Nonlinear Tracking Differentiator Based Prescribed Performance Control for Space Manipulator

Abstract

A low-complexity prescribed performance controller is proposed for motion tracking control of a space manipulator in this paper. First of all, a prescribed-time prescribed performance function is designed. Based on the function, the proposed controller is capable of guaranteeing the system transient and steady-state control performances satisfy the prescribed boundary constraints. Moreover, all tracking errors converge to stability domains before the user-defined settling time. A nonlinear tracking differentiator based on a hyperbolic sine function is adopted to estimate the derivatives of joint angles and reconstruct the angular velocity for the controller, which lowers hardware requirements for the controlled system to a certain extent. Without any time-consuming operations and model information, the proposed control scheme has a superiority in low computation complexity and robustness against model uncertainties. With the Lyapunov theory, the prescribed-time stability within prescribed performances of the closed-loop has been rigorously proven. Numerical simulation and the comparison with the traditional prescribed performance control demonstrates the effectiveness and superior performances of the proposed control scheme.

Event-triggered Stochastic Finite-time Tracking Control of Robot Manipulator with Uncertain Disturbance Neural Network Estimation

“…Many types of manipulators have been developed rapidly due to a wide range of practical applications. Such as modular robot manipulator [1], space manipulator [2,3], hydraulic manipulator [4], underwater manipulator [5], and so on. These manipulators usually need to complete the specified tracking task, so a variety of tracking control methods were proposed.…”

Design of Backstepping Control Based on a Softsign Linear–Nonlinear Tracking Differentiator for an Electro-Optical Tracking System

“…To solve these problems, different tracking differentiators have been used to improve the transient performance of the filtered signal and the differentiation performance at higher frequencies [27][28][29][30][31][32][33][34]. These differentiators can complete the process of tracking and differentiating a real-time signal without relying on the controlled object model, and they use an integration process instead of the differentiation process used in the traditional numerical differentiation method [35] to avoid a "complexity explosion" while performing signal filtering.…”

“…When a tracking differentiator has a relatively fast convergence speed, the speed of the change in state quantities near the equilibrium point increases simultaneously, which leads to convergence chattering and other problems, resulting in a decrease in the tracking accuracy of the differentiator. In this regard, Arctangent Tracking Differentiators (ATDs) in the form of an inverse tangent using an inverse tangent function [31], Modified Tracking Differentiators (MTDs) designed using a nonlinear odd-exponential continuous function that is stable at only one equilibrium point [32], New Nonlinear-Linear Tracking Differentiators (NTDs) using hyperbolic tangent (Tanh) functions [33], and Hyperbolic-Sine-Based Tracking Differentiators (HNTDs) [34] using hyperbolic sinusoidal functions have been proposed, which are based on a common improvement strategy: introducing both nonlinear and linear links into the differentiator design. Linear and nonlinear links exhibit different degrees of action when the state is far from or close to the equilibrium point, ensuring the rapidity and stability of differentiator convergence.…”

“…Therefore, the decision has been made to adopt backstepping control, which can circumvent these issues and provide effective control for an electrooptical tracking system. When solving the complexity explosion present in backstepping control, the existing dynamic surface will introduce filtering errors and reduce the tracking accuracy [21]; the transient performance of the filtered signal of the existing command filter is poor [24]; and existing tracking differentiators have a complex structure and more parameters and the gradient of the function they use disappears faster, so it is not possible to realise an approximate differentiation process with the proposed accuracy [34]. Thus, this paper proposes a linear-nonlinear tracking differentiator based on the Softsign excitation function (SL-NTD) for an electro-optical tracking system.…”

“…A linear-nonlinear tracking differentiator is designed using the Softsign excitation function for the first time. Compared to the dynamic surface used in Liang and Qiu's work, the method proposed in this paper does not introduce filtering errors [21]; compared to the command filter used in Han and Yu's work, the method in this paper can simultaneously take into account the speed and stability of signal convergence [24]; and compared to the tracking differentiator used in Fan and Jing's work, the method in this paper has fewer parameters, the disappearance of the gradient is slowed down, and thus differentiation can be approximated more accurately [34].…”