Underwater Robots - Gianluca Antonelli.pdf

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150 7. Dynamic Control of UVMSs The stability analysis can be found in [185, 252]. In [252], this controller isused together with the kinematic control detailed in Section 6.4 in a simulation study involving a6-DOF vehicle together with a3-DOF planar manipulator subject tojoint limits. The controller has been developed to be used with the UVMS SAUVIM under development and the Autonomous Systems Laboratory, University ofHawaii (Figure 7.4). Fig. 7.4. SAUVIM under development and the Autonomous Systems Laboratory, University ofHawaii (courtesy ofJ.Yuh). The passive joint used for position measurement can be observed
7.6 Sliding Mode Control 7.6 Sliding Mode Control 151 Robust techniques such asSliding Mode Control have been successfully applied in control of awide class of mechanical systems. In this Section the application of aSliding Mode based approach tomotion control of UVMSs is discussed. The basic idea of this approach isthe definition of asliding surface s ( x ,t)= ˙˜x + Λ ˜x = 0 (7.9) where asecond order mechanical system has been assumed, x is the state vector, t is the time, ˜x = x d − x and Λ is apositive definite matrix. When the sliding condition issatisfied, the system is forced to slide toward the value ˜x = 0 with an exponential dynamic (for the scalar case, itis ˙˜x = − λ ˜x ). The control input, thus, has the objective toforce the state laying in the sliding surface. With aproper choice ofthe sliding surface, n -order systems can be controlled considering a1 st -order problem in s . The only information required to design astable sliding mode controller is abound on the dynamic parameters. While this is an interesting property of the controller, one must pay the price ofanhigh control activity. Typically, sliding mode controllers are based onaswitching term that causes chattering in the control inputs. While the first concepts on the sliding surface appeared in the Soviet literature inthe end of the fifties, the first robotic applications of sliding mode control are given in [293, 313]. An introduction on Sliding Mode Control theory con be found in [268]. Control law. The vehicle attitude control problem has been addressed among the others in the paper [121] which extends the work in [108] and [265] to obtain asingularity-free tracking control of an underwater vehicle based on the use of the unit quaternion. Inspired by the work in [121], acontrol law is presented for the regulation problem of an UVMS. Toovercome the occurrence of kinematic singularities, the control law isexpressed in body-fixed and joint-space coordinates soastoavoid inversion of the system Jacobian. Further, to avoid representation singularities of the orientation, attitude control of the vehicle is achieved through aquaternion based error. The resulting control law isvery simple and requires limited computational effort. Let us recall the dynamic equations in matrix form (2.71): M ( q ) ˙ ζ + C ( q , ζ ) ζ + D ( q , ζ ) ζ + g ( q , R I B )=Bu, (2. 71) the control law is u = B † [ K D s + ˆg ( q , R I B )+K S sign(s )] , (7.10) where B † is the pseudoinverse of matrix B , K D is apositive definite matrix of gains, ˆg ( q , R I B )isthe estimate of gravitational and buoyant forces, K S
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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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Page 121 and 122: 5.4 Experiments of Fault Tolerance
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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
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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
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Page 159 and 160: e.e. position error [m] 0.02 0.01 0
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Page 177 and 178: 7.7 Adaptive Control 157 of gravity
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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
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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
Page 201 and 202: [N] [N] [N] 20 0 −20 40 20 0 −2
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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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