Research On Trajectory Tracking And Control For Manipulator Based On Zeroing Neural Network

With the development of society and technology,the connection between robots and people's production and life is getting closer and closer.Robot-related research and application has become an important symbol for measuring the level of smart manufacturing in a country.Some high-speed,high-precision application fields place higher requirements on the performance and accuracy of industrial robot arms.However,since the operation control of the mechanical arm is disturbed by the non-linear factors of joint flexible parts,joint coupling,friction and load disturbance resistance,its tracking accuracy and control accuracy are difficult to achieve the ideal state.This article takes the two-degree-of-freedom manipulator as the research object,and aims to improve the trajectory tracking accuracy of the manipulator,and studies the dynamic modeling and trajectory tracking control of the manipulator,the main work completed in this paper is as follows:(1)Establish a mathematical model of robot arm dynamics.Through detailed comparison and analysis of the advantages and disadvantages of the Newton-Euler method and the Lagrange method to establish the dynamic model of the manipulator,the Lagrange method is used to construct the mathematical model of the manipulator dynamics by combining the kinetic energy and potential energy of each link of the robot arm.(2)Aiming at the trajectory tracking problem of the manipulator,two discrete-time five-step neural network algorithms for solving the trajectory of the manipulator are proposed.First,based on the zeroing neural network technology,the problem of solving the trajectory of the robotic arm is transformed into a time-varying matrix inverse problem.A continuous-time noise-tolerant zeroing dynamic system is constructed by introducing an integral term using a continuous-time zeroing dynamic system.Secondly,combining the Taylor-type discretization formula to discretize the continuous-time noise-tolerant zeroing dynamic system,two types of five-step discrete-time noise-tolerant zeroing neural network models are proposed.Using the root stability theorem,the zero-stability,consistency,and convergence of the two types of neural network models are analyzed.It is proved that the two types of neural network models haveO(?~4)convergence order,which obviously improves the convergence order of the neural network models.Thirdly,through numerical comparison experiments with traditional discrete-time Euler-type neural network model,the numerical results show that the two types of five-step discrete-time noise-tolerant zeroing neural network model is feasible and effective which proposed in this paper.Finally,two types of five-step discrete-time noise-tolerant zeroing neural network models were successfully applied to the trajectory tracking simulation experiment of the manipulator,which realized the fast and real-time trajectory tracking of the manipulator.(3)Aiming at the optimal control problem of the manipulator,a discrete-time zeroing neural network control algorithm is proposed.Based on the zeroing neural network technology,the optimal control problem of the manipulator is transformed into a time-varying quadratic programming problem.The Lagrange equation is used to transform the time-varying quadratic programming problem into a time-varying system of equation solving problems.A time-varying error function is constructed to obtain a nonlinear control system.A five-step discrete-time zeroing neural network model is proposed to solve this type of nonlinear control.The zero-stability,consistency,and convergence of this type of network model are analyzed systematically.The truncation error theory based on Taylor formula proves that the convergence order of the network isO(?~4).The numerical results show that the optimal algorithm of the robot arm based on the zeroing neural network can achieve low energy consumption,high efficiency and stable control.