Underwater Robots - Gianluca Antonelli.pdf

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156 7. Dynamic Control of UVMSs [m] 1 0 −1 x 10−3 2 y x z −2 0 5 10 15 time [s] N 0 −100 −200 −300 −400 −500 X Y −600 0 5 10 15 tim Fig. 7.5. Sliding mode control. Left: vehicle positions. Right: vehicle control forces Figure 7.5 shows that, as expected, the vehicle position is affected by the manipulator motion; however, the displacements are small and the target position is recovered after atransient. It can be recognized that at steady state the force along z is non null; this happens because the manipulator is not neutrally buoyant. Figure 7.6 shows that the dynamic coupling ismostly experienced along the roll direction because of the chosen UVMS structure. This effect was intentional in order to test the control robustness. It can be recognized that vehicle control moments are zero at steady state; this happens because the center of gravity and the center of buoyancy of vehicle body and manipulator links are all aligned with the z -axis of the earth-fixed frame at the final system configuration. [deg] 0.05 0 −0.05 −0.1 φ −0.15 0 5 10 15 time [s] 50 0 −50 −100 −150 −200 −250 0 5 10 15 tim Fig. 7.6. Sliding mode control. Left: vehicle attitude in terms of Euler angles. Right: vehicle control moments Figure7.7 shows the time histories of manipulator jointerrors andtorques. It is worth noting that the initial value of the joint torques is non null because Nm K Z
7.7 Adaptive Control 157 of gravity and buoyancy compensation, while they are null at steady state in view of the particular final system configuration. It can be recognized that control generalized forces are smooth while the task is successfully executed. [deg] 0.5 0 q 2 q 1 −0.5 0 5 10 15 time [s] 100 80 60 40 20 0 τ q,1 τ q,2 0 5 10 15 Fig. 7.7. Sliding mode control. Left: manipulator joint errors. Right: manipulator joint torques. The steady state vehicle moment and manipulator torques are null due tothe restoring force characteristic ofthis specific UVMS 7.7 Adaptive Control Adaptive Control is awide topic in control theory. The basic idea of adaptive control is to modify on-line some control gains to adapt the controller to the plant’s parameters that are supposed to be unknown or slowly varying. However, the term adaptive control can assume slightly different meanings. In this work, acontroller is considered adaptive if it includes explicitly on-line system parameters estimation. Often, the mathematical model of the system to be controlled is known but the dynamic parameters are not known ormay depend from aload. In this case, the adaptive control is mainly based onaPD action plus a dynamic compensation the parameters of which are updated on-line. This dynamic compensation can be intended to cancel the system dynamics, thus achievingdecouplingand linearization of thesystem, or preservethe passivity properties of the closed loop system [223]. While the first concepts of adaptive control appeared, without success, in the aircraft control in the early fifties, the first robotic applications appeared later [223, 267]. Control law. Based on the control law developed in the previous Section, acontrol law ispresented for the tracking problem of UVMSs. As in the previous control law, to overcome the occurrence of kinematic singularities, the control law isexpressed in body-fixed and joint-space coordinates soas
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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
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
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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
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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
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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 −
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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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