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文章在控制输入饱和约束条件下,以非完整移动机器人的运动学模型为对象,研究了移动机器人的轨迹跟踪问题。首先在参考轨迹处对运动学模型进行线性化得到移动机器人线性时变系统,证明了其能观性和能控性,在此基础上设计了饱和约束条件的分段线性二次型控制器(Piecewise Linear Quadratic Regulator,PLQR),并基于Lyapunov方法证明了其稳定性。在MATLAB软件平台下的仿真和实验结果表明,基于PLQR的轮式移动机器人对不同初始位姿及不同的参考轨迹都有较好的跟踪效果,且能够避免控制律跳变现象,满足饱和约束条件。
Under the control input saturation constraints, this paper studies the trajectory tracking problem of mobile robot based on the kinematics model of nonholonomic mobile robot. Firstly, the kinematic model is linearized at the reference trajectory to obtain the linear time-varying system of the mobile robot, and its observability and controllability are proved. Based on this, a piecewise linear quadratic controller with saturation constraints is designed Piecewise Linear Quadratic Regulator, PLQR), and its stability is proved based on Lyapunov method. The simulation and experimental results under the MATLAB software platform show that the wheeled mobile robot based on PLQR has good tracking performance for different initial pose and different reference trajectories and can avoid the phenomenon of control law transition and satisfy the saturation constraints .