隨著四旋翼機的發展越來越成熟，許多實際應用層面更顯得重要。四旋翼機具有高靈活性與體積小之優點。當必須執行具有危險性的任務或探查人力無法接近的區域時，在安全的考量之情況下，四旋翼機就是相當適合的選擇。
由於四旋翼機在控制軌跡與飛行動作方面，多是採用複雜的控制理論，並且設計的控制器只適用特定的軌跡或是動作上，使得控制器的設計過程變得煩瑣。 所以本文採用數學分析的方法，透過建立四旋翼機的動態數學模型，了解四旋翼機的飛行行為。並選擇高空探勘任務時常用的圓周軌跡做為研究對象。利用圓周運動重複的特性與力學分析，找出四旋翼機完成圓周軌跡的推力規畫。數學模型分成理想無空氣阻力以及實際有空氣阻力兩種狀況。在理想無空氣阻力之假設下，四旋翼機可以透過推力規畫完成指定的圓周運動。然而由於空氣阻力的數學模型分析不易，因此本論文提出一簡化之空氣阻力模型。電腦模擬顯示簡化的阻力模型與完整阻力模型有10%的誤差。在可接受此誤差的情況下，所提出模型將有助於四旋翼機圓周軌跡控制器的設計。

With highly development of the quadcopter, many practical applications become even more important. The quadcopter owns advantages of high flexibility and small volume. When it is required to conduct a dangerous task or explore a region where is not accessible by humans, for the purpose of security considerations, the quadcopter is a suitable choice.
In order to achieve trajectory control and flight operations, complex control theories are usually applied. Besides, the designed controller is only applicable to a specific trajectory or operation so the process of controller design becomes cumbersome. Therefore, this thesis employs the approach of mathematical analysis to understand the quadcopter’s flight behavior by establishing its dynamic mathematical model. The circular trajectory commonly used in exploration and investigation missions is chosen for this study. Based on repetitive characteristics and mechanics analysis of a circular motion, find the thrust planning for the quadcopter to complete the circular trajectory. Two mathematical models, without and with the aerodynamic drag are considered. For the case with the aerodynamic drag, the quadcopter is able to accomplish the designated circular task with thrust planning. Nevertheless, the quadcopter with aerodynamic drag is not easy to analyze, a simplified aerodynamic drag model is therefore proposed. Computer simulations show 10% error compared with the complete aerodynamic drag form. If this error is acceptable, the presented aerodynamic drag model can assist controller design for the quadcopter to perform the circular trajectory tasks.

論文審定書 i
致謝 ii
摘要 iii
Abstract iv
圖次 vii
表次 ix
第一章 緒論 1
1.1研究動機與目的 1
1.2文獻回顧 1
1.3論文架構 5
第二章 四旋翼機的動態模型 6
2.1四旋翼機的飛行原理 7
2.2四旋翼機的動力模型[5][7] 13
第三章 圓周軌跡之動態模型 19
3.1定高圓周運動參數 19
3.2無空氣阻力影響時的定高圓周運動的圓周參數 21
3.3有空氣阻力影響時的定高圓周運動的圓周參數 23
3.3.1修正空氣阻力係數 24
3.3.2假設阻力模型與實際阻力模型的差異 25
第四章 模擬結果與分析 29
4.1四種基本飛行運動 29
4.2無空氣阻力影響時的圓周運動模擬 37
4.3有空氣阻力影響時的圓周軌跡模擬 43
第五章 結論與未來展望 54
5.1結論 54
5.2未來展望 54
參考文獻 56

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