Underwater Robots - Gianluca Antonelli.pdf

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212 8. Interaction Control of UVMSs where x t expresses the third task to be projected inthe null space of the higher priority tasks; in fact since the manipulator has a3-link planar structure ameasure of its manipulability issimply given by q 2 ,where q 2 =0corresponds to akinematic singularity. In the initial position the3tasksare activated simultaneously and are performed by exploiting kinematic redundancy. Moreover anunexpected impact along x is considered (for x E =1. 32 m). Aweighted pseudoinverse has been used to compute J # p characterized by the weight matrix W =blockdiag { 10I 6 , I 3 } .Tosimulate an imperfect hovering of the vehicle acontrol law with lower gain for the vehicle was implemented; the performance of the simulated vehicle, thus, has an error that is of the same magnitude as that of areal vehicle in hovering.The motion controller implemented is the virtual decomposition adaptive based control presented inSection 7.9. Equation (8.16) has then been used to compute the desired velocities. The secondary task regarding the vehicle orientation has to be fulfilled only when the relevant variable is outside ofadesired bound. The control gains, in S.I. units, are: k fp =3· 10 − 3 , k fi =8· 10 − 3 , k fv =10 − 4 , Λ p =0. 6 I 3 , Λ s = I 3 . The simulations have been run byadopting separate motion control schemes for the vehicle and the manipulator, since this is the case of many UVMSs. Better results would be obtained by resorting to acentralized motion control scheme in which dynamic coupling between vehicle and manipulator is compensated for. The initial value of the parameters has been chosen such that the gravity compensation at the beginning isdifferent from the real one, adding an error bounded to about 10% for each parameter. In Figure 8.5 the time history of the end-effector variables for the proposed force control scheme without exploiting the redundancy and without unexpected impact is shown. During the first 3s the end effector is not in contact with the plane and the algorithm to handle loss of contact has been used. Itcan be noted that the primary task is successfully achieved. In Figure 8.6 the same task has been achieved by exploiting the redundancy. The different behavior of the force can be explained by considering that the system impacts the plane in adifferent configuration with respect to the previous case because of the internal motion imposed by the redundancy resolution. This also causes adifferent end-effect velocity atthe impact. Figure 8.7 shows the time history of the secondary tasks in the two previous simulations, without exploiting redundancy (solid) and with the proposed control scheme (dashed). It can be recognized that without exploiting the redundancy the system performs the task in anon dexterous configuration, i.e., with abig roll angle and with the manipulator close to akinematic
[N] [m] 350 300 250 200 150 100 50 0 0.2 0.1 0 −0.1 8.5 Explicit Force Control 213 0 5 10 15 time [s] ˜y E ˜x E −0.2 0 5 10 15 time [s] Fig. 8.5. External force control. Force along z (top) and end-effector error components along the motion directions (bottom) without exploiting the redundancy and without unexpected impact singularity. Asuitable use of the system’s redundancy allows to reconfigure the system and to achieve the secondary task. Finally, inFigure 8.8 the time history of the primary task variables in case of an unplanned impact is shown. It can be noted that the undesired force along x ,due to the unexpected impact, is recovered yielding anon-zero position error along that direction. 8.5 Explicit Force Control In this Section, based on [119] two force control schemes for UVMS that overcome many of the above-mentioned difficulties associated with the un-
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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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Page 183 and 184: [deg] 3 2.5 2 1.5 1 0.5 7.8 Output
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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
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Page 205 and 206: 7.9 Virtual Decomposition Based Con
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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
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Page 231: 8.4 External Force Control 211 UVMS
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Page 237 and 238: 8.5 Explicit Force Control 217 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
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References 265 310. Yoerger D.R., S
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