本研究提出一套針對pitch-yaw交互串接型機器蛇之創新表達式：基於空間中移動Trihedron座標的概念，導出針對連續分段直線之Trihedron座標系統表示式，建構高自由度機器蛇各相鄰旋轉軸之簡潔齊次關係。由於pitch-yaw的串接機構與階梯環境的特性，考量機器蛇攀爬階梯時之姿態，將旋轉軸角度分三種狀況：0°、+90°或−90°進行探討。且僅用齊次矩陣的行平移與變號即能表達相鄰關節之座標轉換關係。可完全避免傳統的Denavit-Hartenberg表示法繁雜的矩陣乘積運算。最後，應用於此創新表達式進一步描述攀階運動整個過程，包括六個姿態，初始狀態、前端舉升、前端外展、轉折點平移、尾部抬升與初始化。結果證實一節數18節pitch-yaw交互串接之機器蛇，可攀爬級高25公分、級深25公分與級寬100公分之階梯。此創新表達式可簡化運算之複雜度、更為直觀地和機器蛇的姿態連結。

A novel representation for snake robots with pitch-yaw connection in series is proposed in this research. Trihedron-based coordinate systems for the expression of consecutive segments are established to describe snake robots with pitch-yaw structure, which are derived from the conventional Trihedron, usually for smooth curves in space. Furthermore, considering pitch-yaw structure and staircase environment, we simplify joint angles in three kinds while climbing: 0°, +90°, or −90°. The relation of adjoining joints can be expressed in homogeneous matrix and transformed simply by column shift and sign change. Thus, the complex matrix multiplications can be avoided, which often occur in the traditional Denavit-Hartenberg expression. Finally, we use the novel expression to depict the six configurations in stair climbing: initial state, rising, out-reaching, shifting at turning points, tail lifting, and initializing. The verification is done on the snake robot with 18 pitch-yaw segments by WebotsTM, which could climb the stairs with 25 cm of raiser height, 25 cm of tread depth, and 100 cm of tread width. The novel representation is proved to be much less computational complexity, more intuitive and direct link to robot configurations.

口試委員審定書 i
誌謝 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 vii
表目錄 ix
符號表 x
第一章 前言 1
第二章 文獻探討 3
2.1 機器蛇之型態分類 3
2.2 Pitch-Yaw交互串接機構 7
2.3 串接型之Denavit-Hartenberg表示法 8
2.4 空間中的Trihedron移動座標系統 9
2.5 機器蛇之運動規劃 11
第三章 材料與方法 12
3.1 Pitch-Yaw串接型機器蛇表達式之推導 12
3.1.1 分段直線之Trihedeon表示式與推導 12
3.1.2 調整之Denavit-Hartenberg表示法 20
3.2 階梯環境與攀階規劃 22
3.3 Pitch-Yaw機器蛇於階梯環境下相鄰兩旋轉軸之關係式 28
3.3.1 情況一：旋轉角度θi+1為 0° 28
3.3.2 情況二：旋轉角度θi+1為 +90° 30
3.3.3 情況三：旋轉角度θi+1為 −90° 31
3.3.4 小結 33
第四章 結果與討論 36
4.1 分段直線之Trihedron表示式之攀階步態規劃 36
4.1.1 初始狀態 36
4.1.2 前端舉升 37
4.1.3 前端外展 38
4.1.4 轉折點平移 40
4.1.5 尾部抬升 45
4.1.6 初始化 45
4.2 攀階步態之模擬 46
第五章 結論 48
參考文獻 49

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