臺灣博碩士論文加值系統

微創手術是一種外科手術，醫生只需透過微小的手術切口，就可以幫病患進行手術。然而，在進行微創手術與導引過程中，需要避開許多器官與組織，因此必須利用內視鏡進行觀看與調整，在手術室中，內視鏡是由人手握持，隨時間流逝，握持內視鏡之手部，會因疲勞而產生手部震顫，導致內視鏡影像偏移，進一步造成切口產生支點運動而擴大傷口，本論文期能利用等效兩軸機器臂來幫助醫生進行微創手術。本論文分成三部分，第一部分為建構兩軸機器臂之正/逆向運動學、機器臂運動(動力)方程式、並將方程式轉成線性方程式。第二部分則為利用PID控制器對線性方程式進行控制，找出兩軸最佳PID控制參數，並利用波德圖及根軌跡圖觀察系統穩定性。第三部分為利用逆向運動學與三次方多項式補間法，計算目標點之座標位置與軌跡規劃。我們於本篇論文建構包含: (1)兩軸機器臂之正向運動矩陣、(2)兩軸機器臂之角度逆向回推公式、(3)兩軸機器臂之運動(動力)方程式並線性化、(4)兩軸機器臂之PID控制最佳參數、(5)兩軸機器臂軌跡三次方多項式。透過上述獲得公式及控制法，我們可以控制兩軸機器臂並規劃其軌跡。

Minimally invasive surgery (MIS) is a type of surgical operation which doctors can perform operations on patients through tiny incisions. However, in the process of surgery, the endoscope must be used for viewing and adjustment which may cause the image to shift due to any factors. Hence the equivalent two-axis robotic arm can be used to help doctors perform minimally invasive surgery. This thesis is to design a method that can stably control a 2-R robotic arm. This thesis is divided into three parts. The first part is to construct the forward/reverse kinematics of the two-axis robot arm, and the motion (dynamic) equation, to convert the equation into a linear equation. The second part is to use the PID controller to control the linear equation, find the best PID control parameters of the two axes, and use the Bode plot and root locus to observe the system stability. The third part is the use of inverse kinematics and cubic-polynomial interpolation to calculate the coordinate position of the target point and planning the trajectory. In this thesis we constructed: (1) the forward motion matrix of the two-axis robotic arm, (2) the angle of the two-axis robotic arm reversed derivation formula, (3) the motion (dynamic) equation and linearity of the two-axis robotic arm (4) the optimal parameters for PID control of the two-axis robotic arm, (5) the cubic-polynomial interpolation of the two-axis robotic arm trajectory. Through the above formula and control way, we can control the two-axis robotic arm and plan its trajectory.

摘要..I
Abstract..II
致謝..IV
目錄..V
表目錄..VIII
圖目錄..IX
Chapter 1 緒論..1
1.1 研究背景..1
1.2 研究目的..5
1.3 論文架構..6
Chapter 2 機器手臂..8
2.1 機器手臂與座標系..8
2.2 D-H參數建模法..9
2.3 機器人運動學(正向運動學)..11
2.4 機器人運動學(逆向運動學)..12
2.5 機器手臂運動(動力)方程式..15
2.6 拉格朗日函數..15
2.7 拉格朗日運動方程式..16
2.8 機器人控制法..16
2.9 克萊姆法則..18
Chapter 3 機器臂控制..20
3.1 PID控制器..20
3.2 PID參數調整法(Ziegler-Nichols法)..21
Chapter 4 機器臂軌跡產生與規劃..22
4.1 路徑軌跡生成..22
4.2 三次多項式..22
Chapter 5 結果..25
5.1 計算結果..25
5.2 模擬結果..46
Chapter 6 結論與未來發展..61
附錄..62
參考文獻..66

[1] Chin-Hsing Kuo and Jian S. Dai, 2009, Robotics for Minimally Invasive Surgery: A Historical Review from the Perspective of Kinematics, International Symposium on History of Machines and Mechanisms pp 337-354.
[2] https://www1.cgmh.org.tw/intr/intr5/c6210/laparoscopy%20and%20MIS.html
[3] Akim Kapsalyamov et al., 2019, A novel compliant surgical robot: Preliminary design analysis, Math Biosci Eng. 2019 Dec 19;17(3):1944-1958.
[4] Kenji Kawashima et al., 2019, Robots in laparoscopic surgery: current and future status, BMC Biomedical Engineering. 2019; 1: 12.
[5] Frank S. Tsai et al., 2010, Fluidic lens laparoscopic zoom camera for minimally invasive surgery, J Biomed Opt. May-Jun 2010;15(3):030504.
[6] Sourav Chandra et al., 2016, Differential analysis of muscle fatigue induced elbow and wrist tremor in controlled laparoscopic manoeuvring, Int J Med Robotics Comput Ass ist Surg. 2017;13:e1772.
[7] https://zh.wikipedia.org/wiki/%E7%AC%9B%E5%8D%A1%E5%B0%94%E5%9D%90%E6%A0%87%E7%B3%BB
[8] https://zh.wikipedia.org/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E8%B7%9D%E7%A6%BB