Underwater Robots - Gianluca Antonelli.pdf

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174 7. Dynamic Control of UVMSs L v =blockdiag { I 3 , 20I 3 , 160, 160, 900} , L p =blockdiag { 5000I 3 , 10 5 I 3 , 10 3 , 10 3 , 2 · 10 3 } , K p =blockdiag { 400I 3 , 500I 3 , 1500I 3 } , K v =blockdiag { 4000I 3 , 4000I 3 , 400I 3 } . Adigital implementation ofthe control laws has been considered. The sensor update rate is 100Hzfor the joint positions and 20 Hz for the vehicle position and orientation, while the control inputs to the actuators are updated at 100Hz, i.e., the control law iscomputed every 10 ms. The relatively high update rate for the vehicle position and orientation measurements has been chosen soastoachieve asatisfactory tracking accuracy. Quantization effects have been introduced in the simulation by assuming a16-bit A/D converter onthe sensors outputs. Also, Gaussian zero-mean noise has been added to the signals coming from the sensors. Figure 7.13 shows the time history of the norm ofthe tracking and estimation errors obtained with the control laws (7.41),(7.42) and (7.62), respectively. Figures 7.14 to7.16 show the corresponding control forces, moments and torques. It can be recognized that good tracking is achieved in both cases, although the performance in terms of tracking errors is slightly better for the control law (7.62), where numerical derivatives are used. Onthe other hand, the presence ofmeasurement noise and quantization effects results in chattering of the control commands to the actuators; this ismuch lower when the control law (7.41),(7.42) isadopted, as compared to control law (7.62). An indicator of the energy consumption due tothe chattering atsteady state is the variance of the control commands reported inTable 7.4 for each component; this data clearly show the advantage of using the controller-observer scheme. Of course, the improvement becomes clear when the noise and quantization effects are larger than acertain threshold. The derivation ofsuch athreshold would require astochastic analysis ofanonlinear system, which isbeyond the scope ofthe present work. Moreover, it can beeasily recognized that such abound is strongly dependent on the characteristics ofthe actuators. Second case study. In this case study the same task as above is executed by adopting the control law (7.43),(7.44) and its counterpart using numerical differentiation ofthe measured position/orientation, i.e., u = B † � M � ζ ˙ r + K v ( ζ r − ζ )+K p e d + g ( q , R I � B ) , (7.63) wherethe same parameters as in theprevious case study have been used.Also, the same measurement update rates, quantization resolution and sensory noise have been considered in the simulation. The results are shown in Figure 7.17 interms of tracking and estimation errors. It can be recognized that the errors are comparable to those obtained with the control scheme (7.41),(7.42) inspite ofthe extremely simplified con-
[m] [-] [deg] x 10−3 10 8 6 4 2 0 8 6 4 2 0 0 10 20 30 40 50 60 x 10−3 10 3 2 1 time [s] 0 10 20 30 40 50 60 time [s] 0 0 10 20 30 40 50 60 time [s] 7.8 Output Feedback Control 175 [m] [-] [deg] x 10−3 10 8 6 4 2 0 8 6 4 2 0 0 10 20 30 40 50 60 x 10−3 10 3 2 1 time [s] 0 10 20 30 40 50 60 time [s] 0 0 10 20 30 40 50 60 time [s] Fig. 7.13. Output feedback control; first case study. Comparison between the control laws (7.41),(7.42) and (7.62): norm of the tracking (solid) and estimation (dashed) errors. Left: control law (7.41),(7.42). Right: control law (7.62). Top: vehicle position error; Middle: vehicle orientation error (vector part of the quaternion); Bottom: joint position errors Table 7.4. Variance of control commands Control law (7.41),(7.42) Control law (7.62) X [N 2 ] 0.0149 14.6326 Y [N 2 ] 0.0077 11.4734 Z [N 2 ] 0.0187 3.0139 K [N 2 m 2 ] 0.2142 10.6119 M [N 2 m 2 ] 2.8156 23.2798 N [N 2 m 2 ] 1.6192 26.0350 τ q,1 [N 2 m 2 ] 0.3432 4.0455 τ q,2 [N 2 m 2 ] 0.0725 3.2652 τ q,3 [N 2 m 2 ] 0.3393 1.8259
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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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Page 161 and 162: 7. Dynamic Control of UVMSs 7.1 Int
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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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