Research On Trajectory Tracking Control Of Nonholonomic Wheeled Mobile Robot With Saturation Constraints

In this paper,we mainly study the control strategy of trajectory tracking for nonholonomic wheeled mobile robots under saturation constraints.The basis of the kinematic model of a two-wheeled wheel(2,0)wheeled mobile robot is transformed into a linear time-varying system based on the linearization of the reference system.Based on the linear time-varying system,this paper presents a framework which applies the Piecewise Linear Quadratic Regulator(PLQR)control.Based on the Lyapunov method,it is proved that the designed trajectory tracking controller PLQR can satisfy the control input saturation condition,and can guarantee the stability of the closed-loop system.Simulation results show that the PLQR based wheeled mobile robot has good tracking effect on different initial position and different reference trajectories.Then,based on the linear time-varying discrete system,an adaptive quadratic controller based on genetic algorithm is designed to adjust the gain on-line.Both PLQR and ALQR keep the control input and state in the constraint range to achieve trajectory tracking.Firstly,the nonlinear system of mobile robot is transformed into linear time-varying system based on the approximate linearization method of the reference system,and its observability and controllability are proved.The linear time-varying quadratic control(LTV-QR)algorithm is derived and the LTV-QR optimal problem is transformed into a standard quadratic programming problem which is convenient for computer solving.Then,a linear quadratic regulator(LQR)and a linear quadratic controller(PLQR)considering the saturation constraint are designed respectively.Based on the Lyapunov method,the stability of the linear quadratic regulator(LQR)TheThen the linear discrete system is constructed as the penalty function of the Lagrangian multiplier and the saturation constraint as the penalty factor,and the linear quadratic controller(ALQR)with the penalty function as the objective function is solved by the interior point method.Aiming at the problem that the weighting matrix is different under different conditions in the above realization process,the adaptive selection is achieved by using the weighting matrix with different initial positions and different reference trajectories to control the performance index as the genetic algorithm of the constraint function to obtain the condition Under the optimal control weight matrix.The numerical simulation of the robot system is carried out under the MALLAB software platform,and the mobile robot is tested on the mobile platform.Simulation and experimental results show that the wheeled mobile robot based on PLQR or ALQR has better tracking effect on different initial pose and different reference trajectories,and can avoid the control law transition phenomenon and satisfy the constraint condition.