Adaptive Trajectory Tracking Control Of Robotic Manipulator Based On Barrier Lyapunov Function

With the advancement of science and technology,robotic manipulators are widely used in important fields such as industrial production,living services,medical treatment,and aerospace.Therefore,the steady performance and transient performance of the robot manipulators during operation need to reach higher standards.In the research of robotic arm control problems,we must first establish a dynamic model of the system.However,there must be modeling errors between the mathematical model established for the robotic manipulators system and the actual model.Secondly,in the process of actually operating the robotic arm,the robotic arm system is often subject to external interference.In addition,the robotic manipulators are often limited by certain constraints during operation,such as input constraints,output constraints,and state constraints.Therefore,the manipulators control is challenging,and the design of its control algorithm has become one of the current research hotspots,which is of great significance.Aiming at the problem of trajectory tracking control of manipulators with system constraints,it is necessary to use a constraint control method to design the controller so that the system can implement the trajectory tracking control without violating the constraints.Barrier lyapunov function is one of the most commonly used methods to solve system constraints.It is often used to design controllers combined with other control methods to implement system trajectory tracking control.In view of the influence of uncertain system model on the performance of control system,neural network control is one of the most commonly used solutions.In this dissertation,the robotic arm systems with system constraints and model uncertainties are taken as the controlled object.Based on the barrier lyapunov function,the backstepping method and neural networks are used to design an adaptive controller to realize the tracking control of robotic arms without violating the constraints.The main work of this dissertation is as follows:In order to solve the fixed-time trajectory tracking control problem of a robotic arm with system model uncertainty and all-state constraints,a time-varying secant barrier Lyapunov function is designed in this dissertation.The barrier lyapunov function is used in combination with backstepping and RBF.neural networks design adaptive fixed time controller.The design of the adaptive fixed-time controller ensures that the system's full-state constraints are not violated,and allows the system tracking errors to converge to a neighborhood near zero within a fixed time.In order to make the designed controller more practical,the system model uncertainty,input constraints and full state constraints are considered in the design of the robotic manipulators controller.First,the hyperbolic barrier lyapunov function is designed to solve the system's full state constraint problem.This hyperbolic barrier lyapunov function can not only be applied to symmetric,asymmetric,and unconstrained system control at the same time,but also can be combined with a backstepping method to design a controller to achieve system fixed-time control.Then,the nonlinear input saturation constraints in the common input constraint types are approximated.Then,the neural networks are used to approximate the system model uncertainty and the virtual control variable derivatives to enhance the robust performance of the control system and simplify the controller design.Finally,the system stability analyses are carried out by using lyapunov stability theory,and the effectiveness of the proposed methods are verified by simulation,and the simulation results are analyzed.