軌跡規劃對於機器人的運行相當重要。透過軌跡規劃能夠使機器人的運動軌跡更加平滑、平穩且減少運行時的振動，提高機器人的穩定性、可靠性和工作效率。本論文將三次多項式軌跡、五次多項式軌跡、七次多項式軌跡、4-3-4多項式軌跡、3-5-3多項式軌跡與5-Cubic多項式軌跡方程式，整合並建立一個圖形化使用者介面(Graphical user interface, GUI)，讓使用者輸入欲計算機器人之D-H參數，建立機器人模型後，並輸入其運動定義條件(起點與終點的位置、速度和加速度)，選取計算軌跡之方式便能計算出該機器人的運動軌跡並繪出軌跡位置圖、軌跡速度圖和軌跡加速度圖，並繪出機器人的運動軌跡模擬圖。透過此介面能夠計算出機器人運動軌跡。

Track planning is very important for the operation of robots. Through track planning, the robot's motion trajectory can be smoother, smoother and less vibration, and improve the stability, reliability and efficiency of the robot. This paper integrates third-order polynomial tracks, fifth-order polynomial tracks, seventh-order polynomial tracks, 4-3-4 polynomial tracks, 3-5-3 polynomial tracks and 5-Cubic polynomial trajectories, integrates and establishes a Graphical user interface ( GUI ), allows users to calculate the robot's D-H parameters, build the robot model, and enter its motion definition conditions ( the position and acceleration of the starting point, acceleration ). By calculating the trajectory, we can calculate the trajectory of the robot and draw the trajectory position map, track speed map and track acceleration map, and draw the motion trajectory simulation map of the robot. Through this interface, the robot motion trajectory can be calculated.

摘 要 i
ABSTRACT ii
致謝 iii
目錄 iv
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1 研究背景 1
1.2 研究目的 1
1.3 論文架構 2
第二章 文獻回顧 3
2.1 機器人軌跡規劃 3
2.2 研究方法 5
第三章 機器人運動學 6
3.1 順向運動學介紹 6
3.2 逆向運動學介紹 11
第四章 機器人軌跡規劃推導 17
4.1 三次多項式軌跡方程式 17
4.2 五次多項式軌跡方程式 20
4.3 七次多項式軌跡方程式 23
4.4 高項次(4-3-4)多項式軌跡方程式 27
4.5 高項次(3-5-3)多項式軌跡方程式 33
4.6 5-Cubic多項式軌跡方程式 38
4.7 軌跡計算圖形化使用者介面 45
第五章 機器人軌跡規劃比較結果與討論 52
5.1 三次、五次與七次多項式軌跡規劃比較結果與討論 52
5.2.1 三次多項式軌跡 52
5.2.2 五次多項式軌跡 55
5.2.3 七次多項式軌跡 58
5.2.4 三次、五次多項式軌跡 62
5.2 4-3-4、3-5-3與5-Cubic多項式軌跡比較結果與討論 65
5.2.1 4-3-4多項式軌跡 65
5.2.2 3-5-3多項式軌跡 68
5.2.3 5-Cubic多項式軌跡 71
第六章 結論與未來展望 75
6.1 結論 75
6.2 未來展望 75
參考文獻 76

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