Control And Simulation For Three-link Manipulator Based On Data-driven And Koopman Operator

Industrial manipulators play a very important role in modern industrial manufacturing,assembly and production,driving the rapid development of automated and intelligent manufacturing.For some tasks with high repeatability,high requirements of speed and accuracy,three-link manipulators are widely used.However,for three-link manipulator system,its nonlinearity is always the difficulty and focus of controller design,while the traditional model-based method is complicated and requires prior knowledge of the model.Based on the global linearization characteristics of Koopman operator,this thesis uses a data-driven method to Koopman-linearize the model of three-link manipulator system,and then implements the design of linear quadratic regulator(LQR).The main work are as follows:1.Based on the Newton-Euler recursive algorithm,the dynamic modeling of planar and space three-link manipulator with revolute joints is performed respectively,and the specific form of dynamic equation is given.Then by analyzing the characteristics and compositions of the dynamic equation of manipulator,a set of suitable observation basis function vector is selected,based on the evolutionary characteristics of the generalized Koopman operator.2.For the manipulator dataset with multiple system trajectories,the improved least square method(LSM)and dynamic model decomposition(DMD)are introduced.These two algorithms are applied to calculate the matrix form of Koopman operator for manipulator respectively based on the previously selected basis function vector.Simulation result proves that the LSM has better fitting accuracy and computing performance than DMD.3.The matrix form and basis function vector of Koopman operator for manipulator are divided respectively,so that the original nonlinear dynamic model can be transformed into a linear state equation with input terms.Based on this state equation,the high-dimensional and low-dimensional output equations are constructed respectively and the LQR controller is implemented.Simulation result demonstrates that the performance of high-dimensional output equation is better than the low-dimensional form.Finally,the feasibility and effectiveness of proposed method are proved by simulation experiments on two different platforms.