如何產生適當的運動軌跡命令為循跡控制的重要課題之一。一般而言，根據一預先設定之進給率對路徑進行插值，就可得到運動軌跡對時間之命令。然而，針對機械手臂而言，因其工作空間與關節空間兩者之關係為非線性，並且會隨著機械手臂目前的位置與姿態而改變，上述的運動軌跡命令產生方法很容易產生軸飽和問題，即在運行過程中超出機械手臂的物理限制如，軸速度、軸加速度、軸急跳度及軸轉矩等。有鑑於此，基於B-雲形線具備局部調整的能力，本論文採用3階的B-雲形線來構建進給率曲線，並以此為基礎推導出機械手臂之物理限制及進給率的關係式。最後，利用演化式計算，基於時間最佳化之目的，對上述問題進行求解。此外，輪廓誤差為循跡控制的重要指標之一，一般在工具機相關應用中係採用降低進給率的方法來減少輪廓誤差，然而若採用機械手臂進行循跡控制時卻無具體參考指標。對此，本論文提出了一個基於二軸平面機械手臂的輪廓誤差模型，從而得到輪廓誤差與進給率的關係式，可用於機械手臂循跡運動命令規劃。

The way to generate suitable motion trajectory commands is one of the most important topics in contour following control. In general, motion command is generated by interpolating the desired trajectory with a preset feedrate. However, for robot manipulators, the relationship between the workspace and the joint space is non-linear and depends on the current pose of the robot manipulator. The above method for generating motion trajectory may lead to joint saturation problems; that is, the physical limits of the robot manipulators are exceeded during operation, such as joint velocity, joint acceleration, joint jerk, and joint torque. In view of this, based on the locality property of the B-spline, this thesis uses a 3-order B-spline to construct the feedrate curve, and on this basis, derives the relationship between feedrate and physical constraints of robot manipulators. Finally, evolutionary computation is used to solve the above problem with the purpose of time optimization. In addition, contour error is one of the important indicators of contour following applications. Generally, in machine tool related applications, the commonly used method for contour error reduction is to reduce feedrate. However, if the robot manipulator is used in contour following applications, there is no specific reference index. In this regard, this paper proposes a contour error model based on a two-axis planar robotic arm to obtain the relationship between the contour error and the feedrate. Moreover, the above contour error model can be used in motion planning of contour following tasks for robot manipulators.

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