軌跡規劃經常應用於加工機、機器手臂等之機械設備上，軌跡規劃的好壞會反應至運動的流暢性，進而影響加工結果；良好的軌跡規劃有助於加工成品外觀，並使控制精度近一步提升，尤以在高速加工應用中，軌跡規劃更加顯得格外重要。軌跡規劃之離散點來自CAD/CAM，過多之離散點導致冗長之軌跡規劃時間及加工時間，因此基於加工精度將點雲進行優化；軌跡規劃在經過轉角時，具有過大之輪廓誤差，本研究為了使規劃結果符合預期之加工外型，提出分群策略。另外，軌跡規劃必須滿足加工機構之物理極限，避免造成加工之震動，影響加工品質，因此必須將物理限制整合於軌跡演算法中。本論文提出cubic-spline、B-spline及NURBS之軌跡規劃方法，其中為了滿足加工精度，透過NURBS規劃調整權重達成加工精度限制，且具有良好之運動行為。最後透過雷射切割之實驗，驗證軌跡規劃之可行性，並討論軌跡規劃演算法對於加工結果之影響。基於本論文提出之研究方法，使用者給予物理系統極限、加工精度、曲線種類等參數，自動完成軌跡規劃演算法；此演算法透過點雲之前處理及規劃方法，提升加工速度並使加工速度穩定，並考慮加工速度與雷射功率能量匹配，達到加工速度穩定且切割能量均勻之加工結果。

Path planning is extensively applying to machinery equipment, such as robot arm, processing machining, etc. Path planning affects fluency of motion and machining quality. An outstanding path planning improve surface of work-piece and make controller track command easily. Evidently, high quality products rely on sophisticated machining processes and path planning is definitely one of the key techniques. Sequential discrete points are obtained from CAD/CAM, which are used to interpolate with path planning method. However, great amount of point leads to redundant machining time and path planning time. Deviation of planning path is larger when pass through corner, the velocity and acceleration should decrease as passing corner. To guarantee machining continuities on motion profiles, enhance machining precision as well as reduce machining time, a novel point reduction and segmentation strategy is proposed. The interpolated method is introduced in this paper, which includes cubic-spline, B-spline and NURBS. For satisfying machining tolerance, the weight of NURBS can be modified to guarantee tolerance. The generated path can be used in physical system, the kinematics constraint should be taken into account. In this paper, an automatic path- planning algorithm is proposed, which reduce computation effort and raise machining velocity. The machining tolerance is satisfied with NURBS only, but computation effort of NURBS is more than the other spline curve. Finally, the experiment verify that the proposed method can be applied to laser machining application.

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