多餘軸機器人，以運動學之觀點來說，此機器人具有多餘的自由度去完成某特定任務。多餘的自由度可用來改善機器人運動學與動力學之特性，如增加靈活性、避開障礙、迴避奇異構形，以及優化各軸之速度、加速度、力矩、能量等，但在優化過程中經常使用數值方法搜尋最佳解，故搜索過程頗為費時，因此很難直接應用於機器人之即時控制，本文提出以解二次多項式從事七軸機器人反位移分析之方法。文中首先簡化六軸機器人反位移分析之過程，並說明如何將其延伸到一些具有特殊連桿參數之七軸機器人。文中並討論如何迅速判斷與奇異構形接近的方法，所提出之方法可迅速得到能避開奇異點之反位移解，因此可應用於多餘軸機器人之即時控制之上。

Redundant manipulators have extra degree-of-freedoms to execute some special tasks. For redundant manipulators, numerical or optimization methods are commonly used to optimize kinematic or dynamic properties. It takes time to obtain optimum solutions, so the methods cannot be directly employed on the trajectory planning for the on-line control of manipulators. This thesis proposes methods to solve the inverse kinematics of serial redundant manipulators. The solutions can be easily obtained by solving quadratics. Simplified methods to find the inverse kinematic solutions of 6-DOF manipulators are first summarized and then employed in the inverse kinematics of redundant manipulators. How to develop solutions to stay away from singularities is also investigated. The proposed methods can be utilized for the on-line control of manipulators.

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