本篇論文將針對六軸機械手臂的移動路徑點之角定位誤差開發一種量測系統，此系統以FANUC的M710-ic作為實驗載體，其為常見的六旋轉軸工業型機器人，並使用Laser Tracker以及一高精度球型反射器對其量測，並以改進的DH法（Denavit–Hartenberg Method）為基礎，建立一運動學校準模型對其誤差參數進行補償。
在此之中，我們將會透過機器人之正向運動學計算機器人在空間中姿態之末端位置，將量測到之值與其相減，即可得到機器人的位置誤差，並利用偽逆矩陣法識別運動學參數，接著，將識別的誤差參數補入再對機器人重新建模，並利用逆向運動學計算將誤差參數等效轉換為各點的關節角誤差，並將其數值補償回控制器中，此目的是為了不想直接更改FANUC控制器的內部參數，從而造成安全保固問題，進而將其補入可隨時更改的各關節角值內。在求解誤差前，會先對整個數學算法進行模擬，以確保計算過程的準確性，並證實其可行性。
最後，將透過夾取工作空間內的鋁塊以驗證補償後的值，將反射球放置於欲夾取之鋁塊的位置，並將其相對於機器人座標系的位置資訊輸入於先前的逆向運動學中，即可轉換為角度，以便輸入於控制器內。此方法可以模擬應用於自動化產線之實際情況，若可得知料盤相對於機器人的真實位置，便可運用此方法，而不是手動示教規劃機器人路徑，預期未來能在自動化產線上下料過程中節省其時間，且精度能得到改善。

This paper develops a measurement system for evaluating the angular positioning errors of the moving path points of a six-axis industrial robot. The system utilizes the FANUC M710-ic as the experimental platform, which is a common six-rotating-axis industrial robot. Measurement is performed using a Laser Tracker and a high-precision spherical reflector called SMR. Based on the modified Denavit-Hartenberg Method, a kinematic calibration model is established to compensate for error parameters.
In this process, the end-effector position of the robot in space is calculated using forward kinematics. By subtracting the measured values from the calculated ones, the robot's position error is obtained. Kinematic parameters are then identified using the pseudoinverse matrix method. Subsequently, we can remodel the robot with the identified error parameters, and the error parameters are equivalently transformed into joint angle errors using inverse kinematics. This approach aims to avoid direct modification of the internal parameters of the FANUC controller, thus preventing potential safety and warranty issues. Before error resolution, the entire mathematical algorithm is simulated to ensure computational accuracy and feasibility.
Finally, validation of the compensated values is conducted by clamping and placing aluminum blocks within the workspace. Reflective spheres are placed at the positions of the aluminum blocks, and their position information relative to the robot coordinate system is input into the previously derived inverse kinematics model to obtain angles for input into the controller. This method simulates the applications in automated production lines. By knowing the precise position of the workpiece relative to the robot, this method can be applied instead of manual teaching to plan robot paths, aiming to save time and improve accuracy in the material handling process of automated production lines in the future.

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