中文摘要：

在多轴轮廓运动中，轮廓误差是比跟踪误差更为重要的性能指标，但在实际应用中轮廓误差是难以计算与使用的。通过在期望轨迹上建立Frenet坐标系作为工作坐标系，轮廓误差可以用位置跟踪误差在工作坐标系中的法向分量来近似。然后将系统动力学方程由全局坐标系变换到工作坐标系，在工作坐标系下采用最优线性二次型（LQR）方法来设计最优轮廓控制器，通过提高法向误差分量的权值来改善轮廓精度。在XY平台模型上进行的系统仿真实验表明，与基于全局坐标系的计算力矩控制相比，该方法有效地提高了轮廓精度，具有明显的优越性。

英文摘要：

In multi-axis contouring motion, contouring error is a more important performance index than tracking error. By establishing a Frenet coordinate frame on a desired trajectory as the task coordinate frame, contouring error was approximated by the normal component of tracking error in the task coordinate frame. Then by transforming the system dynamics from the world coordinate frame to the task coordinate frame, the optimal Linear Quadratic Regulator （LQR） approach was used to design the optimal contouring controller. To improve the contouring accuracy, the weight of normal error component was enhanced. The system simulation experiments implemented on a XY bed model verify that the proposed method improves contouring accuracy effectively and has obvious advantages by a comparison with the computed torque control method in the world coordinate frame.