Underwater Robots - Gianluca Antonelli.pdf

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ζ =[ν T 1 ν T 2 ˙q T ] T ∈ IR 6+n system velocity Φ ∈ R (6+n ) × n θ UVMS regressor defined in (2.73) Notation XXIII θ ∈ R n θ vector of the dynamic parameters of the UVMS regressor defined in (2.73) Φ v ∈ R 6 × n θ,v vehicle regressor defined in (2.54) θ v ∈ R n θ,v vector of the dynamic parameters of the vehicle regressor defined in (2.54) η ee1 =[x E y E z E ] T ∈ IR 3 position of the end effector in the inertial frame (denoted with x =[x E y E z E ] T in the interaction control sections) η ee2 =[φ E θ E ψ E ] T ∈ IR 3 orientation of the end effector inthe inertial frame expressed byEuler angles ν ee ∈ IR 6 J k ( R I (6+n ) × (6+n ) B ) ∈ IR J w ( R I 6 × (6+n ) B , q ) ∈ IR J ( R I 6 × (6+n ) B , q ) ∈ IR h i i = � f i T i T i µ i � T 6 ∈ IR h e =[f T e µ T e ] T ∈ IR 6 t ∈ IR time end-effector linear and angular velocities with respect to the inertial frame expressed in the end-effector frame Jacobian matrix defined in (2.58) Jacobian matrix defined in (2.67) Jacobian matrix used in (2.68) forces and moments exerted by body i − 1on body i (see Figure 2.4) forces and moments atthe end effector (see Figure 2.5) λ min(max)( X ) smallest(largest) eigenvalue of matrix X diag { x 1 ,...,xn } Diagonal matrix filled with x i in the i row, i column and zero in any other place blockdiag { X 1 ,...,X n } Block diagonal matrix filled with matrices X 1 ,...,X n in the main diagonal and zero in any other place R ( X ) range of matrix X ˙x time derivative ofthe variable x � x � 2-norm ofthe vector x � � ˆx ˆX estimate of the vector x (matrix X ) x d desired value ofthe variable x
XXIV Notation ˜x error variable defined as˜x = x d − x x T � � T X transpose of the vector x (matrix X ) x i X i,j X † I r O r 1 × r 2 3 × 3 S ( · ) ∈ IR i th element ofthe vector x element atrow i ,column j of the matrix X Moore-Penrose inversion (pseudoinversion) of matrix X If X is low rectangular it is X † � T = X XX T � − 1 If X is high rectangular it is X † = ( r × r )identity matrix ( r 1 × r 2 )null matrix ρ 3 water density � X T � − 1 X X T matrix performing the cross product between two (3 × 1) vectors defined in (2.6) µ fluid dynamic viscosity R n Reynolds number g I gravity acceleration expressed in the inertial frame
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: XXII Notation η q =[η T 1 ε T η
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 and 50: C A ( ν )=− C T A ( ν ) ∀ ν
Page 51 and 52: 2.4 Hydrodynamic Effects 29 effects
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.
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3.2 Earth-Fixed-Frame-Based, Model-
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o x z o b z b x b 3.3 Earth-Fixed-F
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3.4 Vehicle-Fixed-Frame-Based, Mode
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o o b y x y b x b 3.5 Model-Based C
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3.6 Mixed Earth/Vehicle-Fixed-Frame
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3.7 Jacobian-Transpose-Based Contro
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3.8 Comparison Among Controllers 59
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3.9 Numerical Comparison Among the
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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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