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研究生:吳帛霖
研究生(外文):WU, BO-LIN
論文名稱:應用於機器手臂碰撞偵測之OBB演算法晶片設計
論文名稱(外文):Chip Design of OBB Algorithm for Robotic Arm Collision Detection
指導教授:朱元三
指導教授(外文):CHU, YUAN-SUN
口試委員:劉宗憲鍾菁哲朱元三陳中和林榮信
口試委員(外文):LIU, TSUNG-HSIENCHUNG, CHING-CHECHU, YUAN-SUNCHEN, CHUNG-HOLIN, RONG-XIN
口試日期:2023-07-12
學位類別:碩士
校院名稱:國立中正大學
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2023
畢業學年度:111
語文別:中文
論文頁數:68
中文關鍵詞:六軸機器手臂碰撞偵測包圍體分離軸電腦圖學
外文關鍵詞:Six-joint robotic armCollision detectionBounding boxSeparation axisComputer graphics
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機器手臂是工業上常見的設備,近年來機器手臂被應用於人機協作,然而人機協作的環境中沒有柵欄阻隔,人機之間可能發生碰撞。在人機協作的防碰撞方法中,現行的做法會採用空間和距離限制來實現防碰撞,但是這些做法會使用較多的空間,而且人類頻繁靠近機器時會導致生產效率降低,如何改良防碰撞方法是必要的考量。
防碰撞系統最重要的目標就是即時的碰撞偵測。本文的研究環境為六軸機器手臂,而機器手臂控制器的數值更新時間為1ms,因此防碰撞系統的運算時間必須低於1ms。在運算的過程中,本文會先使用多個OBB簡化機器手臂的結構,再根據這些OBB的座標計算出OBB和AABB,即時建立出3層的階層式包圍體,然後使用分離軸定理來偵測人類和階層式包圍體碰撞的情形,並根據結果階段地調整機器手臂的運作速度,改善空間占用和生產效率降低之問題。
本文的階層架構可以簡單的實現人機的碰撞偵測,並降低多數情形下碰撞偵測的運算量。此外藉由調整階層中包圍體的數量,本文的架構也可以應用於6軸以外的機器手臂。不過在系統的運算流程中,建立階層架構的OBB的時間較長,所以本文將OBB演算法實作成晶片以加快運算速度。本文使用TN40G製程來設計OBB晶片,操作頻率可達到277.77Mhz,運算時間則是0.2988us。當資料點的數量低於24時,OBB晶片可以完成包圍體的建立。最終本文的系統可以在1ms的時間限制內建立階層式包圍體並完成碰撞偵測,實現即時運算的目標。

Robotic arms are common equipment in the industry. In recent years, robotic arms have been used in human-robot collaboration. However, there is no fence in the environment of human-robot collaboration, and collisions between humans and machines may occur. In the anti-collision method of human-robot collaboration, the current method uses space and distance restrictions to achieve the goal, but these methods will use more space, and the production efficiency will be reduced when humans frequently approach the robot. How to improve the anti-collision method is a necessary consideration.
The most important goal of an anti-collision system is real-time collision detection. The research environment of this paper is a six-joint robotic arm, and the numerical update time of the robotic arm controller is 1ms, so the calculation time of the anti-collision system must be less than 1ms. In the calculation process, this article will first use multiple OBBs to simplify the structure of the robotic arm, then calculate the OBB and AABB based on the coordinates of these OBBs, and establish a three-layer bounding volume hierarchy. Next, use the separation axis theorem to detect collisions between humans and bounding volume hierarchy, and adjust the operating speed of the robotic arm according to the results of collision detection to improve the problems of space occupation and reduced production efficiency.
The hierarchical structure of this article can easily complete the collision detection between human and robot, and reduce the computational load of collision detection in most cases. In addition, by adjusting the number of bounding volumes in the hierarchy, the architecture of this paper can also be applied to robotic arms other than six-joint. However, in the calculation process of the system, it takes a long time to establish the OBB of the hierarchical structure, so this article implements the OBB algorithm into a chip to speed up the calculation. This paper uses TN40G process to design OBB chip, its operating frequency can reach 277.77Mhz, and the operation time is 0.2988us. When the number of data points is less than 24, the OBB chip can complete the establishment of the bounding box. In the end, the system in this paper can establish a bounding volume hierarchy and complete collision detection within the time limit of 1ms, achieving the goal of real-time computing.

誌謝 i
摘要 ii
Abstract iii
目錄 v
圖目錄 ix
表目錄 xi
第一章 簡介 1
1.1 研究動機與目標 1
1.2 論文架構 2
第二章 背景知識 3
2.1 人機協作方法 3
2.1.1 安全額定監控停止 3
2.1.2 手動導引 3
2.1.3 速度與分隔監控 3
2.1.4 動力與力量限制 4
2.2 包圍體(Bounding Box) 4
2.2.1 Bounding Sphere 5
2.2.2 AABB 5
2.2.3 OBB 5
2.2.4 K-DOP 5
2.2.5 Convex Hull 5
2.3 階層式包圍體 6
2.4 碰撞偵測演算法 7
2.4.1 Bounding Sphere碰撞偵測 7
2.4.2 GJK演算法 7
2.4.3 分離軸定理 9
第三章 相關研究 11
3.1 Collision Detection System for the Practical Use of the Humanoid Robot [6] 11
3.2 Collision-Free Manipulation of a Robotic Arm Using the MS Windows Kinect 3D Optical System [7] 12
3.3 System for Automatic Collisions Prevention for a Manipulator Arm of a Mobile Robot [8] 14
3.4 A Hybrid Bounding Volume Algorithm to Detect Collisions between Deformable Objects [9] 15
3.5 Efficient Collision Detection Using a Dual OBB-Sphere Bounding Volume Hierarchy [10] 16
第四章 OBB演算法分析 18
4.1 OBB演算法介紹 18
4.1.1 共變異矩陣 19
4.1.2 特徵向量 20
4.1.3 座標轉換 23
4.1.4 計算OBB頂點 23
4.2 實驗環境 23
4.3 實驗結果分析 24
4.3.1 QR分解 25
4.3.2 Algebraic Solution 26
4.3.3 Jacobi Method 26
4.3.4 演算法比較結果 27
第五章 系統流程與架構 29
5.1 防碰撞系統流程 29
5.2 模擬環境 30
5.2.1 應用環境 30
5.2.2 軟體實驗環境 31
5.3 階層式包圍體架構 33
5.3.1 架構說明 33
5.3.2 碰撞偵測流程 34
5.3.3 軟體運算時間 35
5.4 簡化資料點演算法 36
5.4.1 Convex Hull 36
5.4.2 Approximate Convex Hull 37
5.5 模擬結果分析 39
第六章 OBB硬體架構與設計 40
6.1 OBB硬體規格與架構 40
6.2 設計環境 43
6.3 硬體設計之模擬分析 44
6.3.1 近似除法器 45
6.3.2 三角函數 47
6.3.3 CORDIC VM 48
6.3.4 定點數模擬結果 50
6.4 硬體區塊說明 51
6.4.1 REG ARRAY 51
6.4.2 COV 51
6.4.3 JACOBI 52
6.4.4 obbpoint 57
6.5 合成結果與晶片佈局 59
6.5.1 電路合成結果 59
6.5.2 電路布局結果 60
6.6 實驗結果分析 61
第七章 結論與未來規劃 63
7.1 結論 63
7.2 未來規劃 64
參考文獻 65

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