機器手臂在工業界的應用非常廣泛，一般工廠的機器手臂運作模式為: 工程師預先使用電腦設定目標點及運作路徑，則手臂只能於預設好路徑中移動。而在實際使用中往往會遇到多目標點的情況，在這種情況下原先已由工程師設定好的移動順序則不一定是最好的。因此為了提高生產效率，需減少手臂每次移動的時間成本。
以工業界中規劃鎖螺絲的路徑為範例，每一個螺絲孔即為一個目標點，由於每個螺絲孔均需鑽入螺絲，都需經過螺絲孔一次，這問題就是著名的旅行者問題(Travelling salesman problem, TSP)。當加工物件為立體的情況時，螺絲孔位置的分布會有高度不一的問題，造成目標點與目標點之間可能遇到被障礙物隔開的情況。本研究就以規劃SCARA機器手臂在高低不平的不規則加工物上鎖多個螺絲之路徑作為示範實驗。
在本研究中使用深度攝影機Kinect建立加工物件的模型，並使用影像處理偵測螺絲孔的位置。遇到障礙物的情況下，使用基於可視法的3D避障演算法來避障。已知的一般可視法只適用於2D平面的避障問題，為了在3D空間下也能使用可視法，提出了一個新增節點的機制，將可視法轉換到3D空間中。此避障演算法是將目標點與目標點之間的距離成本計算出來，接著將每點間的移動成本帶入粒子群演算法(Particle Swarm Optimization，PSO)與2-Opt演算法來求解TSP問題，計算出最優路徑。最後將影像座標轉換為手臂座標，讓機器手臂精準抵達所有目標點。

In the modern community, various robot arms are widely used in different industrial areas. In general, the engineer manually set target point and pathway via the computer in advanced so that the robot arm can strictly move along with the preset path. If there exists a problem of visiting multiple targets, the preset path cannot be ensured that is the best arrangement. In order to improve the production efficiency, the moving cost of the robot arm needs to be reduced to carry out our study purpose.
In this paper, we will present an experiment of locking screws to clearly introduce our proposed algorithm. Each point needs to be passed only once for the overall experimental procedure. Obviously, this is a typical travelling salesman problem (TSP). To be honest, the previous algorithms can only solve some problems in 2D space. However, this study is applied to cope with the issue of optimal path of locking screws in 3D space by the Selective Compliance Assembly Robot Arm (SCARA).
The heights of screw holes are different when the detected object is 3D structure. Then, it is observed that the path between two points may be obstructed by certain obstacles to seriously disturb the normal work of a robot arm. In order to solve this problem, Kinect is used to build the 3D model of the object and simultaneously detect screw holes based on the image processing method. To avoid the robot arm hitting the obstacle on the path, we have to utilize avoiding algorithm to stop this situation appearance. The avoiding algorithm based on the visibility graph algorithm has been proposed in this study in order to let the general visibility graph algorithm transfer to 3D space. Namely, we propose a strategy to add new nodes so that it can help us easily calculate the moving cost of each point. Substituting the moving cost into TSP to calculate the optimal path where the TSP problem can be solved by the Particle Swarm Optimization (PSO) and 2-Opt algorithms. Finally, transferring the image coordinate to SCARA coordinate to let the robot arm complete the whole task.

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