Design Of High Precision Algorithm For Solving Time-varying Nonlinear Equations And Application Of Manipulator

In science and engineering,the solution of nonlinear equations is widely involved,which is generally regarded as the basic part of many important fields.In practical applications,the nonlinear equations involved are usually time-varying,while previous studies mainly focus on time-invariant nonlinear equation problems.Time-invariant models solve time-varying problems and obtain approximate solutions,or study nonlinear time-varying equations with the scalar form off(x(t),t)=0 is proposed,in this paper put forward the nonlinear equations of parameters change over time(f(x(t),t)=0?R~n)the high precision of algorithm,this is not implemented or not good when using traditional numerical algorithm.In order to solve the time-varying nonlinear equations in real time,this paper presents a neural dynamics model,and then designs different difference rules based on Taylor series expansion.In these two kinds of algorithms,the derivative information can be used to predict time-varying problems,so it can provide more accurate solutions for time-varying nonlinear problems.This paper through the theoretical analysis shows that the proposed two types of discrete algorithm under different sampling interval and step length has a wide range of index of convergence and the error is small enough(i.e.,cubic error and fourth power error change rule),and a large amount of numerical experiments show that the proposed two new algorithms on the validity and reliability of time-varying nonlinear system of equations.Considering that redundant manipulator has become a research hotspot at home and abroad,this paper will further discuss the application of the proposed high-precision algorithm to the motion planning of redundant manipulator,so as to reflect the practical application value of the algorithm.In particular,the proposed high-precision algorithm can realize the motion planning of the redundant manipulator by solving the kinematics equation of the manipulator.Then,a planar five-link manipulator is simulated by computer,and the corresponding simulation results show that the proposed algorithm can successfully realize the motion planning of the manipulator.Moreover,by adjusting the parameters of the algorithm,the motion planning of the manipulator can be highly accurate(i.e.,the corresponding motion planning error still has the variation rule of cubic and fourth power).This provides important guiding significance and reference value for motion planning of redundant manipulator.