所謂的逆運動學(Inverse Kinematics)問題是在尋找一組機械手臂的轉軸角度，使得機械手臂能將末端夾爪以朝向目標方向的姿態呈現於目標位置。一般來說，逆運動學問題能夠透過數值解，以迭代的方式求解。但若目標手臂的自由度數量上升，或是目標任務帶有額外的限制，整個迭代過程所需的時間就會顯著拉長。
本論文提出了一個藉由查找表來來加速數值解型逆運動學計算的方法。透過查找表所提供手臂轉軸角度，手臂的末端點將會被移至鄰近目標的位置，並以該姿勢作為迭代計算的起始姿勢。這樣的作法能夠顯著的減少計算所需的迭代次數以及運算時間。當目標任務有額外的條件時，本論文選擇在進行迭代計算之前就提前滿足那些條件，而非把那些條件加入迭代的計算式中，以減低迭代過程中的運算複雜度。本查找表僅需在機械手臂開發完成時一次性的建立，便能適用於各種不同的數值解逆運動學方法。論文中的實驗也表明，結合查找表的數值解逆運動學方法，其運算速度能夠被顯著的提升。

Inverse kinematics (IK) for a robotic arm solves for the joint variables to move its end effector to a target position with an optional orientation. IK can be solved by iterative numerical methods. However, as the degree-of-freedom (DoF) of the robotic arm increases or the applications impose extra constraints, the iterative process will be lengthened dramatically. In this study, we propose to use a look-up table to accelerate the numerical IK methods. Given a target position, the table outputs a set of joint variables that can move the end effector to the positions near the target, from where the numerical method can start the iterative process. This significantly decreases the number of iterations and the total time in solving IK. In addition, extra constraints of the applications can be checked after table lookup, instead of "formulating into" the numerical formulations. This simplifies the formulations and reduces the computation complexity. The proposed look-up table only needs to be built once when the robotic arm is developed and can be coupled with any numerical IK methods. The experimental results show that the look-up table can significantly accelerate different numerical IK methods.

摘要 i
Abstract ii
1 Introduction 1
2 Related Work 3
2.1 Jacobian Inverse Methods 4
2.2 Newton Methods 4
2.3 Heuristic IK Methods 4
3 Method 7
3.1 The Look-up Table 7
3.2 IK Acceleration with the Look-up Table 8
3.2.1 Offering a Nearby Initial Guess 8
3.2.2 Extracting the Orientation Requirement 9
4 Experiments 13
4.1 The Look-up Table 14
4.1.1 Effects of Nearby Initial Solution 15
4.2 Effects on Orientation Requirement 16
4.3 Generality of Look-up Table 19
4.4 Application: Obstacle Avoidance 20
5 Conclusion and Future Work 23
References 25

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