一機器人在工作空間中之路徑必需要避開奇異點及障礙物，其中與奇異點接近之程度可利用賈氏矩陣行列式值之大小評估，但在避開障礙物方面則非常不易處理。目前避開障礙物之方法大多以構造較為簡單之幾何元件(例如圓球或橢球)代表機器人連桿及障礙物，當兩元件有交集時代表發生干涉現象。為了安全起見，這些幾何元件均大於實際連桿及障礙物之尺寸。因此方法無法精確判斷是否真正發生干涉現象。
　　此論文研究工業機器人避開障礙物之方法。一般方法必須判斷機器人之每一連桿是否與障礙物發生干涉現象，本文利用工業機器人外型之特徵提出可迅速判斷哪些連桿不可能發生干涉現象而提高運算效率，並利用可能發生干涉現象之連桿及障礙物兩中心線之距離判斷是否真正發生干涉現象。所提出之方法不需使用到代表連桿及障礙物之幾何方程式且不需判斷每一連桿與障礙物是否發生干涉現象，因此具有較高之運算效率，本文亦研究當機器人可能碰撞到障礙物時，如何以有效率之方法使機器人避開障礙物。

A trajectory needs to stay away from singularity and obstacles. The closeness to singularity can be easily detected using the determinant of the Jacobian matrix, but obstacle avoidance is much more difficult to deal with. Existing methods use simple geometric models (such as spheres or ellipsoids) to represent the links and the obstacles. Interferences occur if any two models intersect. For safety considerations, the sizes of geometric models are relatively larger than the sizes of links and obstacles, so the methods can only roughly evaluate possible collisions.
　　This thesis studies obstacle avoidance for industrial manipulators. In theory, it needs to check if each link interferes with a foreign object. Some simple rules based on the special structure of the manipulators are proposed in this work that can directly determine which link might interfere with the object. Next, the distance between the centerlines of the link and the object is used to check if link interactions occur. The proposed methods are efficient because no complicated geometric equations are involved, and there is no need to check if the foreign object interferes with each link. How to quickly move the manipulator away from an obstacle to avoid collisions is also investigated.

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