Research On Nonlinear Tracking Control Of Series Manipulators

The nonlinear tracking control of serial manipulators has always been a very active research direction in the robotics field and has very important research value.As a typical nonlinear controlled object,the serial manipulator has unique dynamic characteristics.It is a better method to use the knowledge of nonlinear control theory to track and control it.In the nonlinear control theory,Lyapunov method is in a very important position and is an effective means to solve the nonlinear tracking control.It can not only analyze the stability of the system,but also analyze and design the controller.It is widely used in nonlinear control algorithms such as PID control,adaptive control,and robust control.In this paper,based on Lyapunov stability theory,the nonlinear tracking controller design,closed-loop system stability analysis,and control system simulation verification of the dynamic model of the serial manipulator are performed.In this paper,taking the two-link manipulator as an example,the dynamic model of the manipulator is derived in detail through the second-type Lagrangian equation.The dynamic model of the robotic arm is a multi-input,multi-output,strongly coupled nonlinear differential equation.The dynamic characteristics of the dynamic model of the manipulator are analyzed.The dynamic characteristics of the manipulator have important applications for the analysis and design of the nonlinear controller.Next,nonlinear tracking control of the serial manipulator is performed.Based on the Lyapunov method,the PD tracking control,the nonlinear feedback tracking control based on linear filtering,and the adaptive tracking control based on the minimum inertial parameters of the manipulator are performed.Among them,the imitation PD tracking control can realize the fixed-point tracking control of the joint angular displacementwithout considering the system gravity,and can make the position tracking error and the speed tracking error converge to zero.Compared with the PD control,the tracking speed of the system is improved and the initial torque has decreased.Considering the influence of gravity on tracking control,nonlinear feedback tracking control based on linear filtering reduction is based on a complete dynamic model.In the open-loop system,a linear filter error variable is introduced,and the system is transformed into the first-order linear differential equations for filter error variable.The nonlinearity of the system is offset by the feed-forward compensation in the design of the controller.The stability analysis shows that the closed-loop control system designed can achieve the global exponential convergence of position error and velocity error.Dynamic control schemes based on precise models do not consider the effects of system uncertainties.Considering the influence of inertial parameter uncertainties of the system,an adaptive tracking control scheme based on the minimum inertial parameters of the manipulator is designed.Based on the introduction of the filter error variable,the dynamic model of the manipulator is transformed into the linear function of inertial parameters.The adaptive law identifies the inertial parameters online and changes the controller parameters at the same time.The simulation results of the control scheme in this paper show the effectiveness of the control method used.