Study On Dynamic Analysis And Control Of Nonlinear Systems Based On Differential Geometry

Nonlinear systems dynamics and control is always a key problem in the study of dynamic systems.In recent years,the theories and methods of nonlinear dynamics have gradually developed from low dimension to high dimension or even infinite dimension.Meanwhile,due to the rapid development of computer science,numerical simulation and graphics technology,the scale and difficulty of the problems solved by nonlinear systems dynamics and control have become increasingly larger and closer to the actual systems.The introduction of differential geometry theory provides a new idea and method to solve the problems of nonlinear systems dynamics and control,and has attracted extensive attention of scholars at home and abroad.Based on differential geometry theory,this paper derived the recursive analytical algorithm of the second order autonomous dynamical system of the nonlinear oscillator.Meanwhile the nonlinear dynamics and control problems of the snake-like robot are studied by differential geometry method,too.The main research contents are as follows:First,based on the differential geometry theory and the variational principle,the recursive analytical algorithm of the second order dynamic equation of the nonlinear oscillator is derived,and three different autonomous nonlinear systems are selected for the verification calculation.At the same time,used the Runge-Kutta method to solve the continuous differential equation of the nonlinear dynamical systems.By comparing the calculation results and the computational time of the two algorithms.The results illustrate that the recursive analytical algorithm has the advantages of higher accuracy and shorter time,and can achieve the analytical solution of a certain time node according to the need of specific situation.Then,based on the relevant theory of differential geometry,the position-pose space of snake-like robot was extended to Riemannian manifold space,and the unified model of nonlinear dynamics and control of the snake-like robot was established.According to the unified model and the local feedback linearization control method,the head trajectory tracking controller of snake-like robot was designed.The numerical simulation of robot head trajectory is also realized based on MATLAB platform.Moreover,the simulation results indicate that the snake-like robot can track the preset trajectory stably under the action of the controller.Finally,compared with the classical Euler-Lagrange dynamic modeling method,the unified model of dynamics and control of snake-like robot based on differential geometry method has some advantages,such as simpler calculation and so on.