proposed scheme can guarantee the predefined-time convergence of tracking errors. (ii) Compared with the conventional PTC algorithm, the proposed modified PTC algorithm can reduce the initial control peaking and enhance the precision of convergence time. The performance and effectiveness of the proposed control scheme are illustrated by comparing with the existing methods.

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Terminal Sliding-Mode Control of Uncertain Robotic Manipulator System with Predefined Convergence Time

We present an analytical design and experimental verification of trajectory tracking control of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a finite terminal time. A key feature of this control strategy is that this terminal convergence time is explicitly prescribed by the control designer, and is thus independent of the initial conditions of the tracking errors. In order to achieve this beneficial property of the proposed controller, a scaling of the state by a function of time that grows unbounded towards the terminal time is employed. Through Lyapunov analysis, we first demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, non-vanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large initial conditions of the tracking errors and a sinusoidal disturbance being applied in each joint.

Experimental and Analytical Prescribed-Time Trajectory Tracking Control of a 7-DOF Robot Manipulator

We present an analytical design and experimental veriﬁcation of trajectory tracking con- trol of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a ﬁnite terminal time, also referred to as the “settling time.” A key feature of this control strategy is that the settling time is explicitly assigned by the control designer to a value desired, or “prescribed” by the user and that the settling time is independent of the initial conditions and of the reference signal. In order to achieve this bene- ﬁcial property with the controller, a scaling of the state by a function of time that grows unbounded toward the terminal time is employed. Through Lyapunov analysis, we ﬁrst demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, nonvanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large distance between the initial conditions and the reference trajectory, i.e., in spite of large initial tracking errors, and in spite of a sinusoidal disturbance being applied in each joint. [DOI: 10.1115/1.4055023]

Design and Experiment of a Prescribed-Time Trajectory Tracking Controller for a 7-DOF Robot Manipulator

Fixed-time Disturbance Observer-based Sliding Mode Control for Mismatched Uncertain Systems

This paper proposes a novel robust fixed-time control for the robot manipulator system with uncertainties. Based on the uniform robust exact differentiator (URED) algorithm, a robust control term is constructed. Then, a robust fixed-time inverse dynamics control (IDC) is proposed. For the proposed control method, the fixed-time stability of a closed-loop system with uncertainties is strictly proved. The newly proposed method exhibits the following two attractive features. First, the proposed control scheme extends the existing fixed-time IDC for the robot manipulator system to the robust control scheme. Second, the proposed method is strictly nonsingular rather than the commonly used approximate approach. Simulation result demonstrates the effectiveness of the proposed control scheme.

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Yu Song

Papers

Robust Fixed-Time Inverse Dynamic Control for Uncertain Robot Manipulator System

Terminal Sliding-Mode Control of Uncertain Robotic Manipulator System with Predefined Convergence Time