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Introduction to modeling and control of underwater vehicle-manipulator systems.

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  • 1. Introduction to modeling and controlof underwater vehicle-manipulator systemsGianluca Antonelli Universit` di Cassino e del Lazio Meridionalea antonelli@unicas.ithttp://webuser.unicas.it/lai/robotica http://www.eng.docente.unicas.it/gianluca antonelli TRIDENT schoolGianluca Antonelli TRIDENT school, Mallorca, 1 october 2012

2. Targeted audience and talks shape50 minutes talk about the mathematical foundations ofUnderwater Vehicle Manipulator Systems (UVMS)Educational shape (entry level)knowledge of mathematics, physics control basic roboticsequations, equations still equations. . . SAUVIMGianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 3. OutlineUVMSs Introduction Mathematical modeling Two words about dynamic control Kinematic control ALIVEGianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 4. (semi)autonomus UVMSs Use of a manipulator is common for ROV, mainly in remotelycontrolled or in a master-slave congurationAmong the rst autonomus modes:AMADEUS I & II before 2000, EUSAUVIM 1997, USAPETASUS, KoreaALIVE 2000-2003, EUTwin Burger + manipulator, JapanTRIDENT 2010-2012, EU PETASUSGianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 5. Notation1 (roll) (surge) (pitch) xb (sway) (yaw) 1yb (heave) x zb yForces and 1, 2 1, 2 zmomentsMotion along xSurge XuxMotion along ySwayYvyMotion along zHeave ZwzRotation about xRollKpRotation about yPitch MqRotation about zYaw Nr 1 [Fossen(1994)] Gianluca AntonelliTRIDENT school, Mallorca, 1 october 2012 6. Rigid body attitude yaw rollEuler angles commonly used pitchok for the vehicle, designed stable in roll and pitchFor the end-eector possible issues of representation singularities non-minimal representations (quaternions) Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 7. Rigid body kinematics1 1= R6 = R62 2Iand by dening the matrix J e (RB ) R66B RIO 33J e (RI ) =BI O 33 J k,o (RB )it isI = J e (RB ) body-fixed velocities Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 8. Rigid body dynamicsmoving in the free spacebody-fixed acceleration M RB + C RB () = v 6-dof force/moment at the body mI 3mS(r b )M RB = b )C R66mS(r C I Ob Gianluca AntonelliTRIDENT school, Mallorca, 1 october 2012 9. Added mass and inertiaA body moving in a uid accelerates it ( 1000 kg/m3 )Need to account for an additional inertia(the added mass is not a quantity to be added to the body such thatit has an increased mass)For submerged bodies, with common AUV shape at low velocities: M A = diag {Xu , Yv , Zw , Kp , Mq , Nr } 000 0 Zw w Yv v 0 00 Zw w 0 Xu u 0 00Yv vXu u 0 CA = 0 Zw w Yv v 0 Nr r Mq q Zw w 0Xu u Nr r 0 Kp p Yv v Xu u 0 Mq q Kp p0 Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 10. DampingViscosity of the uid causes dissipative drag and lift forces to the body liftdrag relative owThe simplest model is drag-only, diagonal, linear/quadratic in velocityD RB ()DRB () = diag {Xu , Yv , Zw , Kp , Mq , Nr } + diag Xu|u| |u| , Yv|v| |v| , Zw|w| |w| , Kp|p| |p| , Mq|q| |q| , Nr|r| |r|Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 11. CurrentAssume a current constant and irrotational in the inertial framec,xc,y Ic,z c = I = 0 c 0 0 0eects added considering the relative velocity in body-xed frame r = RB II cin the Coriolis/centripetal and damping Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 12. CurrentI c o x yob xb ybxb obybintuitively, the current is pushing the vehicle Gianluca AntonelliTRIDENT school, Mallorca, 1 october 2012 13. Gravity and buoiancy 0gIf G (RB ) = RB 0 IIWox z0ob fbfb Mr B B xbrbrbf B (RI ) = RI 0 zbr B rg fg fgg obxb zbMR = r G f G (RB ) + r B f G (RB ) B I B Ilinear in the 3 parameters: W r B Br B constant in body-fixedGBGianluca AntonelliTRIDENT school, Mallorca, 1 october 2012 14. Some dynamic considerationsConsidering the sole vehicle two eects aects steady state current eect, constant in the inertial frame restoring forces, (depends on) constant in the body-xed frameProper integral/adaptive actions need to be designed for nepositioning to avoid disturbance caused by the controller 22[Antonelli(2007)]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 15. Some dynamic considerationsConsidering the sole vehicle two eects aects steady state current eect, constant in the inertial frame restoring forces, (depends on) constant in the body-xed frameProper integral/adaptive actions need to be designed for nepositioning to avoid disturbance caused by the controller 2 II currentc ccompensationduring a 90rotation inertialbody-xed2[Antonelli(2007)]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 16. Thrusters 6 or more for full vehicle control (thrust required also in hovering)force/moment (nonlinear) function ofpropeller revolutionuid speedinput torqueaected by several parametersuid densitytunnel cross-sectional areatunnel lengthpropeller diameter and input-output volumetric owratemain cause of bandwidth constraints and limit cyclesGianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 17. Some referencesFor modeling and control of marine vehicles in a control perspective: [Fossen(1994)] [Fossen(2002)] [Antonelli et al.(2008)Antonelli, Fossen, and Yoerger] [Fossen(2011)] Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 18. UVMS kinematics 1 ee1 I ee = = J w (RB , q) = 2 system velocities ee2 q end-effector velocities 1 Jacobian eeOiGianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 19. UVMS dynamicsDynamics via classical Newton-Euler equations by propagating thevelocities and forcesi gf i+1 , i+1r i1,B Bi Oi1r i1,i Oi r i,C r i1,CCif i , i dimi g Gianluca AntonelliTRIDENT school, Mallorca, 1 october 2012 20. UVMS dynamics in matrix form M (q) + C(q, ) + D(q, ) + g(q, RI ) = B formally equal to a ground-fixed industrial manipulator 3however. . . Uncertainty in the model knowledge Low bandwidth of the sensors readings Diculty to control the vehicle in hovering Dynamic coupling between vehicle and manipulator Kinematic redundancy of the system3[Siciliano et al.(2008)Siciliano, Sciavicco, Villani, and Oriolo]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 21. UVMS dynamicsMovement of vehicle and manipulator coupledmovement of the vehicle carrying the manipulatorlaw of conservation of momentumNeed to coordinateat velocity level kinematic controlat torque level dynamic control 44 [McLain et al.(1996b)McLain, Rock, and Lee][McLain et al.(1996a)McLain, Rock, and Lee] Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 22. Need for coordinationCoordination and redundancy exploitation is required5 : Redundancy at torque level?Space manipulator literature? Need to exactly compensate for The assumption of the the dynamics, not appropriatemomentum conservation is not for the underwater environment valid5 [Khatib(1987), Sentis(2007),Nenchev et al.(1992)Nenchev, Umetani, and Yoshida] Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 23. Need for coordinationCoordination and redundancy exploitation is required5 : Redundancy at torque level?Space manipulator literature? Need to exactly compensate for The assumption of the the dynamics, not appropriatemomentum conservation is not for the underwater environment valid5 [Khatib(1987), Sentis(2007),Nenchev et al.(1992)Nenchev, Umetani, and Yoshida] Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 24. Need for coordinationCoordination and redundancy exploitation is required5 : Redundancy at torque level?Space manipulator literature? Need to exactly compensate for The assumption of the the dynamics, not appropriatemomentum conservation is not for the underwater environment valid5 [Khatib(1987), Sentis(2007),Nenchev et al.(1992)Nenchev, Umetani, and Yoshida] Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 25. Needs for coordinationlet us move to the kinematical levelWhat is coming nextan examplea short reviewalgorithms & tasks for UVMSsbalance movement between vehicle/manipulator Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 26. A rst kinematic solutionHoping the vehicle in hovering is not the best strategy to e.e. nepositioning6 , better to kinematically compensate with the manipulator6[Hildebrandt et al.(2009)Hildebrandt, Christensen, Kerdels, Albiez, and Kirchner]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 27. Kinematic control in pillsA robotic system is kinematically redundant when it possesses moredegrees of freedom than those required to execute a given taskRedundancy may be used to add additional tasks and to handlesingularitiesExample for the sole end-eector trajectory ee,d d , qd , qIK controloff-line trajectory planning not appropriate underwater Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 28. Kinematic control in pills -2-Starting from a generic m-dimensional task = f (, q) Rmit is required to invert = J (, q)The congurations at which J Rm6+n is rank decient arekinematic singularitiesThe mobility of the structure is reducedInnite solutions to the inverse kinematics problem might existClose to a kinematic singularity at small task velocities cancorrespond large joint velocities Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 29. Kinematic control in pills -3- = J inverted by solving proper optimization problemsPseudoinverse1 = J = J T J J T Transpose-based = J TWeighted pseudoinverse 1 = J = W 1 J T J W 1 J TW Damped Least-Squares1 = J T J J T + 2 I m need for closed-loop also. . .Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012 30. Kinematic control in pills -4-Handling several tasks7Extended JacobianAdd additional (6 + n) m constraintsh(, q) = 0 with associated J hsuch that the problem is squared with J = 0 Jh7[Chiaverini et al.(2008)Chiaverini, Oriolo, and Walker] Gianluca Antonelli TRIDENT