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研究生： 林彥岑
Yan-Cen Lin
論文名稱： 基於直接閃避方向及共軛梯度法的機械手臂避障路徑規劃
Robot Path Planning with Obstacle Avoidance Based on Straight Escaping Direction and Conjugate Gradient Method
指導教授： 林柏廷
Po-Ting Lin
口試委員: 張敬源
Ching-Yuan Chang
蕭欽奇
Chin-Chi Hsiaoa
學位類別： 碩士
Master
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2023
畢業學年度： 111
語文別： 中文
論文頁數： 214
中文關鍵詞： 人機協作 、空間安全評估模型 、干涉檢測 、即時動態避障
外文關鍵詞： human-machine collaboration, space safety assessment model, interference detection, real-time dynamic obstacle avoidance
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    • 隨著工業4.0與智慧製造的持續發展，生產模式逐漸改變，人機協作（Human-Robot Collaboration, HRC）模式應運而生，在提高生產線之效率和精度。然而，當機械手臂與其操作人員互動時，操作人員可能因不慎動作而與機械手臂發生碰撞或干涉，因此人機協作模式下的安全考量成為了研究重點。
    本論文提出了新方法：首先於模擬空間中建立「空間安全評估模型」與「手臂模型」。此方法使用圓柱體將機械手臂的各軸進行包覆，以建立模型。而後透過正向運動學，將機械手臂的實際運動情形複製至模擬空間中。同時，將空間切分為相同大小的空間安全評估模型，透過分析安全評估模型與機械手臂之間的危險程度，建立危險值，以了解它們之間的安全情況。在機械手臂運動過程中，透過安全評估模型進行干涉檢測，當檢測到運動路徑可能與模型發生碰撞或干涉時，我們將啟用最佳化方法—共軛梯度法（Conjugate Gradient Method），以找到適當的避障組態。相較於傳統的牛頓法（Newton's Method），這種最佳化方法更快速（約3.5倍），甚至透過Ubuntu系統的應用，能夠提升整體速度（約7.5倍）。透過新的目標方程式，我們使計算出的避障組態能均勻地分配到避障區間內，同時使路徑規畫更加平滑。最後，我們利用機械手臂控制器將這些避障組態進行串聯，實現即時的動態避障。同時，本論文將這項技術應用於不同場景和不同機械手臂上，以改善人機協作模式下機械手臂的路徑規劃，提升安全性及效率。

    With the continuous development of Industry 4.0 and smart manufacturing, the production mode is gradually changing, and the Human-Robot Collaboration (HRC) mode has emerged to improve the efficiency and precision of the production line. However, when the robot arm interacts with its operator, the operator may collide or interfere with the robot arm due to inadvertent movements. Therefore, safety considerations in the human-machine collaboration mode have become the focus of researchers
    This paper proposes a new method: firstly, a "space safety assessment model" and an "arm model" are established in the simulated space. This method wraps the axes of the robotic arm with cylinders to model them. Then, through forward kinematics, the actual movement of the robotic arm is copied into the simulation space. At the same time, the space is divided into several space safety assessment models with the same size. By analyzing the degree of danger between the safety assessment model and the robot arm, the risk value is established to understand the safety situation between them. During the movement of the robot arm, interference detection is performed through the safety evaluation model. When it is detected that the motion path may collide with or interfere with the model, we will use the optimization method—Conjugate Gradient Method to find proper obstacle avoidance configuration. This optimization method is about 3.5 times faster compared with the traditional Newton's Method, and through the application of the Ubuntu system, the overall speed can be increased further till about 7.5 times. Through the new objective equation, we are able to calculate the obstacle avoidance configuration to be evenly distributed in the obstacle avoidance interval, and make the path smoother. Finally, we use the robotic arm controller to connect these obstacle avoidance configurations in series to occur real-time dynamic obstacle avoidance. At the same time, this paper applies this technology to different scenarios and different robotic arms to improve the path planning of the robotic arm in the human-machine collaboration mode, improving safety and efficiency.

    摘要 I ABSTRACT II 誌謝 IV 目錄 V 圖目錄 IX 表目錄 XXI 符號索引 XXIII 第一章 緒論 1 1.1 前言與研究目標 1 1.2 論文架構與簡介 4 第二章 文獻回顧 6 2.1 機器人運動學 6 2.1.1 齊次轉換（Homogeneous Transformation）旋轉及平移關係 6 2.1.2 D－H參數表（Denavit－Hartenberg Parameters Method） 9 2.1.3 正向運動學（Forward Kinematics） 12 2.1.4 逆向運動學（Inverse Kinematics） 14 2.2 機械手臂路徑規劃 18 2.2.1 人工勢場法（Artificial Potential Fields Method） 18 2.2.2 快速探索隨機樹演算法（Rapidly－exploring Random Tree, RRT） 23 2.2.3 梯度下降法（Gradient Descent） 28 2.2.4 牛頓法（Newton’s Method） 28 2.2.5 共軛梯度法（Conjugate Gradient Method） 29 第三章 研究方法 30 3.1 建立機械手臂基本資訊 31 3.1.1 機械手臂模型建立 31 3.1.2 定義空間與安全評估模型 32 3.1.3 危險評估安全值設置與計算 34 3.1.4 安全評估模型與機械手臂關係 38 3.2 不同位置碰撞的危險值情形 39 3.2.1 桿件側邊碰撞（區域 Ⅰ） 42 3.2.2 桿件側邊未碰撞（區域 Ⅱ） 43 3.2.3 桿件邊角碰撞（區域 Ⅲ） 44 3.2.4 桿件邊角未碰撞（區域 Ⅳ） 46 3.2.5 桿件頭尾碰撞（區域 Ⅴ） 47 3.2.6 桿件頭尾未碰撞(區域 Ⅵ) 48 3.3 人機共工安全規範 49 3.3.1 獲取三維影像 51 3.3.2 獲取目標物點雲（人） 52 3.3.3 三維點雲濾波 54 3.3.4 轉移矩陣（Transition Matrix） 56 3.3.5 計算點雲質心 57 3.4 軌跡修正法 58 3.4.1 最佳化目標方程式 60 3.4.2 共軛梯度法（Conjugate Gradient Method） 62 第四章 實驗結果 68 4.1 探測距離實際與誤差值 68 4.1.1 鏡頭正前方距離測試 69 4.1.2 鏡頭左方距離測試 71 4.1.3 鏡頭右方距離測試 73 4.2 最佳化方法比較 75 4.3 機械手臂路徑修正方法與結果 76 4.3.1 六軸路徑一的碰撞情形 76 4.3.1.1 原始目標方程式最佳化 78 4.3.1.2 新目標方程式最佳化 84 4.3.2 六軸路徑二的碰撞情形 92 4.3.2.1 原始目標方程式最佳化 93 4.3.2.2 新目標方程式最佳化 100 4.3.3 八軸路徑一的碰撞情形 108 4.3.3.1 原始目標方程式最佳化 109 4.3.3.2 新目標方程式最佳化 116 4.3.4 八軸路徑二的碰撞情形 124 4.3.4.1 原始目標方程式最佳化 125 4.3.4.2 新目標方程式最佳化 132 4.4 動態避障應用 140 4.4.1 六軸動態避障（固定障礙物） 140 4.4.2 八軸動態避障（固定障礙物） 149 4.4.3 動態障礙物避障（障礙物位置變換） 158 第五章 結論與未來展望 167 5.1 結論 167 5.2 未來展望 167 參考文獻 169 附錄A 175

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