Underwater Robots - Gianluca Antonelli.pdf

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190 7. Dynamic Control of UVMSs Fig. 7.22. Virtual decomposition control. Sketch ofthe initial configuration of the system and trace of the desired path The redundancy of the system is used to keep still the vehicle. Notice, that this choice isaimed only at simplifying the analysis of the discussed controller. More complex secondary tasks can easily be given with the inverse kinematics algorithm [20, 24, 25]. The control law parameters are: λ p,0 =0. 4 λ o,0 =0. 6 λ i =0. 9 i =1,...,n K v,0 =blockdiag { 15000I 3 , 16000I 3 } K v,i =blockdiag { 900I 3 , 1100I 3 } K θ,0 =14I 4 i =1,...,n K θ,i =21I 4 i =1,...,n
7.9 Virtual Decomposition Based Control 191 Figures 7.23 and 7.24 report the time history of the end-effector position and orientation errors. It can benoted that, since the trajectory is repeated 4times in the first 16 seconds, after alarge initial error, the adaptive action can significantly reduce the tracking error. At steady state the errors tend to zero. e.e. position error [m] 0.1 0.05 0 −0.05 ˜x e ˜z e −0.1 0 10 20 30 time [s] Fig. 7.23. Virtual decomposition control. Time history of the end-effector position error. The periodic desired trajectory makes it clear the advantage of the adaptive action e.e. orientation error [deg] 1 0.5 0 −0.5 ˜ψ e ˜φ e −1 0 10 20 30 time [s] Fig. 7.24. Virtual decomposition control. Time history of the end-effector attitude error in terms of Euler angles ˜θ e ˜y e
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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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Page 159 and 160: e.e. position error [m] 0.02 0.01 0
Page 161 and 162: 7. Dynamic Control of UVMSs 7.1 Int
Page 163 and 164: 7.2 Feedforward Decoupling Control
Page 165 and 166: 7.2 Feedforward Decoupling Control
Page 167 and 168: 7.4 Nonlinear Control for UVMSs wit
Page 169 and 170: 7.5 Non-regressor-Based Adaptive Co
Page 171 and 172: 7.6 Sliding Mode Control 7.6 Slidin
Page 173 and 174: 7.6 Sliding Mode Control 153 u = B
Page 175 and 176: 7.6 Sliding Mode Control 155 Practi
Page 177 and 178: 7.7 Adaptive Control 157 of gravity
Page 179 and 180: Let us consider the scalar function
Page 181 and 182: 7.7 Adaptive Control 161 The vehicl
Page 183 and 184: [deg] 3 2.5 2 1.5 1 0.5 7.8 Output
Page 185 and 186: 7.8 Output Feedback Control 165 It
Page 187 and 188: 7.8 Output Feedback Control 167 whe
Page 189 and 190: 7.8 Output Feedback Control 169 C T
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 209: 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
Page 225 and 226: 8.4 External Force Control 205 The
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
Page 233 and 234: [N] [m] 350 300 250 200 150 100 50
Page 235 and 236: [deg] [deg] 10 5 0 −5 −10 50 40
Page 237 and 238: 8.5 Explicit Force Control 217 wher
Page 239 and 240: 8.5 Explicit Force Control 219 wher
Page 241 and 242: [m] [deg] 0.2 0.1 0 −0.1 8.5 Expl
Page 243 and 244: [m] [deg] 0.2 0.1 0 −0.1 −0.2 0
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 .
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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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