機器人運動學的建模一直是機器人的主要研究課題之一，本論文目的是要賦予一個以快速成型建立的仿人形機器手臂可以即時地用手指指向目標位置的定位能力。為了實現這一目標，此機器人系統必須具備一個高效能的逆向運動學建模的解決方案。 在本篇論文提出了一個用於仿人形機器人手臂的類自我組織特徵映射圖的逆運動學建模方法，該建模方法背後的主要思維是將機器人手臂的工作空間離散化成一個由N_x×N_y×N_z取樣點所組成的立方晶格。每個取樣點定義了一個相對應的區域，並分配一顆網格節點j，其中儲存五種不同的參數：〖W_j〗^i-為網格節點於晶格狀網格的索引值向量，〖W_j〗^c-為此網格節點的座標向量，〖W_j〗^x-為網格節點的目前位置向量，〖W_j〗^θ-為對應此網格節點位置之各關節角度向量，〖W_j〗^J-為對應此網格節點位置之Jacobian矩陣。我們提出的建模方法可以透過一組訓練資料來快速學習到此五種資訊之正確值，訓練資料集的生成方案可以透過均勻分佈的量化方式或是實際操作機械手臂來構建起來。我們利用以下兩個步驟來從工作空間中的目標位置推算出相對應的關節角度：首先，我們先找到離目標位置最接近的對應網格節點；其次，透過對應網格節點內的位置向量 〖W_j〗^x、角度向量 〖W_j〗^θ以及Jacobian矩陣〖W_j〗^J等資訊，以Jacobian矩陣的線性逼近 "Θ(" ▁x) 的方式，來推導到達此目標位置所需要的關節角度向量。 我們用以立體成型的仿人形機器人手臂來對所提出的建模方法的性能進行測試。第一個實驗是在機器人手臂的模擬環境中進行的，在20800筆訓練資料和9072測試資料下，其平均準確度分別可以達到4.95毫米與4.91毫米的平均誤差，且可在0.03毫秒下以一種多步驟疊代方式修正到只有0.37毫米的誤差。 ;Robot kinematics modeling has been one of the main research issues in robotics research.The goal of this thesis is to endow a 3-D printed humanoid robot arm with the ability of positioning its fingers to a target position in real time. To achieve this goal, the robot system has to seek a high efficiency solution to inverse kinematics modeling. In this thesis, an SOM-like inverse kinematics modeling method for humanoid robot arms is proposed. The principal idea behind the proposed modeling method is to discretize the work space of the robot arm into a cubic lattice consisting of N_x×N_y×N_z sampling points. Each sampling point corresponds to a reciprocal zone and is assigned one grid node, storing five different data items: the index vector of the sampling point〖▁W_j〗^i, the coordinate vector of sampling point〖▁W_j〗^c, the position vector〖▁W_j〗^x, the output vector〖▁W_j〗^θ, and the Jacobian matrix〖▁W_j〗^J. All these five data terms can be quickly learned by the proposed modeling method from acollected training data set in an SOM-like manner. The training data set can be constructed by either the uniformly discretization scheme or the real-life data generation scheme. The computations of the joint angles corresponding to a target position in the work space involve the following two steps. First of all, we search the reciprocal zone which is closest to the target position. Secondly, the joint angles are approximated by a linear Jacobian expansion of the transformation"Θ(" ▁x) via the position vector 〖▁W_j〗^x, the output vector 〖▁W_j〗^θ, and the Jacobian matrix 〖▁W_j〗^J within the reciprocal zone. The performance of the proposed SOM-like inverse kinematics modeling method was tested on a 3-D printed robot arm with 5 degrees of freedom(DOF). The first experiment was conducted on a simulated robot arm environment. An averag eerror of 4.95mm and 4.91mm could be achieved over the 20,800 training data and 9,072 testing data, respectively. In addition, we can use a multi-step method to improve the performance to achieve 0.37mm errors in 0.03milliseconds.
