多餘軸機器人有無限多組構形可到達空間中一指定位置及方位，因此可利用多餘之自由度改善機器人之運動或動力特性以並可選擇各種最佳路徑。目前多餘軸機器人之反位移分析是以最佳化方法搜尋最佳解，此數值方法不但過程困難、複雜而且不一定會得到最佳解。本文首先提出方法將七軸串聯式機器人轉換成特殊六軸串聯式機器人並利用二次多項式進行反位移分析後將各軸位移轉換回原來七軸機器人之軸位移。其次將提出之方法應用於七軸多餘軸機器人之最短路徑規劃。此方法之最大優點為利用局部搜尋即可保證得到最佳解而且還可調整各軸貢獻之權重以得到不同之最佳路徑並同時偵測與奇異點接近之程度。

A specific position and orientation in task space can be reached by infinite number of configurations for a redundant manipulator. Thus the kinematic or dynamic performance can be significantly improved and different types of optimal paths can be developed in trajectory planning. Optimization methods are commonly used to obtain the inverse kinematic solutions of a redundant manipulator. Those numerical approaches are generally difficult, complicated and might not get the real optimum solutions. This work first presents methods to transform a 7-DOF redundant manipulator into a 6-DOF industrial manipulator and then find the inverse kinematic solutions by solving quadratic equations. The inverse kinematic solutions of the original 7-DOF redundant manipulator can be easily developed from the solutions of the 6-DOF manipulator. The proposed methods are then employed to search for optimal solutions or optimal paths in trajectory planning. Different types of optimal paths can be developed by searching through a small subspace of the joint space, and the closeness to a singular position can be checked simultaneously in the searching process.

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