Underwater Robots - Gianluca Antonelli.pdf

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216 8. Interaction Control of UVMSs [N] [m] 350 300 250 200 150 100 50 0 0.2 0.1 0 −0.1 0 5 10 15 time [s] ˜y E ˜x E f e,z f e,x −0.2 0 5 10 15 time [s] Fig. 8.8. External force control. Force along z and x (top) and end-effector error components along the motion directions (bottom) exploiting the redundancy and with unexpected impact along x Explicit force control, scheme 1. Asketch ofthe implemented scheme is provided in Figure 8.9. Inour case, the inverse kinematics is solved via anumerical algorithm based onvelocity mapping to allow the handling of system redundancy efficiently (see previous Section and Section 6.5). It is possible to decompose the input torque as the sum of the torque output from the motion control and the torque output from the force control: τ = τ M + τ F .The force control action τ F is computed as: τ F = J T posu F = J T pos � − f e + k f,p ˜ f e − k f,v ˙ f e + k f,i � t 0 � ˜f e ( σ ) dσ , (8.17)
8.5 Explicit Force Control 217 where k f,p , k f,v , k f,i are scalar positive gains, and ˜ f e = f e,d − f e is the force error. Equation (8.17), thus, is aforce control action in the task space that is further projected, via the transpose of the Jacobian, onthe vehicle/joint space. x p,d, x s,d IK ζ d − 1 J k � + Fig. 8.9. Explicit force control scheme 1 − Motion Control + + UVMS +env. J T posu F Explicit force control, scheme 2. Asketch ofthe implemented scheme is provided in Figure 8.10. The force control action iscomposed oftwo loops; the action − J T posf e is aimed at compensating the end-effector contact force (included in the block labeled “UVMS +env.”). The input of the motion control is asuitable integration of the velocity vector: ζ r = ζ d + ζ F = ζ d + J T pos( k ∗ f,p ˜ f e − k ∗ f,v ˙ f e + k ∗ f,i � t 0 f e,d ˜f e ( σ ) dσ) , where k ∗ f,p , k ∗ f,v , k ∗ f,i are positive gains, and ζ d is the output ofthe inverse kinematics algorithm described inprevious Section. x p,d, x s,d IK ζ d + + − 1 J k � + J T pos − η , q Fig. 8.10. Explicit force control scheme 2 8.5.1 Robustness Motion Control J T pos + − UVMS +env. In the following, the robustness of the schemes to react against unexpected impacts or errors in planning desired force/position directions is discussed. PID + η , q − f e f e f e,d
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Springer Tracts in Advanced Robotic
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Gianluca Antonelli Underwater Robot
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Editorial Advisory Board EUROPE Her
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Elalocomotiva sembrava fosse un mos
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Acknowledgements The contributions
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Preface to the Second Edition The p
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XVIII Preface to the First Edition
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XX Preface tothe First Edition mani
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XXII Notation η q =[η T 1 ε T η
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XXIV Notation ˜x error variable de
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XXVI Contents 3. Dynamic Control of
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XXVIIIContents A. Mathematical mode
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2 1. Introduction Maybe the first i
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4 1. Introduction (Massachusetts, U
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6 1. Introduction Fig. 1.4. Coordin
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8 1. Introduction Fig. 1.5. Pig, ma
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10 1. Introduction An example of cr
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12 1. Introduction Fig. 1.8. Romeo
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2. Modelling ofUnderwater Robots
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2.2 Rigid Body’s Kinematics 17 Th
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J T k,oqJ k,oq = 1 4 I 3 , that all
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5. compute the quaternion Q by the
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2.3 Rigid Body’s Dynamics 23 Let
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2.4 Hydrodynamic Effects 25 τ 1 =
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C A ( ν )=− C T A ( ν ) ∀ ν
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2.4 Hydrodynamic Effects 29 effects
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2.5 Gravity and Buoyancy 2.5 Gravit
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2.6 Thrusters’ Dynamics 33 Fig. 2
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2.7 Underwater Vehicles’ Dynamics
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y z 2.8 Kinematics of Manipulators
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2.9 Dynamics ofUnderwater Vehicle-M
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2.9 Dynamics ofUnderwater Vehicle-M
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2.11 Identification 43 f e = K ( x
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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
Page 185 and 186: 7.8 Output Feedback Control 165 It
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Page 191 and 192: 7.8 Output Feedback Control 171 wit
Page 193 and 194: [m] [deg] [deg] 0.1 0.05 0 −0.05
Page 195 and 196: [m] [-] [deg] x 10−3 10 8 6 4 2 0
Page 197 and 198: [Nm] [Nm] [Nm] 500 0 −500 50 0
Page 199 and 200: [m] [-] [deg] x 10−3 10 8 6 4 2 0
Page 201 and 202: [N] [N] [N] 20 0 −20 40 20 0 −2
Page 203 and 204: [Nm] [Nm] [Nm] 50 0 −50 350 300 2
Page 205 and 206: 7.9 Virtual Decomposition Based Con
Page 215 and 216: joint torques [Nm] 200 0 −200 −
Page 217 and 218: e.e. orientation error [deg] 2 1 0
Page 219 and 220: vehicle position [m] 0.1 0.05 0 −
Page 221 and 222: 8. Interaction Control of UVMSs 8.1
Page 223 and 224: 8.3 Impedance Control 203 8.2 Dexte
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Page 227 and 228: 8.4 External Force Control 207 be f
Page 229 and 230: 8.4 External Force Control 209 that
Page 231 and 232: 8.4 External Force Control 211 UVMS
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Page 239 and 240: 8.5 Explicit Force Control 219 wher
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Page 245 and 246: 226 9. Coordinated Control of Plato
Page 257 and 258: 238 10. Concluding Remarks control
Page 259 and 260: 240 A. Mathematical models ⎡ 6 .
Page 261 and 262: 242 A. Mathematical models using th
Page 263 and 264: 244 A. Mathematical models L = 2 m
Page 265 and 266: References 1. Alekseev Y.K., Kosten
Page 267 and 268: References 249 28. Antonelli G.and
Page 269 and 270: References 251 62. Caccia M., Indiv
Page 271 and 272: References 253 96. Cui Y. and Sarka
Page 273 and 274: References 255 134. Garcia R., Puig
Page 275 and 276: References 257 168. Kato N. and Lan
Page 277 and 278: References 259 mera. In: IEEE Inter
Page 279 and 280: References 261 235. Podder T.K. and
Page 281 and 282: References 263 273. Solvang B., Den
Page 283: References 265 310. Yoerger D.R., S
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