六自由度機械手臂之NURBS曲線擬合與插值

本文主旨在於提供一個系統化的六自由度機械手臂之NURBS曲線擬合與插值方法，其中包括:(1)針對離散點之空間濾波器;(2)針對軌跡之空間中離散點萃取;(3)NURBS曲線擬合;(4)機械手臂之正向與逆向運動學。本文之機械手臂末端運動軌跡考量曲面之平滑度及機械性能之極限，前述之終端點運動軌跡配合決定之末端姿態再藉由逆向運動學運算出六軸關節之伺服命令，藉此改善各軸伺服響應。由擷取的離散點資訊，兩相鄰曲線在擬合Non-Uniform Rational B-Spline (NURBS)曲線後相似度低，導致運用六軸機械手臂加工之曲面不夠平滑問題，本論文運用空間濾波器概念，針對獲得離散點資訊，調整相鄰曲線間離散點相似度，使得相鄰曲線間更具有平滑化效果。在曲線擬合前處理過程中，滿足弦誤差離散點過多，導致運算量過大，本論文提出利用三點離散點定義一圓弧，並去除滿足弦誤差之離散點，此可降低運算量，並且維持規範的精度。實驗部分，本論文提出之方法實現在工研院之智慧運動控制平台(Intelligent Motion Platform, IMP)中，並實際驅動六自由度機械手臂，利用六軸馬達之編碼器獲得各軸之響應，然後利用正向運動學計算出機械手臂末端實際運動軌跡，由實驗結果可以驗證本論文之方法可減少運算量並維持相似之追蹤性能。值得一提的是，本研究為國內第一次將NURBS曲線運動實現於六自由度機械手臂。

關鍵字

NURBS ；曲線擬合；空間濾波器；六軸機械手臂

並列摘要

This thesis proposes the systematic design of NURBS curve fitting and interpolation for 6-DOF manipulator, which includes: (1) Space filtering for discrete points, (2) Discrete points extraction; (3) NURBS curve Fitting; (4) Kinematics and inverse of kinematics for manipulator. The continuity of the desired surface and the mechanical limitations corresponding to the motion trajectory are considered to get the optimal trajectory. Then, the servo commands of 6-DOF manipulator will be generated by inverse kinematics to get the excellent servo response. Since the discrete points from measure devices will yield the non-continuity in the desired surface and the roughness of work piece will be degraded when these datum are applied to generate the cutting path, this thesis proposes the spatial filtering for discrete points to overcome the drawback. Furthermore, the discrete points extraction algorithm will reduce the computation load because some discrete points will be removed under the cord error specification. In experiment, the proposed algorithms are evaluated on ITRI’s 6-DOF manipulator which is controlled by Intelligent Motion Platform (IMP). The servo responses of 6 axes are captured to calculate the actual trajectory by forward kinematics. The experimental results show the proposed algorithms are effective to improve the computation load and sustain the similar tracking performance.

並列關鍵字

NURBS ； Curve fitting ； Spatial filter ； 6-DOF Manipulator

參考文獻

23.賴政賢，考量機械性能之NURBS曲線速度規劃運用於補償式插值器，碩士論文，國立臺北科技大學自動化科技研究所，台北，2011。

6.高天一，多維NURBS曲線擬合及考量加減速之插值器實現，碩士論文，國立臺北科技大學自動化科技研究所，台北，2009。

7.S. S. Yeh and H. C. Su, "Implementation of online NURBS curve fitting process on CNC machine," International Journal Advanced Manufacturing Technology, vol. 40, 2009, pp. 531-540.

8.蔡政穎，CNC運動控制器之最佳化NURBS曲線規劃與插值器設計，碩士論文，國立臺北科技大學自動化科技研究所，台北，2011。

9.T. Yong and R. Narayanaswami, "A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining," Computer Aided Geometric Design, vol. 35, 2003, pp. 1249-1259.

國際替代計量

六自由度機械手臂之NURBS曲線擬合與插值

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