具有改進式自動導引系統之網路三維 自主式水下載具模擬器之數學建模

Abstract

本文發展一具有進化的自動導航系統以及操縱模型約束的導引系統之智能化自主水下載具(AUV)模擬器。載具的系統動力結合尤拉-羅德里格斯(Euler-Rodriguez)四元法、尤拉角(Euler-angle)及尤拉軸(Euler-axis)等方法，基於三維六自由度的尤拉-拉格朗日(Euler-Lagrange)運動方程式，使載具姿勢以四階龍格-庫塔(Runge-Kutta)時步方法解運動方程式沒有奇異點。本研究中，應用具四元法控制系統的AUV運動模擬器來測試一迷你型及一大尺寸的AUV之運動性能及操縱能力，包括追跡性能、路徑穩定性、路徑改變與維持能力及下潛能力。關於該AUV模擬程式的驗証，本研究採用ISiMI AUV的實驗數據作驗証，包括廻旋及Zigzag測試，比較結果說明本模擬器所使用的方法及數據是合理的。本文所提出的導引系統中，包括三維的瞄準線方法、四元法為基礎的比例-積分-微分控制器以及路徑產生器，可以自動產生由AUV的操縱性能、尤拉-拉格朗日運動方程式及航點所限制的曲率連續的三次B型木條路徑，及以高斯-雷建德(Gauss-Legendre)方法計算目標路徑的長度。一艘3000噸級的AUV用來測試該導引系統。本文討論不同的路徑設計策略，方法包括直線、常規的三次木條曲線及三種不同的參數方法所設計出來的三次B型木條曲線，以及具有一整合迭代方法B型木條曲線用以改善及擴充該路徑產生器的功能。追跡性能的模擬結果顯示，使用本文所提出的導引系統可以改善此型AUV的交叉追跡誤差將近80%，同時在航程時間上亦有5% 的減少。此外，本模擬器具有網路基礎之三維AUV可視化的系統，可以透過網路互動呈現AUV的三維模型、運動軌跡及航行姿勢。

An intelligent autonomous underwater vehicle (AUV) simulator with improved navigation, autopilot and guidance systems that constrained by maneuvering models was developed. The dynamics system of the AUV’s navigation on the base of 3-D Euler-Lagrange equations of motion in six degrees of freedom (6-DOF) was integrated with Euler-Rodriguez quaternion, Euler-angle and Euler-axis methods to represent singularity-free AUV’s attitude intuitively; the fourth-order Runge-Kutta method was a time-marching model in the simulator. In this study, the simulator with a quaternion-based control system was used to test motion performance, maneuverability both of a mini AUV and a large-scale AUV, including tracking performance, path motion stability, course changing, course keeping and diving abilities, etc. For validation of the simulation codes, experimental results of the ISiMI AUV open-loop tests, including turning test and zigzag test, were used to compare with simulation results of the AUV simulator. Comparisons of the results implied the adopted methods and hydrodynamics reasonable. The proposed guidance system in the simulator includes a 3-D line-of-sight (LOS) algorithm, a quaternion-based proportional-Integer-derivative (PID) controller and a path generator, which automatically generates continuous-curvature paths of cubic B-spline class constrained by AUV maneuverability, 3-D Euler-Lagrange formulation and waypoints. Gauss-Legendre method was applied to calculate length of objective paths. A 3000-T AUV was used to test the guidance system. Comparisons of linear and cubic path-planning strategies were discussed, including a straight line and a conventional cubic spline method, three parametric methods for planning cubic B-spline paths, and an iterative method for improving and expanding the function of the path generator. Simulation results of the tracking performance tests show that the AUV can precisely approach targets using the proposed method. The improvement in the cross-tracking error was approximately 80%, whereas reduction in travelling time was 5% in this case. In addition, a Web-based 3-D AUV visualization system was developed to render 3-D models, attitudes and position of AUV with Web-based interactive function experienced.