Underwater Robots - Gianluca Antonelli.pdf

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28 2. Modelling of <strong>Underwater</strong> <strong>Robots</strong> that theadded mass matrixisstate-dependentand itscoefficients are function of the distance traveled by the cylinder. 2.4.2 Damping Effects The viscosity ofthe fluid also causes the presence ofdissipative drag and lift forces onthe body. Acommon simplification is to consider only linear and quadratic damping terms and group these terms in amatrix D RB such that: D RB( ν ) > O ∀ ν ∈ IR 6 . The coefficients of this matrix are also considered to be constant. Fora completely submerged body, the following further assumption can be made: D RB( ν )=− diag { X u ,Yv ,Zw ,Kp ,Mq ,Nr } + − diag � X u | u | | u | ,Y v | v | | v | ,Z w | w | | w | ,K p | p | | p | ,M q | q | | q | ,N r | r | | r | � . Assuming adiagonal structure for the damping matrix implies neglecting the coupling dissipative terms. The detailed analysis of the dissipative forces isbeyond the scope ofthis work. In the following, only the natureoftheseforceswill be briefly discussed. Introductory analysis ofthis phenomenon can be found in [127, 157, 208, 220, 255], while indepth discussion in [253, 274]. The viscous effects can be considered as the sum of two forces, the drag and the lift forces. The former are parallel to the relative velocity between the body and the fluid, while the latter are normal to it. Both drag and lift forces are supposed toact on the center of mass of the body. Inorder to solve the distributed flow problem, an integral over the entire surface is required to compute the net force/moment acting on the body. Moreover, the model of drag and lift forces isnot known and, also for some widely accepted models, the coefficients are not known and variables. Forasphere moving in afluid, the drag force can be modeled as [157]: F drag =0. 5 ρU 2 SCd ( R n ) , where ρ is the fluid density, U is the velocityofthe sphere, S is the frontal area of the sphere, C d is the adimensional drag coefficients and R n is the Reynolds number. For ageneric body, S is the projection of the frontal area along the flow direction. The drag coefficient isthen dependent on the Reynolds number, i.e., on the laminar/turbulent fluid motion: R n = ρ | U | D µ where D is the characteristic dimension of the body perpendicular to the direction of U and µ is the dynamic viscosity ofthe fluid. In Table 2.2 the drag coefficients in function of the Reynolds number for acylinder are reported [255]. The drag coefficients can be considered as the sum of two physical
2.4 Hydrodynamic Effects 29 effects: africtional contribution of the surface whose normal isperpendicular to the flow velocity, and apressure contribution ofthe surface whose normal is parallel to the flow velocity. Table 2.2. Lift and Drag Coefficient for acylinder Reynolds number regime motion C d C l R n < 2 · 10 5 2 · 10 5
Page 1 and 2: Springer Tracts in Advanced Robotic
Page 3 and 4: Gianluca Antonelli Underwater Robot
Page 5 and 6: Editorial Advisory Board EUROPE Her
Page 7 and 8: Elalocomotiva sembrava fosse un mos
Page 9 and 10: Acknowledgements The contributions
Page 11 and 12: Preface to the Second Edition The p
Page 13 and 14: XVIII Preface to the First Edition
Page 15 and 16: XX Preface tothe First Edition mani
Page 17 and 18: XXII Notation η q =[η T 1 ε T η
Page 19 and 20: XXIV Notation ˜x error variable de
Page 21 and 22: XXVI Contents 3. Dynamic Control of
Page 23 and 24: XXVIIIContents A. Mathematical mode
Page 25 and 26: 2 1. Introduction Maybe the first i
Page 27 and 28: 4 1. Introduction (Massachusetts, U
Page 29 and 30: 6 1. Introduction Fig. 1.4. Coordin
Page 31 and 32: 8 1. Introduction Fig. 1.5. Pig, ma
Page 33 and 34: 10 1. Introduction An example of cr
Page 35 and 36: 12 1. Introduction Fig. 1.8. Romeo
Page 37 and 38: 2. Modelling ofUnderwater Robots
Page 39 and 40: 2.2 Rigid Body’s Kinematics 17 Th
Page 41 and 42: J T k,oqJ k,oq = 1 4 I 3 , that all
Page 43 and 44: 5. compute the quaternion Q by the
Page 45 and 46: 2.3 Rigid Body’s Dynamics 23 Let
Page 47 and 48: 2.4 Hydrodynamic Effects 25 τ 1 =
Page 49: C A ( ν )=− C T A ( ν ) ∀ ν
Page 53 and 54: 2.5 Gravity and Buoyancy 2.5 Gravit
Page 55 and 56: 2.6 Thrusters’ Dynamics 33 Fig. 2
Page 57 and 58: 2.7 Underwater Vehicles’ Dynamics
Page 59 and 60: y z 2.8 Kinematics of Manipulators
Page 61 and 62: 2.9 Dynamics ofUnderwater Vehicle-M
Page 63 and 64: 2.9 Dynamics ofUnderwater Vehicle-M
Page 65 and 66: 2.11 Identification 43 f e = K ( x
Page 67 and 68: 3. Dynamic Control of 6-DOF AUVs 3.
Page 69 and 70: 3.2 Earth-Fixed-Frame-Based, Model-
Page 71 and 72: o x z o b z b x b 3.3 Earth-Fixed-F
Page 73 and 74: 3.4 Vehicle-Fixed-Frame-Based, Mode
Page 75 and 76: o o b y x y b x b 3.5 Model-Based C
Page 77 and 78: 3.6 Mixed Earth/Vehicle-Fixed-Frame
Page 79 and 80: 3.7 Jacobian-Transpose-Based Contro
Page 81 and 82: 3.8 Comparison Among Controllers 59
Page 83 and 84: 3.9 Numerical Comparison Among the
Page 87 and 88: force [N] moment [Nm] 20 10 0 −10
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80 4. Fault Detection/Tolerance Str
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5. Experiments of Dynamic Control o
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5.3 Experiments of Dynamic Control
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[m] [m] 5 4 3 2 1 0 0 100 200 300 4
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5.3 Experiments of Dynamic Control
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5.4 Experiments of Fault Tolerance
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[deg] 120 100 80 60 40 20 0 −20 5
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6. Kinematic Control of UVMSs “.
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6.2 Kinematic Control 107 UVMS. Thi
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6.2 Kinematic Control 109 singulari
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6.2 Kinematic Control 111 case of t
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6.5 Singularity-Robust Task Priorit
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6.6 Fuzzy Inverse Kinematics 121 It
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Simulations 6.6 Fuzzy Inverse Kinem
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6.6 Fuzzy Inverse Kinematics 125 Fi
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vehicle attitude [deg] 20 10 0 −1
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6.6 Fuzzy Inverse Kinematics 129 It
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[-] 1 0.8 0.6 0.4 0.2 0 close 0 20
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joint positions 1-3 [deg] joint pos
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e.e. position error [m] 0.02 0.01 0
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7. Dynamic Control of UVMSs 7.1 Int
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7.2 Feedforward Decoupling Control
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7.2 Feedforward Decoupling Control
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7.4 Nonlinear Control for UVMSs wit
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7.5 Non-regressor-Based Adaptive Co
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7.6 Sliding Mode Control 7.6 Slidin
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7.6 Sliding Mode Control 153 u = B
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7.6 Sliding Mode Control 155 Practi
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7.7 Adaptive Control 157 of gravity
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Let us consider the scalar function
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7.7 Adaptive Control 161 The vehicl
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[deg] 3 2.5 2 1.5 1 0.5 7.8 Output
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7.8 Output Feedback Control 165 It
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7.8 Output Feedback Control 167 whe
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7.8 Output Feedback Control 169 C T
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7.8 Output Feedback Control 171 wit
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[m] [deg] [deg] 0.1 0.05 0 −0.05
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[m] [-] [deg] x 10−3 10 8 6 4 2 0
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[Nm] [Nm] [Nm] 500 0 −500 50 0
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[m] [-] [deg] x 10−3 10 8 6 4 2 0
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[N] [N] [N] 20 0 −20 40 20 0 −2
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[Nm] [Nm] [Nm] 50 0 −50 350 300 2
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7.9 Virtual Decomposition Based Con
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joint torques [Nm] 200 0 −200 −
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e.e. orientation error [deg] 2 1 0
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vehicle position [m] 0.1 0.05 0 −
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8. Interaction Control of UVMSs 8.1
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8.3 Impedance Control 203 8.2 Dexte
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8.4 External Force Control 205 The
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8.4 External Force Control 207 be f
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8.4 External Force Control 209 that
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8.4 External Force Control 211 UVMS
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[N] [m] 350 300 250 200 150 100 50
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[deg] [deg] 10 5 0 −5 −10 50 40
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8.5 Explicit Force Control 217 wher
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8.5 Explicit Force Control 219 wher
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[m] [deg] 0.2 0.1 0 −0.1 8.5 Expl
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[m] [deg] 0.2 0.1 0 −0.1 −0.2 0
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226 9. Coordinated Control of Plato
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238 10. Concluding Remarks control
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240 A. Mathematical models ⎡ 6 .
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242 A. Mathematical models using th
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244 A. Mathematical models L = 2 m
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References 1. Alekseev Y.K., Kosten
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References 249 28. Antonelli G.and
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References 251 62. Caccia M., Indiv
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References 253 96. Cui Y. and Sarka
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References 255 134. Garcia R., Puig
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References 257 168. Kato N. and Lan
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References 259 mera. In: IEEE Inter
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References 261 235. Podder T.K. and
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References 263 273. Solvang B., Den
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References 265 310. Yoerger D.R., S
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