基于内模扩展LQ方法的WMR轨迹跟踪控制

针对现有非线性控制方案的一些瓶颈问题,从线性控制的角度出发,开展了一种用于WMR的线性二次型最优控制方法设计的研究.首先,基于WMR的运动学模型采用动态反馈线性化技术将非线性运动学模型转化为线性模型；然后,选取跟踪误差及误差收敛速度作为设计指标；同时考虑实现渐进跟踪，针对不同形式的参考轨迹,根据内模原理对控制器模态进行扩展,利用线性模型设计基于内模扩展LQ最优轨迹跟踪控制器；最后通过动态反馈反变换得到实际控制器.此外,通过将此方法的控制效果与几种经典方法进行仿真比对,说明了此方法对于跟踪的精确性和快速性上有较大优势.

Trajectory Tracking Control Based on Internal Model Expanded LQ Method for WMR Systems

To deal with some bottleneck problems from the view of linear control, this paper developed a linear quadratic (LQ) optimal method applied in WMR. First of all, based on the kinematics model, this work used dynamic feedback linearization technique to transform a non-linear system to a linear one. Then, this method selected tracking error and error convergence rate as design indicators to design LQ optimal trajectory tracking controller on the basis of such linear model. Moreover, according to different reference trajectory, it expanded the controller model to achieve the request of asymptotic tracking. Finally, it obtained actual controller by applying dynamic feedback inverse transformation. In addition, by comparing the control results with some of other classical solutions through simulation, these results illustrates that the solution of this paper has shown larger advantage based on the accuracy and rapidity in tracking.