多維NURBS曲線擬合及考量加減速之即時插值器實現

An error-bounded multidimensional curve fitting and real-time interpolator with Acc/Dec in NURBS

高天一(Tien-I Kao)

指導教授 ： 陳金聖

國立臺北科技大學/機電學院/自動化科技研究所/碩士(2009年)

https://doi.org/10.6841/NTUT.2009.00328

摘要

本論文提出ㄧ運動控制所需之NURBS曲線擬合及NURB插值器演算法則，擬合部份使用Offset Window評估NURBS曲線擬合品質，其評估的準則為離散點群與NURBS曲線上對應點之Hausdorff 距離，根據評估的結果決定是否要增加擬合的控制點數量，使擬合完成的NURBS曲線與欲擬合的離散點群之軌跡誤差滿足訂定之規格。插值器部份，首先找出NURBS曲線上曲率較高且曲率變化較大的尖點，利用這些尖點將該NURBS曲線分為數個區段，然後使用適應性進給率求得上述各區段之起始點與終點滿足軌跡精度所對應之進給率，最後，為了滿足各驅動軸之伺服能力，本論文提出ㄧ”最低速優先進給率規劃法”，可同時考量精度、加速度的限制規劃出適當之進給率，此方式並可減少因各區段內之減速距離不足而需重新規劃其他區段進給率的次數。在規劃完進給率後，插值器會依照進給率求出運動系統在每次系統取樣時間對應到之位置命令，此位置即為伺服系統之輸入命令。本論文所提之演算法除了以軟體模擬之外，最後並搭配一PC_based即時多工次系統與一多軸運動平台進行實機測試，驗證本論文所提方法之可行性。

關鍵字

NURBS曲線 ； 進給率 ； 曲線擬合 ； 插值器

並列摘要

This thesis proposes the novel NURBS fitting and NURBS interpolator algorithms for motion control applications. The “offset window” is used to evaluate the fitting quality based on the Hausdorff distance of discrete points and the corresponding points located on the NURBS curve. Then, the number of control points will be increased to improve the fitting quality according to the evaluating results. For the NURBS interpolator, we first find out the sharp corners, which have local maximum curvature on the NURBS curve, and then cut the NURBS curve into a lot of segments based on the above corners. The feedrate in starting and ending corners for each segment are calculated by the adaptive federate method. Then, this thesis proposes the “Lowest Velocity Precedence planning (LVP)” method, which aims the chord accuracy and limitation of acceleration to plan the feederate profile for motion control. The LVP method can dramatically reduce the feederate re-planning numbers when both the NURBS curve is cut into many short segments and the acceleration capability is bounded. After the federate planning process, the position commands of the servo loop will be calculated in each sampling time according to the generated federate profile. Finally, the feasibility of our proposed algorithms is verified by the simulation and experiment results in a PC_based real time control system with a multi-axis platform.

並列關鍵字

NURBS, ； Feedrate ； curve fitting ； Interpolator

參考文獻

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