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研究生:陳振緯
研究生(外文):Chen-Wei Chen
論文名稱: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
論文名稱(外文):Mathematical Modeling of a Web-Based 3-D AUV SimulatorWith Improved Autopilot and Guidance Systems
指導教授:郭真祥郭真祥引用關係
口試委員:邱逢琛方銘川丁肇隆張瑞益方志中
口試日期:2013-04-15
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:工程科學及海洋工程學研究所
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:英文
論文頁數:81
中文關鍵詞:自主式水下載具 (AUV)自動導航B木條曲線Euler-Rodriguez 四元法導引系統操縱運動路徑規劃比例-積分-微分控制器
外文關鍵詞:Autonomous underwater vehicle (AUV)autopilotB-splineEuler-Rodriguez quaternionguidancemaneuveringpath-planningproportional–integral–derivative (PID) controller.
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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.

誌謝…………………………………………………ii

摘要……………………………………………………………iii

Abstract………………………………………………………iv

1. Introduction…………………………………………………………1
1.1. Preface……………………………………………………………………1
1.2. Integrated Modeling Scheme……………………………………3
1.2.1. Kinematics Modeling ………………………………………3
1.2.2. Maneuvering Modeling…………………………………………4
1.2.3. Automatic and Control Modeling……………………………5
1.2.4. Path Planning and Waypoints Representation ………6
1.3. Objectives of the Dissertation…………………………7
1.3.1. System Architecture and Implement………………… 9
2. Integrated Motion and Control System Formulation……11
2.1. Kinematic System……………………………………………11
2.1.1. Generalized Coordinate System………………………11
2.1.2. Euler-Rodriguez Kinematic Formulation……………13
2.2. Dynamic System………………………………………………14
2.3. External and Hydrodynamic Forces and Moments………16
2.3.1. Axisymmetric Hull with Sail…………………………16
2.3.2. Propulsion System with Propeller Located 3-D Advance Ratio……………………………………………………………… 17
2.3.3. Control System………………………………………… 19
2.3.4. Hydrostatics Terms Analysis…………………………20
3. Integrated Maneuvering and Propeller Design…………21
3.1. Objectives of Integrated Models………………………21
3.2. Conventional Propeller Design…………………………22
3.3. Course-Changing Ability…………………………………23
3.3.1. Objectives of Turing Test……………………………23
3.3.2. Quaternion-based Zigzag Test……………………… 24
3.4. Course-Keeping Ability………………………………… 24
3.4.1. Pull-out Test for Straight-Line Stability………24
3.4.2. Put-out Test for Directional Stability………… 24
3.5. Discussion………………………………………………… 25
4. Integrated Autopilot and Guidance Systems Formulation .26
4.1. Autopilot System…………………………………………26
4.2. B-spline Trajectory Planning…………………………28
4.2.1. B-spline basis function and its properties……28
4.2.2. Impact of Parameter Spacing and Knots………… 28
4.2.3. Curvature-Constrained B-spline Curve………… 30
4.2.4. Arc Length of the B-spline Curve…………… 30
4.3. Web3D Design and Visualization………………………31
4.3.1. 3-D AUV Prototype Design……………………………33
5. Maneuvering Simulation Results-Mini AUV…………… 37
5.1. Principle Dimension of the ISiMI AUV………………37
5.2. Validation of Turing Test…………………………… 38
5.2.1. Turing Test using the Quaternion Method……… 38
5.2.2. Turing Test using the Euler-Angle Method…… 41
5.3. Validation of Zigzag Test…………………………… 42
5.3.1. Zigzag Test using the Quaternion Method……… 42
5.3.2. Zigzag Test using the Euler-angle Method………43
5.4. Diving Abilities and Depth Control…………………45
5.5. Discussion…………………………………………………46
5.6. Conclusion Remarks………………………………………48
6. Maneuvering Simulation Results- 3000-T AUV…………49
6.1. Physical Condition and Initial State of a 3000-T AUV………………………………………………………………… 49
6.2. Determining the AUV’s Straight-Line Stability… 50
6.3. Determining the AUV’s Directional Stability…… 51
6.3.1. The Directional Stability in Horizontal Plane…51
6.3.2. The Directional Stability in Vertical Plane……54
6.4. Determining the AUV’s Turing Ability………………59
7. Integrated Maneuvering Results for Path Planning… 61
7.1. Case Study………………………………………………… 61
7.2. Path Reference to the Cubic B-spline……………… 62
7.3. Comparisons of Generated Paths and Dynamic Trajectories……………………………………………………… 63
7.4. Determining Curvature-Constrained B-spline Paths…66
7.5. Analysis of the Hydrodynamic Curvature and Velocity…………………………………………………………… 68
7.6. Discussion……………………………………………………70
8. Conclusion and Future Work…………………………………72
9. Reference……………………………………………………… 73
10. Appendix……………………………………………………… 77


Figures

Figure 1-1. Roadmap of procedure design of the proposed AUV simulator with guidance system constrained by AUV maneuverability…10
Figure 2-1. Generalized coordinate system of current work…12
Figure 2-2. Definition of hydrodynamics angles, including flow incidence, orientation angles, and angles of attack and drift…………12
Figure 3-1. The designed flow chart shows a maneuvering design combined with a propeller design with/without environmental disturbances (ENV) model…21
Figure 3-2. Modeling of marine vessels with wide variety of design process, including propeller design, control design, path planning and safety and stability considered, etc…25
Figure 4-1. Integrated AUV autopilot system with a LOS guidance, a quaternion-based PD control system, 6-DOF navigation system and a path generator with waypoints setting constrained by the maneuvering ability……26
Figure 4-2. Web-based simulator system comprising the client and server sides…32
Figure 4-3. Servlet design and java class analysis with AUV guidance system…32
Figure 4-4. Interactive HTML user interface for the AUV autopilot simulator as in (a)–(e) successively. X3D and 2-D canvas were gathered from the server side as in (f) and (g), respectively.…………………………………………33
Figure 4-5. Interface design of 3-D AUV prototypes. Geometric modeling of AUV were encapsulated using X3D Prototypes, including fins, hull, propeller…………34
Figure 4-6 Constructed X3D propeller prototype embedded into HTML and user can use HTML Form interactively to update propeller span wise and chord wise airfoils and its mean line……………34
Figure 4-7. A succession of steps 1~5 for constructing X3D propeller prototype and for visualizing a 3-D propeller with geometrical and topological consistency in grid points……………………35
Figure 4-8. X3D AUV combined with Yahoo User Interface (YUI) for real-time interactive AUV hull form design and solving working advance ratio with commanded velocity …36
Figure 4-9. Modeling and fabricating of an underwater vehicle using designed X3D prototypes successively in the Web-based interactive visualization system……36
Figure 5-1. Experimental results of open-loop turning test (Jun et al. [14]): (a) turning radius about 6 m, (b) steady state turning rate about (c) steady state turning speed about 0.6 m/s.…………………………………………39
Figure 5-2. Simulated results of the turning test using quaternion method:(a) turning radius 6.28 m, (b) angle of rudder and steady state turning rate about per second, (c) steady state turning speed about 0.61m/s………39
Figure 5-3. Trajectory of the quaternion-based turing test in vertical plane with maximum depth being about 4.9 m in this test…………………………………40
Figure 5-4. Time varying of quaternion and its constraint in the simulation of the turning test and the zigzag test………………….……………………………40
Figure 5-5. Simulation results of the turning test using Euler angles method:(a) turning radius about 6.28 m, central point (-8.3,-2.39); (b) angle of rudder and steady state turning rate about per second and (c) The steady state turning speed is about 0.61 m/s……41
Figure 5-6. Initial steady velocity achieving 0.8 m/s before simulating the zigzag test……42
Figure 5-7. AUV velocity oscillating between 0.7 and 0.8 m/s when the zigzag testing with rudder toggled between ………………………………42
Figure 5-8. The time varying of angles of rudder and yaw in the zigzag test…………………………43
Figure 5-9 AUV time-varying trajectory in depth referred to the Earth-fixed coordinate. The objective depth is set as 1 m below the surface……………43
Figure 5-10 Variations of the AUV stern fin deflection and pitch rate in the time history…………………44
Figure 6-1. Overview of a put-out test. Three lines in the plot present the rudder deflection , yaw rate , and heading angle in the time history, respectively. The marked numbers correspond to the above description of procedures 1) ~11).………………………………51
Figure 6-2. Overview of a put-out-based spiral test. Three lines in the plot present the rudder deflection , yaw rate , and heading angle in the time history, respectively.………………………………51
Figure 6-3. Symbolic trajectory of put-out test relative to Fig. 6-1…………………………52
Figure 6-4. Symbolic trajectory of put-out-based spiral test relative to Fig. 6-2……………52
Figure 6-5. Simulation results of the spiral test in the horizontal plane……………………52
Figure 6-6. Time varying of quaternion with constrained condition during the spiral test……52
Figure 6-7. Overview of a put-out test in vertical plane……………………53
Figure 6-8. Velocity variation of the put-out test in the time history……………………53
Figure 6-9. Time-varying quaternion variation and the constrained condition of the put-out test in the time history………………54
Figure 6-10. Trajectory of the put-out test in the plane……………………54
Figure 6-11. Overview of the spiral test in the vertical plane with variation of pitch rate and angle of stern fin in time history……………55
Figure 6-12. Variation of angle of attack in the spiral test…………………55
Figure 6-13. Trajectory of the spiral test in the x-z plane…………………56
Figure 6-14. Simulation results of the AUV spiral test in vertical plane…………56
Figure 6-15. The horizontal (a) and vertical (b) trajectories of the turning test (propeller revolution 3 rps and constant rudder angle 35°) were illustrated……57
Figure 6-16. Velocity distribution in the time history during the turning test with the propeller revolution 3 rps………………………58
Figure 6-17. Time of the total 6-DOF hydrodynamic forces and moments exerted on the AUV reference to body-fixed coordinates during the test………………………………58
Figure 6-18.The upper figure (a) presents the AUV’s attitude of the turning test in the time courses of Euler angles in roll, pitch and yaw (heading) and those were interpreted by the quaternion satisfied with the constraint condition shown in the lower one (b)…………60
Figure 7-1. Three open uniform cubic B-spline curves generated by different parameter spaced methods to interpolate waypoints by centripetal, chord length and uniformly space methods………………………………63
Figure 7-2. Comparisons of linear and cubic interpolation strategies to generate trajectories for the AUV dynamic tracking by the PD controller, including B-spline curves parameterized by uniformly spaced (a), chord length (b)
and centripetal (c) methods and a conventional cubic spline (d), and a linear path (e), the AUV’s propeller revolution was set 3 rps (forward speed 5.2 m/s). Another case of the linear path (f) (the AUV’s propeller revolution over 3 rps), the AUV was missing the targets on the sharper turn.……………65
Figure 7-3. Curvature distribution of the cubic B-spline path parameterized by the chord length method [Fig. 7-2(b)]…………67
Figure 7-4. Curvature distribution of the new path improved by iterating the spaced parameter of the chord length method of the original one [Fig. 7-2(b)] until the curvature distribution under the AUV’s curvature limit of 0.014 m-1…………67
Figure 7-5. Dynamic trajectory of the improved reference path using an iterative method for spacing and rearranging parameters of the cubic B-spline path with chord length method. The numerical analysis was shown in Table 7-2…68
Figure 7-6. Dynamic curvatures of the reference paths in Fig. 7-2(b) and (c) were illustrated in this (a) and (b), respectively. The two methods caused curvature overshooting while AUV passing the sharpest corner in this case………69
Figure 7-7. Dynamic curvatures in the improved case [Fig. 7-5]. The values implied that the hydrodynamic curvature appeased this AUV’s maneuverability……………………69
Figure 7-8. The upper (a) was velocity distribution of the original chord length method [Fig. 7-2(b)] and the lower one was that of the improved case [Fig. 7-5]…………70
TABLES
TABLE 2-1. COMMON NOTATIONS FOR MARINE VEHICLE MOTION……………………15
TABLE 2-2. LIST OF CONTROL PARAMETERS…………………………………………19
TABLE 2-3. PARAMETERS OF THE STERN FORCES AND MOMENTS……………………20
TABLE 2-4. PARAMETERS OF THE RUDDER FORCES AND MOMETNS………………… 20
TABLE 5-1. PRINCIPLE DIMENSIONS OF THE ISIMI AUV…………………………38
TABLE 5-2. INITIAL CONDITION OF THE ISIMI AUV MANUVERING SIMULATIONS: TURNING AND ZIGZAG TESTS……………………38
TABLE 5-3. RESULTS OF TURNING TESTS………………………45
TABLE 5-4. RESULTS OF ZIGZAG TESTS…………………………45
TABLE 6-1. LIST OF THE AUV’S PRINCIPAL CONDITIONS……48
TABLE 6-2. LIST OF THE AUV’S INITIAL CONDITIONS………48
TABLE 7-1. SIMULATION RESULTS OF THE AUV TURNING TEST.
PROPELLER REVOLUTION VARIES FROM 1 TO 7 RPS………………61
TABLE 7-2. COMPARISONS OF DIFFERENT STRATEGIES FOR PATH PLANNING AT THE SPECIFIED ENDPOINT (1400, 400)……66
TABLE 10-1. TRANSLATION-ROTATION COUPLING ALTERNATIVE TERMS IN TRANSLATION………………………………………………77
TABLE 10-2. TRANSLATION-ROTATING COUPLING ALTERNATIVE TERMS IN ROTATION……………………………………………………77
TABLE 10-3. THE REST OF NON-DIMENSIONAL TRANLATION-ROTION COEFFICIENTS……………………………………………………79
TABLE 10-4. NON-DIMENSIONAL ADDED MASS COEFFICIENTS IN TRANSLATION………………………………………………………80
TABLE 10-5. NON-DIMENSIONAL ADDED MASS COEFFICIENTS IN ROTATION…………………………………………………………80
TABLE 10-6. BASIC PHYSICAL DIMENSIONS…………………80


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