A COLLISION AVOIDANCE SYSTEM FOR AUTONOMOUS UNDERWATER VEHICLES

The work in this thesis is concerned with the development of a novel and practical collision avoidance system for autonomous underwater vehicles (AUVs). Synergistically, advanced stochastic motion planning methods, dynamics quantisation approaches, multivariable tracking controller designs, sonar data processing and workspace representation, are combined to enhance significantly the survivability of modern AUVs. The recent proliferation of autonomous AUV deployments for various missions such as seafioor surveying, scientific data gathering and mine hunting has demanded a substantial increase in vehicle autonomy. One matching requirement of such missions is to allow all the AUV to navigate safely in a dynamic and unstructured environment. Therefore, it is vital that a robust and effective collision avoidance system should be forthcoming in order to preserve the structural integrity of the vehicle whilst simultaneously increasing its autonomy. This thesis not only provides a holistic framework but also an arsenal of computational techniques in the design of a collision avoidance system for AUVs. The design of an obstacle avoidance system is first addressed. The core paradigm is the application of the Rapidly-exploring Random Tree (RRT) algorithm and the newly developed version for use as a motion planning tool. Later, this technique is merged with the Manoeuvre Automaton (MA) representation to address the inherent disadvantages of the RRT. A novel multi-node version which can also address time varying final state is suggested. Clearly, the reference trajectory generated by the aforementioned embedded planner must be tracked. Hence, the feasibility of employing the linear quadratic regulator (LQG) and the nonlinear kinematic based state-dependent Ricatti equation (SDRE) controller as trajectory trackers are explored. The obstacle detection module, which comprises of sonar processing and workspace representation submodules, is developed and tested on actual sonar data acquired in a sea-trial via a prototype forward looking sonar (AT500). The sonar processing techniques applied are fundamentally derived from the image processing perspective. Likewise, a novel occupancy grid using nonlinear function is proposed for the workspace representation of the AUV. Results are presented that demonstrate the ability of an AUV to navigate a complex environment. To the author's knowledge, it is the first time the above newly developed methodologies have been applied to an A UV collision avoidance system, and, therefore, it is considered that the work constitutes a contribution of knowledge in this area of work.

[1]  W. Carpenter.  The Gulf-Stream , 1870, Nature.

[2]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[3]  A. Moscow.  Collision course : the Andrea Doria and the Stockholm , 1959 .

[4]  J. Halton.  On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[5]  J. Hammersley.  MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS , 1960 .

[6]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[7]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[8]  J. R. V. BROOKS,et al.  Earth Science , 1973, Nature.

[9]  A. N. Cockcroft,et al.  A guide to the collision avoidance rules: International Regulations for Preventing Collisions at Sea 1972, in force 1977 , 1976 .

[10]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[11]  Michael A. Arbib,et al.  Perceptual Structures and Distributed Motor Control , 1981 .

[12]  Richard A. Cahill.  Collisions and their causes , 1983 .

[13]  Hans P. Moravec,et al.  High resolution maps from wide angle sonar , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[14]  Rodney A. Brooks,et al.  A Robust Layered Control Syste For A Mobile Robot , 2022 .

[15]  Larry S. Davis,et al.  Multiresolution path planning for mobile robots , 1986, IEEE J. Robotics Autom..

[16]  Bruce H. Krogh,et al.  Integrated path planning and dynamic steering control for autonomous vehicles , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[17]  Samuel S. Blackman,et al.  Multiple-Target Tracking with Radar Applications , 1986 .

[18]  C. Greene,et al.  Oceanography: A view of the earth , 1987, IEEE Journal of Oceanic Engineering.

[19]  David M. Lane,et al.  A DISTRIBUTED PROBLEM SOLVING ARCHITECTURE FOR SONAR IMAGE INTERPRETATION , 1988 .

[20]  Edward R. Dougherty,et al.  Morphological methods in image and signal processing , 1988 .

[21]  B.D. Van Veen,et al.  Beamforming: a versatile approach to spatial filtering , 1988, IEEE ASSP Magazine.

[22]  J. C. Hyland,et al.  Optimal Obstacle Avoidance Path Planning for Autonomous Underwater Vehicles , 1989, Proceedings of the 6th International Symposium on Unmanned Untethered Submersible Technology,.

[23]  T. M. Cook,et al.  Intelligent Waypoint Transiting in Complex Auv Environs , 1989, Proceedings of the 6th International Symposium on Unmanned Untethered Submersible Technology,.

[24]  J. C. Toomay.  Radar Principles for the Non-Specialist , 1989 .

[25]  J.D. McKendrick,et al.  Autonomous Knowledge-Based Navigation in an Unknown Two-Dimensional Environment with Convex Polygon Obstacles , 1989, Proceedings of the 6th International Symposium on Unmanned Untethered Submersible Technology,.

[26]  J. H. Hino,et al.  Intelligent Planning for a Search and Surveillance Unmanned Underwater Vehicle (uuv) , 1989, Proceedings of the 6th International Symposium on Unmanned Untethered Submersible Technology,.

[27]  David M. Lane,et al.  A pyramidal architecture for knowledge-based sonar image interpretation , 1989 .

[28]  J. C. Hyland,et al.  A comparison of two obstacle avoidance path planners for autonomous underwater vehicles , 1990, Symposium on Autonomous Underwater Vehicle Technology.

[29]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[30]  G. DeMuth,et al.  Obstacle avoidance using neural networks , 1990, Symposium on Autonomous Underwater Vehicle Technology.

[31]  D. B. Fogel,et al.  Optimal routing of multiple autonomous underwater vehicles through evolutionary programming , 1990, Symposium on Autonomous Underwater Vehicle Technology.

[32]  S. Sastry,et al.  Steering nonholonomic systems using sinusoids , 1990, 29th IEEE Conference on Decision and Control.

[33]  G.N. Williams,et al.  A collision avoidance controller for autonomous underwater vehicles , 1990, Symposium on Autonomous Underwater Vehicle Technology.

[34]  C. W. Warren,et al.  A technique for autonomous underwater vehicle route planning , 1990, Symposium on Autonomous Underwater Vehicle Technology.

[35]  Yoram Koren,et al.  Potential field methods and their inherent limitations for mobile robot navigation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[36]  Prof. Dr. Kikuo Fujimura.  Motion Planning in Dynamic Environments , 1991, Computer Science Workbench.

[37]  Yoram Koren,et al.  The vector field histogram-fast obstacle avoidance for mobile robots , 1991, IEEE Trans. Robotics Autom..

[38]  J.F. Grassle,et al.  Leo-15 An Unmanned Long Term Environmental Observatory , 1992, OCEANS 92 Proceedings@m_Mastering the Oceans Through Technology.

[39]  Don Brutzman,et al.  Autonomous Sonar Classification Using Expert Systems , 1992, OCEANS 92 Proceedings@m_Mastering the Oceans Through Technology.

[40]  Narendra Ahuja,et al.  Gross motion planning—a survey , 1992, CSUR.

[41]  B. Butler,et al.  Theseus: a cable-laying AUV , 1993, Proceedings of OCEANS '93.

[42]  Anthony Stentz,et al.  Optimal and efficient path planning for partially-known environments , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[43]  N. Storkersen,et al.  The control system of an autonomous underwater vehicle , 1994, 1994 Proceedings of IEEE International Conference on Control and Applications.

[44]  L. Henriksen.  Real-time underwater object detection based on an electrically scanned high-resolution sonar , 1994, Proceedings of IEEE Symposium on Autonomous Underwater Vehicle Technology (AUV'94).

[45]  Don Brutzman,et al.  Evaluation of the NPS PHOENIX autonomous underwater vehicle hybrid control system , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[46]  David M. Lane,et al.  A spatial-temporal approach for segmentation of moving and static objects in sector scan sonar image sequences , 1995 .

[47]  James A. Hendler,et al.  A motion description language and a hybrid architecture for motion planning with nonholonomic robots , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[48]  Tamaki Ura,et al.  An on-line adaptation method in a neural network based control system for AUVs , 1995 .

[49]  F. Nussbaum,et al.  Sensors for a forward-looking high resolution AUV sonar , 1996, Proceedings of Symposium on Autonomous Underwater Vehicle Technology.

[50]  R. Zapata,et al.  Collision avoidance and bottom following of a torpedo-like AUV , 1996, OCEANS 96 MTS/IEEE Conference Proceedings. The Coastal Ocean - Prospects for the 21st Century.

[51]  Naomi Kato,et al.  Autonomous underwater vehicle AQUA EXPLORER 1000 for inspection of underwater cables , 1996, Proceedings of Symposium on Autonomous Underwater Vehicle Technology.

[52]  D. Lane,et al.  Motion estimation and tracking of multiple objects in sector scan sonar using optical flow , 1996 .

[53]  Dinesh Manocha,et al.  Collision Detection: Algorithms and Applications , 1996 .

[54]  E. Rimon,et al.  A new range-sensor based globally convergent navigation algorithm for mobile robots , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[55]  Murray Hill.  Constructing Good Partitioning Trees , 1996 .

[56]  Tamaki Ura,et al.  Development of an autonomous underwater robot “Twin-Burger” for testing intelligent behaviors in realistic environments , 1996, Auton. Robots.

[57]  H. Okabe,et al.  A motion planning method for an AUV , 1996, Proceedings of Symposium on Autonomous Underwater Vehicle Technology.

[58]  Charles V. Jakowatz,et al.  Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach , 1996 .

[59]  Nancy M. Amato,et al.  A randomized roadmap method for path and manipulation planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[60]  Ming C. Lin.  Fast and Accurate Collision Detection for Virtual Environments , 1997, Scientific Visualization Conference (dagstuhl '97).

[61]  D. Lane,et al.  Subsea vehicle path planning using nonlinear programming and constructive solid geometry , 1997 .

[62]  R. W. R. DARLING.  Classroom Note: Converting Matrix Riccati Equations to Second-Order Linear ODE , 1997, SIAM Rev..

[63]  Kevin A. Wise,et al.  Nonlinear control of agile missiles using state dependent Riccati equations , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[64]  John T. Wen,et al.  Trajectory tracking control of a car-trailer system , 1997, IEEE Trans. Control. Syst. Technol..

[65]  Tien D. Bui,et al.  Robot Path Planning Using Fluid Model , 1998, J. Intell. Robotic Syst..

[66]  Jeffrey B. Burl,et al.  Linear Optimal Control: H(2) and H (Infinity) Methods , 1998 .

[67]  Naoji Shiroma,et al.  Time-scaling control of an underactuated manipulator , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[68]  R. N. Carpenter,et al.  Concurrent mapping and localization with FLS , 1998, Proceedings of the 1998 Workshop on Autonomous Underwater Vehicles (Cat. No.98CH36290).

[69]  E. Tunstel,et al.  Multiobjective evolutionary path planning via fuzzy tournament selection , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[70]  Barry Brumitt,et al.  Framed-quadtree path planning for mobile robots operating in sparse environments , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[71]  Y. Wang,et al.  Underwater vehicle path planning using a multi-beam forward looking sonar , 1998, IEEE Oceanic Engineering Society. OCEANS'98. Conference Proceedings (Cat. No.98CH36259).

[72]  Gregory Dudek,et al.  A global topological map formed by local metric maps , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[73]  Jean-Paul Laumond,et al.  Robot Motion Planning and Control , 1998 .

[74]  Naoji Shiroma,et al.  Time-scaling control of an underactuated manipulator , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[75]  Hugh F. Durrant-Whyte,et al.  Using sonar in terrain-aided underwater navigation , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[76]  David M. Lane,et al.  Robust tracking of multiple objects in sector-scan sonar image sequences using optical flow motion estimation , 1998 .

[77]  Daniel Vallejo,et al.  OBPRM: an obstacle-based PRM for 3D workspaces , 1998 .

[78]  J. Cloutier,et al.  Control designs for the nonlinear benchmark problem via the state-dependent Riccati equation method , 1998 .

[79]  S. LaValle.  Rapidly-exploring random trees : a new tool for path planning , 1998 .

[80]  Kazuo Sugihara,et al.  GA-based On-line Path Planning for SAUVIM , 1998, IEA/AIE.

[81]  Mark H. Overmars,et al.  The Gaussian sampling strategy for probabilistic roadmap planners , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[82]  Maria Petrou,et al.  Image processing - the fundamentals , 1999 .

[83]  David Wettergreen,et al.  Autonomous Guidance and Control for an Underwater Robotic Vehicle , 1999 .

[84]  Emilio Frazzoli,et al.  A hybrid control architecture for aggressive maneuvering of autonomous helicopters , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[85]  Joan Batlle,et al.  Recent trends in control architectures for autonomous underwater vehicles , 1999, Int. J. Syst. Sci..

[86]  Gianluca Antonelli,et al.  Real-time path planning and obstacle avoidance for an autonomous underwater vehicle , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[87]  Yvan Petillot,et al.  Tracking objects in underwater multibeam sonar images , 1999 .

[88]  B. Abdul-Baki,et al.  Independent validation and verification of the TCAS II collision avoidance subsystem , 1999, Gateway to the New Millennium. 18th Digital Avionics Systems Conference. Proceedings (Cat. No.99CH37033).

[89]  Steven M. LaValle,et al.  Randomized Kinodynamic Planning , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[90]  Joel W. Burdick,et al.  An autonomous sensor-based path-planner for planetary microrovers , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[91]  Steven M. LaValle,et al.  Rapidly-Exploring Random Trees: Progress and Prospects , 2000 .

[92]  Junku Yuh,et al.  On AUV control architecture , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[93]  E. Feron,et al.  Robust hybrid control for autonomous vehicle motion planning , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[94]  Kristin Ytterstad Pettersen,et al.  Underactuated dynamic positioning of a ship-experimental results , 2000, IEEE Trans. Control. Syst. Technol..

[95]  Fumin Zhang,et al.  The MDLe Engine -- A Software Tool for Hybrid Motion Control , 2000 .

[96]  Emanuele Trucco,et al.  Feature Tracking in Video and Sonar Subsea Sequences with Applications , 2000, Comput. Vis. Image Underst..

[97]  T. Ura,et al.  Collision avoidance controller for AUV systems using stochastic real value reinforcement learning method , 2000, SICE 2000. Proceedings of the 39th SICE Annual Conference. International Session Papers (IEEE Cat. No.00TH8545).

[98]  Patrick Pérez,et al.  Sonar image segmentation using an unsupervised hierarchical MRF model , 2000, IEEE Trans. Image Process..

[99]  Michael R. M. Jenkin,et al.  Computational principles of mobile robotics , 2000 .

[100]  N. Seube,et al.  Guidance algorithms for UUVs obstacle avoidance systems , 2000, OCEANS 2000 MTS/IEEE Conference and Exhibition. Conference Proceedings (Cat. No.00CH37158).

[101]  Kay Chen Tan,et al.  Evolutionary artificial potential fields and their application in real time robot path planning , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[102]  Whitney Cornforth,et al.  Development of an environment-sensitive navigation system for the AUV Autolycus , 2000 .

[103]  Chris OliverbaN.  An Optimal Approach to SAR Image Segmentation and Classification , 2000 .

[104]  Robert Sutton,et al.  Adaptive steering of a containership based on neural networks , 2000 .

[105]  Alain Liégeois,et al.  Near Optimal Robust Path Planning for Mobile Robots: the Viscous Fluid Method with Friction , 2000, J. Intell. Robotic Syst..

[106]  Lydia E. Kavraki,et al.  Path planning using lazy PRM , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[107]  Michael L. Nelson,et al.  A Generic Path Planning Strategy for Autonomous Vehicles , 2000 .

[108]  Thierry Siméon,et al.  Visibility-based probabilistic roadmaps for motion planning , 2000, Adv. Robotics.

[109]  U. Zimmer.  Embedding local metrical map patches in a globally consistent topological map , 2000, Proceedings of the 2000 International Symposium on Underwater Technology (Cat. No.00EX418).

[110]  Ser Yong Lim,et al.  Virtual obstacle concept for local-minimum-recovery in potential-field based navigation , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[111]  Dana R. Yoerger,et al.  Fine-scale seafloor survey in rugged deep-ocean terrain with an autonomous robot , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[112]  P. Cheng,et al.  RRT-based trajectory design for autonomous automobiles and spacecraft , 2001 .

[113]  E. Feron,et al.  Real-time motion planning for agile autonomous vehicles , 2000, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[114]  C. D. Loggins,et al.  A comparison of forward-looking sonar design alternatives , 2001, MTS/IEEE Oceans 2001. An Ocean Odyssey. Conference Proceedings (IEEE Cat. No.01CH37295).

[115]  Evrin Bilge Erdem.  Analysis and Real-Time Implementation of State -Dependent Riccati Equation Controlled Systems , 2001 .

[116]  Robert Sutton,et al.  A Fuzzy Fault Tolerant Control Scheme for an Autonomous Underwater Vehicle , 2001 .

[117]  Roland Siegwart,et al.  Simultaneous localization and map building: a global topological model with local metric maps , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[118]  Zbigniew Pietrzykowski.  The Analysis of a Ship Fuzzy Domain in a Restricted Area , 2001 .

[119]  David M. Drumheller,et al.  A Parameter-Insensitive False Alarm Rate Detection Processor , 2001 .

[120]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[121]  Philip A. Wilson,et al.  Vessel management expert system , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[122]  G. Tortora.  Fault-tolerant control and intelligent instrumentation , 2001 .

[123]  Yvan Petillot,et al.  Underwater vehicle obstacle avoidance and path planning using a multi-beam forward looking sonar , 2001 .

[124]  F. Bullo,et al.  Randomized searches and nonlinear programming in trajectory planning , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[125]  Mark H. Overmars.  Recent Developments in Motion Planning , 2002, International Conference on Computational Science.

[126]  Robert Sutton,et al.  Review of multisensor data fusion techniques and their application to autonomous underwater vehicle navigation , 2002 .

[127]  Tsai-Yen Li,et al.  An incremental learning approach to motion planning with roadmap management , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[128]  Anthony J. Healey,et al.  Obstacle avoidance control for the REMUS autonomous underwater vehicle , 2003 .

[129]  James P. Ostrowski,et al.  Motion planning a aerial robot using rapidly-exploring random trees with dynamic constraints , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[130]  Joan Batlle,et al.  Designing a Fuzzy-like PD controller for an underwater robot , 2003 .

[131]  Michael A. Greenspan,et al.  Approximate k-d tree search for efficient ICP , 2003, Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings..

[132]  Emilio Frazzoli,et al.  Quasi-random algorithms for real-time spacecraft motion planning and coordination , 2003 .

[133]  J. N. Morrison,et al.  Gambit MCM AUV: overview and system performance , 2003, Oceans 2003. Celebrating the Past ... Teaming Toward the Future (IEEE Cat. No.03CH37492).

[134]  Wasif Naeem,et al.  LQG/LTR Control of an Autonomous Underwater Vehicle Using a Hybrid Guidance Law , 2003 .

[135]  Robert Sutton,et al.  Dynamic Modelling of a Remotely Operated Vehicle , 2003 .

[136]  John Hunt,et al.  State-Dependent Riccati Equation Control of a Small Unmanned Helicopter , 2003 .

[137]  D. E. Brown,et al.  The over-extended Kalman filter - don't use it! , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[138]  Yoshiaki Kuwata,et al.  Experimental demonstrations of real-time MILP control , 2003 .

[139]  Joao P. Hespanha,et al.  Logic-based switching control for trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty , 2004, Proceedings of the 2004 American Control Conference.

[140]  Robert Sutton,et al.  An incremental stochastic motion planning technique for autonomous underwater vehicles , 2004 .

[141]  Robert Allen,et al.  Composite control of a tethered underwater flight vehicle , 2004 .

[142]  Thierry Fraichard,et al.  From Reeds and Shepp's to continuous-curvature paths , 1999, IEEE Transactions on Robotics.

[143]  Ernest J. Ohlmeyer,et al.  Nonlinear Discrete-Time Design Methods for Missile Flight Control Systems , 2004 .

[144]  Perry Y. Li,et al.  Motion Planning and Control of a Swimming Machine , 2004, Int. J. Robotics Res..

[145]  Junku Yuh,et al.  Development of a real-time control architecture for a semi-autonomous underwater vehicle for intervention missions , 2004 .

[146]  Wei Ren,et al.  Constrained nonlinear tracking control for small fixed-wing unmanned air vehicles , 2004, Proceedings of the 2004 American Control Conference.

[147]  Francesco Bullo,et al.  Vehicle Motion Planning with Time-Varying Constraints , 2004 .

[148]  Zhong-Ping Jiang,et al.  Robust adaptive path following of underactuated ships , 2004, Autom..

[149]  Munther A. Dahleh,et al.  Maneuver-based motion planning for nonlinear systems with symmetries , 2005, IEEE Transactions on Robotics.

[150]  Robert Sutton,et al.  QUASI-RANDOM, MANOEUVRE-BASED MOTION PLANNING ALGORITHM FOR AUTONOMOUS UNDERWATER VEHICLES , 2005 .

[151]  A. D. Lewis,et al.  Geometric control of mechanical systems : modeling, analysis, and design for simple mechanical control systems , 2005 .

[152]  Evangelos Papadopoulos,et al.  Trajectory Planning and Tracking Control of Underactuated AUVs , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[153]  Li Jia-wang.  A study of autonomous underwater vehicle hull form using computational fluid dynamic , 2006 .

[154]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[155]  G. Swaminathan.  Robot Motion Planning , 2006 .

[156]  António Manuel Santos Pascoal,et al.  Dynamic positioning and way-point tracking of underactuated AUVs in the presence of ocean currents , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[157]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.