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研究生: 紀韋鴻
Chi, Wei-Hung
論文名稱: 基於賽局理論與控制障礙函數之人機協作任務研究
Study on Human-Robot Collaborative Tasks Based on Game Theory and Control Barrier Functions
指導教授: 鄭銘揚
Cheng, Ming-Yang
學位類別: 碩士
Master
系所名稱: 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年: 2026
畢業學年度: 114
語文別: 中文
論文頁數: 156
中文關鍵詞: 人機協作 、動態運動原語 、導納控制 、賽局理論 、Riccati方程式 、控制障礙函數
外文關鍵詞: Human-Robot Collaboration, Dynamic Movement Primitives, Admittance Control, Game Theory, Riccati Equation, Control Barrier Function
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  • 隨著協作機器人與智慧製造技術的快速發展,機械手臂已逐漸由傳統隔離式工業環境,至現在可與人類共享工作空間之人機協作場域。有鑑於此,本論文提出一套結合動態軌跡生成、順應控制、賽局決策與安全控制之人機協作控制架構。在軌跡規劃方面,本論文採用動態運動原語作為參考軌跡生成方法,使系統具有示範軌跡重現、起終點重設與執行速度調整之能力。為提升人機互動下之柔順性,本論文結合導納控制,利用外力資訊產生位置與速度修正量,使機械手臂在執行任務的同時,仍能對人類施力作出柔順回應。於外層決策部分,本論文引入賽局理論,透過動態報酬矩陣與納許均衡分析最佳動作,決定機械手臂之互動策略;於內層控制部分,則透過基於 Riccati 方程式之合作追蹤控制器,權衡動態運動原語與導納控制兩類輸出,使控制結果同時兼顧任務追蹤性能與順應互動需求。為確保人機協作過程中之安全性,本論文導入控制障礙函數,並結合符號距離函數與二次規劃方法,建立安全控制架構。最後本論文將提出之方法進行整合,完成一套完整人機協作控制架構,可作為未來協作機器人應用於共享工作空間與服務型場域之控制基礎。

    With the rapid development of collaborative robots and intelligent manufacturing technologies, robotic manipulators have gradually evolved from traditional isolated industrial environments to human-robot collaboration scenarios in which they share the workspace with humans. Consequently, this thesis proposes a human-robot collaboration control framework that integrates dynamic trajectory generation, compliant control, game-theoretic decision-making, and safety control.
    For trajectory planning, Dynamic Movement Primitives (DMPs) are adopted as the reference trajectory generation method, enabling the system to reproduce demonstrated trajectories, reset start and goal positions, and adjust execution speed. To improve compliance during human-robot interaction, admittance control is employed to generate position and velocity command corrections based on external force information, allowing the manipulator to respond compliantly to human-applied forces while still performing the task. At the outer decision-making layer, game theory is introduced to determine the interaction strategy of the manipulator through a dynamic payoff matrix and Nash equilibrium analysis of the best action. At the inner control layer, a cooperative tracking controller based on the Riccati equation is employed to balance the outputs of DMPs and admittance control, so that the resulting control action can simultaneously satisfy task tracking performance and compliant interaction requirements. To ensure safety during human-robot collaboration, Control Barrier Functions are further incorporated, together with signed distance functions and quadratic programming, to establish a safety control framework. Finally, the proposed methods are integrated into a complete human-robot collaboration control architecture, which can serve as a control foundation for future collaborative robot applications in shared workspaces and service-oriented environments.

    中文摘要 I EXTENDED ABSTRACT II 誌謝 XVI 目錄 XVIII 表目錄 XXI 圖目錄 XXII 符號 XXV 第一章 緒論 1 1.1 研究動機與目的 1 1.2 文獻回顧 2 1.3 論文架構與貢獻 5 第二章 機械手臂運動學與動態軌跡規劃 8 2.1 順逆向運動學模型[31] 9 2.1.1 順向運動學模型 9 2.1.2 逆向運動學模型 12 2.2協作任務之動態軌跡規劃 19 2.2.1 動態運動原語(Dynamic Movement Primitives, DMP)[36] 19 2.2.2 改良型動態運動原語(Modified Dynamic Movement Primitives) 23 2.2.3 更改目標下之軌跡不連續問題與軟啟動機制 25 2.3 本章小結 26 第三章 結合動態軌跡之順應控制 27 3.1 結合動態運動原語之導納控制架構 28 3.1.1 導納控制介紹與外力修正關係 28 3.1.2 力感測器資料處理與座標轉換 30 3.1.3 動態運動原語參考軌跡與導納修正量之結合 32 3.2 動態運動原語相位調整[39] 33 3.2.1人機互動狀態下之動態調整 33 3.2.2 基於追蹤狀態與空間關係之相位調整[40] 35 3.3本章小結 37 第四章 賽局決策、合作追蹤與安全控制 38 4.1賽局理論 39 4.1.1 賽局理論基本概念 39 4.1.2 合作賽局與非合作賽局 39 4.1.3 分層賽局觀點 41 4.2賽局模型建立與動態報酬矩陣 42 4.2.1 玩家動作集合與人類意圖辨識 43 4.2.2 動態報酬矩陣 44 4.2.3 納許均衡(Nash Equilibrium)[46] 46 4.2.4 策略輸出與目標切換 47 4.3 基於Riccati方程式之合作追蹤控制 49 4.3.1 離散時間誤差模型與狀態定義 49 4.3.2 二次成本函數與權重設計 51 4.3.3 離散時間LQR、Riccati方程式與輸出權衡機制[14] 52 4.4 控制障礙函數(Control Barrier Function, CBF)[43] 54 4.4.1 安全集合與障礙函數 54 4.4.2 控制障礙函數基本定義 55 4.4.3高階障礙函數之必要性 58 4.4.4 高階控制障礙函數推導[47] 59 4.5 安全控制設計與最終整合架構 61 4.5.1 基於符號距離函數之障礙描述與幾何建模[48] 61 4.5.2 安全限制與二次規劃 63 4.5.3 最終整合架構 63 4.6本章小節 66 第五章 模擬與實驗 67 5.1 模擬實驗介紹 68 5.1.1 模擬實驗一:人機協作賽局實驗設置 69 5.1.2 模擬實驗二:安全避障實驗設置 71 5.2 模擬實驗結果與討論 74 5.2.1 模擬實驗一:人機協作賽局驗證 74 5.2.2 模擬實驗二:安全避障驗證 80 5.3 上機實驗介紹 85 5.3.1 上機實驗一:人類阻擋與引導實驗設置 87 5.3.2 上機實驗二:多目標人機協作實驗設置 89 5.3.3 上機實驗三:整合實驗設置 90 5.4 上機實驗結果與討論 93 5.4.1 上機實驗一:人類阻擋與引導實驗驗證 93 5.4.2 上機實驗二:多目標人機協作實驗驗證 99 5.4.3 上機實驗三:整合實驗驗證 105 5.5 本章小結 112 第六章 結論與建議 113 6.1結論 113 6.2未來建議與展望 115 參考文獻 116

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