扁平機器魚升力之動態地面效應研究

Abstract

本文探討使用一雙帶狀胸鰭推進之機器魚在接近平面水底時，其尾鰭擺角、胸鰭游動模式與身體離地高度，對於機器魚姿態，包含機器魚的上升加速度、縱搖角加速度及縱搖角速度等，在開始上升時受到動態地面效應的影響。 本研究使用拉格朗日法建立機器魚之垂直面運動模式，其推進及操縱機構採用帶狀胸鰭之推力計算近似模式，垂直面之操控採用尾鰭之流體作用力模式。機器魚本體外型之附加質量及流體阻尼力估算則使用近似橢球公式。帶狀胸鰭的游動模式採用常數振幅與向尾部放大之線性振幅模式。帶狀胸鰭可驅動機器魚之縱移運動，以及利用左右胸鰭振動相位差異產生旋轉。而縱搖運動則由尾鰭帶動，使機器魚下潛到水底或向上游動。機器魚動力模型的建構中亦包含動態地面效應對機器魚之受力影響，其估算方式是採用二維水平長條振動鰭與底面之鏡射關係，使用勢流理論推求離底高度對於升力與推進力之近似解。本研究利用置於實驗水槽上方的攝影機記錄載具外殼上部呈三角形的燈泡亮點位置，以取得載具的縱移與橫移的位置數據，並使用壓力計量測深度，以電子羅盤量測機器魚之航向，所提供的壓力與姿態資訊，能被用於機器魚之深度、航向自動控制與縱搖角度的計算。本文對於多個尾鰭擺角與胸鰭游動模式的變因組合，記錄各約二十次的離地向上升起運動，並比較實驗數據與模擬數據的差異，驗證動態地面效應對機器魚的垂直面運動之影響。

This thesis aims to explore how the dynamic ground effect affects the lifting behavior of a robotic flat-fish when it is near a flat bottom. The robotic fish is propelled by a pair of ribbon side fins, and a caudal fin controls the pitching in the vertical plane. Variables related to the swimming behavior of the robotic fish including the angle of the caudal fin, the swimming modes of the ribbon fin, and the distance of the fish body to the ground. The outputs of the robotic fish motion are the acceleration and the velocity in the vertical direction, the angular acceleration, the angular rate of the pitch while the robot is starting to pitch. A dynamic model of the robotic fish is derived using the Lagrange method. The added mass and damping coefficients of the fish body are estimated by equations of an equivalent ellipsoid. Ribbon-fin generated forces and the hydrodynamic interaction with the caudal fin are the driving forces and moments of the fish body. A robotic fish testbed is built to tank tests. The testbed’s ribbon fins perform two types of swimming modes, either a constant amplitude or a linear amplitude mode for the surge and turning motions. The caudal fin is mainly responsible for the pitching motion. In the construction of the vehicle motion model, the dynamic ground effect on the pitch and surge motions are approximated by potential theory derived by a linear oscillating fin and its mirror image with respect to solid ground. A video camera placed above the tank was used to record the position and velocity of a triangle formed by three light bulbs on the top cover of the vehicle. A pressure sensor and electronic compass are placed on the main case to measure the pressure and pose information, they are also used as feedback signals for automatic depth control and pitch angle calculations. More than twenty trials of independent variable combinations of caudal angle and swimming modes are conducted at various distances to the ground. Experimental data and simulated data are compared to verify the dynamic model of the ground effects on the robotic fish.