本研究主要是利用NURBS規劃模型來進行軌跡規劃與曲面擬合，並進階應用至搭載有深度感測器之六軸機械手臂加工。在真實情況下執行任務之機械手臂通常會受到許多限制，包含加工之物理量限制、加工精度與末端致動器之方向限制，這都間接影響至加工品質。在軌跡規劃上，透過給定之路徑控制點，提出基於滿足加工精度條件下，剔除冗餘之離散點，進而達到點雲優化成效，並根據轉角角度大小來做分群優化，使規劃效率提高；軌跡規劃部分利用NURBS模型規劃出連續之曲線與物理量，藉此提高運動的流暢度；最後，所規劃之物理量必須符合機構之最大物理限制。有別於傳統規劃，本研究所提出之方法使軌跡可調整性更高，並同步提升加工品質。在曲面擬合中，在不規則曲面上利用深度感測器拿到有限之曲面控制點資訊，透過NURBS曲面規劃模型來擬合出曲面結構，並提出定義曲面控制點誤差之方法，進行有效率之權重修正方法，使得擬合曲面更接近真實曲面結構，進而利用參數化曲面資訊得知曲面上任一擬合點之法向量。本論文提出之演算法透過多軸伺服加工平台實測，驗證本研究於工程實務之可行性。最後，結合規劃軌跡與曲面擬合資訊，讓搭載有深度攝影機之六軸機械手臂來進行加工模擬，驗證此具有末端致動器方向限制之軌跡規劃具有極高之可行性。

This research mainly uses the NURBS model to execute trajectory planning and surface fitting applications to six-axis robot arms equipped with depth sensors. Under real circumstances, the robotic arm that performs the task is usually subject to many restrictions. Including the physical limitations of the processing, the processing accuracy and the direction limitations of the end-effector, which indirectly affect the processing quality. In trajectory planning, the control points of path is obtained at the beginning, and some invalid discrete points are eliminated based on the processing accuracy. Consequently, point cloud optimization is finish. Grouping optimization based on the angle of the corners to improve planning efficiency; Using the NURBS model plans a continuous curve and physical value to improve the smoothness of the movement; Finally, the physical value of the planning must satisfy the maximum physical limit of the mechanism, which is different from traditional planning to make the trajectory more adjustable and improve the processing quality. In the surface fitting, the depth sensor is used to obtain the limited surface control point information on the irregular surface. Using the NURBS model fits the surface structure, and propose a method to define the control point error of the surface. An effective weighting modification method is used to make the fitted surface closer to the real surface structure, and use the parametric surface information to know the normal vector of any fitting point. The algorithm proposed in the paper verifies the feasibility of this research in engineering experiment through two-axis and four-axis servo processing mechanism. Finally, combined with the planned trajectory and surface fitting information. A six-axis robot arm equipped with a depth camera is used for processing simulation to verify that the trajectory planning with end-effector direction limitation is quite feasible.

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