Modeling and Control of Underwater Robotic Systems Dr.ing. thesis Ingrid Schj0lberg Department of Engineering Cybernetics Norwegian University of Science and Technology March 1996 Report 96-21-W Department of Engineering Cybernetics Norwegian University of Science and Technology N-7034 Trondheim, Norway OBmetmoN of im doombst b mwia DISCLAI R Portions of tins document may be Illegible in electronic image products. Images are produced from the best available original document Preface This thesis is submitted for the Doktor ingenipr degree at the Norwegian University of Science and Technology (NTNU). The research was carried out at the Norwegian Institute of Technology (NTH), Department of Engi ­ neering Cybernetics, in the period from January 1991 to March 1996. The work was funded by The Research Council of Norway (NFR) through the MOBATEL project. Professor Dr.ing. Olav Egeland was my supervisor. During the academic year 1992-1993 I worked at the European Organization for Nuclear Research (CERN). This stay was funded by TOTAL Norge. The work performed during this stay has not been included in this thesis. I am indebted to Professor Egeland for giving me the opportunity to take this study. I am also grateful for advice and comments during the writing of scientific articles and for the introduction to the fields of force control and vibration damping. I am thankful to the administrator of the MOBATEL project, Professor Jens G. Balchen, for letting me take part in this project. I am grateful to Professor Dr.ing. Thor I. Fossen for useful discussions on hydrodynamics. I want to express my gratitude to Dr.ing. Rakel K. Kanestrpm and Dr.ing. Gunleiv Skofteland, for valuable comments and remarks to the draft of this thesis. I am grateful to Prof. Egeland for proofreading the final manuscript. I gratefully acknowledge • NFR for my three year scholarship • TOTAL Norge for one year scholarship in France The MOBATEL board for financial support to attend the 3rd Inter ­ national Conference on Manoeuvring and Control of Marine Craft. Iffifjd iclyJjxa Ingrid Sctijolberg Trondheim, Norway Summary This doctoral thesis describes modeling and control of underwater vehicle- manipulator systems. The thesis also presents a model and a control scheme for a system consisting of a surface vessel connected to an underwater robotic system by means of a slender marine structure. The recursive Newton-Euler scheme for computing the dynamics of robot- manipulators is extended to include the added mass forces, vortex-induced forces, buoyant forces, rotational damping moments and current loads act­ ing on an underwater manipulator. The dynamics of the underwater ma­ nipulator is written in a matrix-vector form. The equations of motion of an underwater vehicle are re rieved taking into account the forces acting from the manipulator on the vehicle. The equation of motion of the total system is written in a matrix vector form and structural properties like symmetry, skew-symmetry and positiveness are established. This simplifies the control design and facilitates the use of Lyapunov theory in the stability analysis. The feedback linearization technique is evaluated through a simulation study. Two decoupling schemes are considered, 1) decoupling of the end- effector velocity from the vehicle velocity and 2) decoupling of the end- effector velocity from the system momentum. Passivity-based controllers for set-point control of the vehicle and joint- space control of the manipulator are proposed. The scheme makes it possi ­ ble to achieve manipulator tracking without perfect knowledge of the vehicle dynamics. The controllers can be implemented with different bandwidths, and the vehicle can be used for slow-gross positioning while the manipula ­ tor performs fast joint-space tasks. This provides a large workspace for the system. A control scheme for coordinated motion control of the vehicle and ma­ nipulator in world coordinates is proposed. In both the proposed control schemes velocities are not measured and 1st order observers are used to reconstruct the velocity signals. IV Equations of motion for a cable/riser system connected to a surface vessel at the top end and to a robotic system at the bottom end are presented. A control system is proposed for position and velocity control of the robotic system. A control scheme for coordinated position control of the surface vessel and the robotic system is proposed. The total system is shown to be passive. The concept of connecting a thruster unit/robotic system to the bottom end of a slender marine structure can be applied in the operation of connecting a production riser to an underwater well-head. Contents Preface i Summary iii List of Tables ix List of Figures xii Nomenclature xiii 1 Introduction 1 1.1 Previous work.................. 2 1.1.1 Underwater vehicle-manipulator systems ................. 2 1.1.2 Underwater robotic system connected to a cable/riser system.............................................................................. 4 1.2 Contributions of the thesis ........................................................ 5 1.3 Outline of the thesis ................................................................. 7 2 Underwater vehicle and manipulator dynamics 9 2.1 Coordinate frames.................................................................... 10 2.2 System dynamics ........................................................................ 11 2.2.1 Fluid forces on a manipulator link ......................... 11 2.2.2 Equations of motion for the manipulator .................... 15 2.2.3 Equations of motion for the combined system .... 17 VI CONTENTS 2.2.4 Equations of motion in the inertial frame................ 19 2.3 System properties ....................................................................... 21 2.4 Conclusions ........................ 23 3 Control of underwater vehicle and manipulator 25 3.1 Feedback linearization .............................................................. 26 3.1.1 Kinematic equations ..................................................... 27 3.1.2 System momentum ........................................................ 27 3.1.3 Control laws ................................................................. 28 3.1.4 Simulation study........................................................... 30 3.1.5 Discussion ....................................................................... 34 3.1.6 Conclusions ..................................................................... 34 3.2 Regulation and tracking control ................................................ 35 3.2.1 Control strategy........................................................... 35 3.2.2 Stability analysis .................................................... 37 3.2.3 Simulations ............................... 40 3.2.4 Discussion ....................................................................... 42 3.2.5 Conclusions .................. 45 3.3 Coordinated motion control ..................................................... 46 3.3.1 Control law.................................................................... 47 3.3.2 Stability analysis ..................... 47 3.3.3 Simulations ..................................... 49 3.3.4 Discussion ....................................................................... 50 3.3.5 Conclusions .................................................................... 51 3.4 Conclusions ........................................ 51 CONTENTS vii 4 Lateral motion control of an underwater thruster module connected to a slender marine structure 53 4.1 Dynamic models ........................................................................ 54 4.1.1 Equation of motion of the thruster system................ 55 4.1.2 Equations of motion of the cable/riser system .... 56 4.1.3 Equations of motion of the total system on matrix- vector form ..................................................................... 61 4:2 Control strategy ....................................................................... 62 4.2.1 Stability analysis . ..................................................... 62 4.2.2 Robustness ..................................................................... 65 4.3 Simulations ................................................................................. 65 4.3.1 Frequency response ........................................................ 68 4.3.2 Constrained modes........................................................ 69 4.4 Discussion .................................................................................... 71 4.5 Conclusions .................. 72 5 Control of an underwater robotic system connected to a slender marine structure in 3 DOF 73 5.1 Dynamic models ....................................................... 74 5.1.1 Coordinate frames........................................................ 74 5.1.2 Dynamics of an underwater robotic system.............. 75 5.1.3 Dynamics of the cable/riser system.............................. 75 5.2 Control strategy.............................................. 80 5.2.1 Stability analysis ........................................................... 80 5.2.2 Discussion ........................................................................ 81 5.3 Coordinated position control of the robotic system and sur­ face vessel.................................................................................... 81 5.3.1 Stability analysis of the total system with PD-control 83 5.3.2 Discussion .................................