Underwater Robots - Gianluca Antonelli.pdf

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100 5. Experiments Dynamic Control of a6-DOF AUV In Figure 5.6 the 2-norm of the position error ( x, y and z components) is shown. It can be noted that the mean error atsteady state, in the last 40 s, is about 7cm. These data need to be be related tothe low accuracy and to the big noise that affect the sonar’s data. [m] 1.5 1 0.5 0 0 100 200 time [s] 300 400 Fig. 5.6. Experiments of adaptive control on ODIN. 2-norm of the 3D position errors in the inertial frame
5.4 Experiments of Fault Tolerance to Thrusters’ Fault 101 5.4 Experiments of Fault Tolerance to Thrusters’ Fault The desired trajectory is the same shown in the previous Section. The experiments were run several times simulating different thruster’s fault. The fault was simulated via software just imposing zero voltage to the relevant thrusters. It is worth noticing that, while the desired trajectory is always the same, some minor differences arise among the different experiments due to different factors: the presence ofstrong noise on the sonar that affected the xy movement (see [215] for details), the presence of apool current. Meanwhile the controller guarantees agood tracking performance tolerant to the occurrence of thruster’s fault and it is robust with respect to the described disturbances. In next plots the movement ofthe vehicle without fault and with 2faults are reported. The two faults arise asfollow: at t = 260 s, one horizontal thruster is off, at t =300 salso the corresponding vertical thruster is off. We chose to test afault of the same side thrusters because this appears to be the worst situation. Notice that the control law isdifferent from the control law tested in the previous Section. Fordetails, see [232, 233, 234, 251]. In Figure 5.7 the behavior of the vehicle along xy without and with fault is reported. It can be noted that, as for the previous experiments, the vehicle is controlled only after 100 sinorder for the sonar towork properly and wait for the transient ofthe position filter [216]. From the right plot in Figure 5.7 we can see that the first fault, at t =260 s, it does not affect the tracking error while for the second, at t =300 s, it causes only asmall perturbation that is fully recovered by the controller after atransient. Some comments are required for the sonar based error: during the experiment with fault it has been possible to see asmall perturbation in the xy plane but, according to the data, this movement has been of 60 cm in 0 . 2s,this is by far awrong data caused by the sonar filter. In Figure 5.8 the behavior of the vehicle along z without and with fault is reported. It can be noted that the vehicle tracks the trajectory with the same error with and without thrusters’ faults. Since the control law was designed in 6DOFs, the difference in the behavior between the horizontal plane, where asmall perturbation has been observed, and the vertical plane is caused mainly by the different characteristics ofthe sensors rather than by the controller itself. In other words, we can expect this nice behavior also in the horizontal plane if amore effective sensorial system would be available. Another comment need to be done about the depth data. In Figure 5.3 the plot of the depth for adifferent control law isshown. It could appear that the tracking performance is better in the last experiment shown in Figure 5.8. However ithas to be underlined that the experiments are expensive interms of time and of people involved, the latter are simply successive tothe first, the gains, thus, are better tuned. In Figure 5.9 the attitude without and with fault is reported. It can be noted that, in case of fault, only after when the two faults arise simultaneously
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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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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
Page 101 and 102: 80 4. Fault Detection/Tolerance Str
Page 113 and 114: 5. Experiments of Dynamic Control o
Page 115 and 116: 5.3 Experiments of Dynamic Control
Page 117 and 118: [m] [m] 5 4 3 2 1 0 0 100 200 300 4
Page 119: 5.3 Experiments of Dynamic Control
Page 123 and 124: [deg] 120 100 80 60 40 20 0 −20 5
Page 125 and 126: 6. Kinematic Control of UVMSs “.
Page 127 and 128: 6.2 Kinematic Control 107 UVMS. Thi
Page 129 and 130: 6.2 Kinematic Control 109 singulari
Page 131 and 132: 6.2 Kinematic Control 111 case of t
Page 133 and 134: 6.5 Singularity-Robust Task Priorit
Page 141 and 142: 6.6 Fuzzy Inverse Kinematics 121 It
Page 143 and 144: Simulations 6.6 Fuzzy Inverse Kinem
Page 145 and 146: 6.6 Fuzzy Inverse Kinematics 125 Fi
Page 147 and 148: vehicle attitude [deg] 20 10 0 −1
Page 149 and 150: 6.6 Fuzzy Inverse Kinematics 129 It
Page 151 and 152: [-] 1 0.8 0.6 0.4 0.2 0 close 0 20
Page 155 and 156: joint positions 1-3 [deg] joint pos
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
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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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