Underwater Robots - Gianluca Antonelli.pdf

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60 3. Dynamic Control of 6-DOF AUVs 3.8.2 Compensation ofthe Ocean Current The presence of an ocean current isseldom taken into account inthe literature. The effect of the current, however, can bereally significant ([127, 323]). In this discussion amain assumption ismade: roughly speaking the current is considered as constant inthe earth-fixed frame and its effect on the vehicle is modeled as aforce, proportional to the current magnitude, that pushes the vehicle. The considerations below, thus, are based on this assumption. It is worth noticing that inthe simulation the dynamic effect of the current is correctly taken into account bycomputing the relative velocity inthe vehicle model. The accuracy of this assumption, thus, seems tobeverified. Controller C and F does not consider at all the current, as aresult the developed controller does not reach anull steady state error. Controller D compensates the current with aterm designed on the purpose; this term adapts on vehicle-fixed parameters, as discussed inSection 3.5 this action experiences adrawback. The remaining controllers correctly compensate for the current adapting/integrating on aset of earth-fixed based parameters. Table 3.2 summarizes the discussed properties of the 6controllers with respect to the persistent dynamic terms. It is worth noticing that only the controller E correctly compensates for both actions. Table 3.2. Summary of the behavior of the controllers with respect to compensation of the hydrodynamic persistent terms control law current effect restoring forces null error with current A fit unfit yes B fit unfit yes C unfit fit no D unfit fit yes E fit fit yes F unfit unfit no 3.9 Numerical Comparison Among the Reduced Controllers Aperformance comparison among the controllers discussed has been developed bynumerical simulations. The simulations have been run onthe 6-DOF mathematical model of ODIN, anAUV built at the Autonomous Systems Laboratory of the University ofHawaii (see the Appendix for adescription and the model used in the simulation).
3.9 Numerical Comparison Among the Reduced Controllers 61 An aspect to be considered for proper reading ofthis study is that the control problem athand ishighly nonlinear, coupled and the controller to be compared are intrinsically different one from the other. Any effort to chose the gains soastoensure similar performance to the controllers has been made; nevertheless, this is impossible in astrict sense. Forthis reason, the presented results have to be interpreted mainly looking at the error behavior rather then focusing on direct numeric comparison. On the other hand, itwas chosen tonot emphasize vehicle-related effects that would not bepresent in general applications. In particular, ODIN has asmall metacentric height, yielding low restoring moments; simulations of the controllers to vehicles of larger metacentric height would make even more evident the drawbacks in the compensation of the restoring forces. Test trajectory In order to demonstrate the effects discussed in this paper, the simplest task to be considered is one involving successive changes of the vehicle orientation in presence ofocean current. The simulation length can be divided indifferent period of60s duration. The vehicle is firstly put in the water at the position η d ( t =0)=[0 0 1 0 0 0] T [m/deg] without knowledge of the current but with an estimation of the restoring parameters. The first 60 sare used toadapt the effect ofthe current. Inthe successiveperiodthe vehicle is requiredtomove in roll and pitchfrom0deg to 10 deg and − 15 deg, respectively and come back tothe original configuration. In the successive two periods the vehicle is required tomove of 90 deg in yaw and come back to the initial position. Finally, 60s of steady state are given. Figure 3.3 plots the desired trajectory. Initial conditions Table 3.3 reports the initial condition for the adaptive/integral parameters of the controllers, it can be observed that the same values have been used in the estimation ofthe restoring forces. This isalso true for the controller A ,where the gravity estimation ˆg � RB, even ifnot adaptive, isobtained resorting to ˆθ v,R =[− 9 0 0 50] T . From the model in the Appendix it can be noticed that the true value of the restoring parameters is θ v,R =[− 8 . 0438 0 0 61 . 3125 ] T . The vehicle initial position is also η =[0 0 1 0 0 0] T [m,deg] , meaning that the vehicle is supposed tostart its motion under the water, at 1m depth, moreover, there is no initial estimation of the ocean current.
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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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Page 33 and 34: 10 1. Introduction An example of cr
Page 35 and 36: 12 1. Introduction Fig. 1.8. Romeo
Page 37 and 38: 2. Modelling ofUnderwater Robots
Page 39 and 40: 2.2 Rigid Body’s Kinematics 17 Th
Page 41 and 42: J T k,oqJ k,oq = 1 4 I 3 , that all
Page 43 and 44: 5. compute the quaternion Q by the
Page 45 and 46: 2.3 Rigid Body’s Dynamics 23 Let
Page 47 and 48: 2.4 Hydrodynamic Effects 25 τ 1 =
Page 49 and 50: C A ( ν )=− C T A ( ν ) ∀ ν
Page 51 and 52: 2.4 Hydrodynamic Effects 29 effects
Page 53 and 54: 2.5 Gravity and Buoyancy 2.5 Gravit
Page 55 and 56: 2.6 Thrusters’ Dynamics 33 Fig. 2
Page 57 and 58: 2.7 Underwater Vehicles’ Dynamics
Page 59 and 60: y z 2.8 Kinematics of Manipulators
Page 61 and 62: 2.9 Dynamics ofUnderwater Vehicle-M
Page 63 and 64: 2.9 Dynamics ofUnderwater Vehicle-M
Page 65 and 66: 2.11 Identification 43 f e = K ( x
Page 67 and 68: 3. Dynamic Control of 6-DOF AUVs 3.
Page 69 and 70: 3.2 Earth-Fixed-Frame-Based, Model-
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: 3.8 Comparison Among Controllers 59
Page 85 and 86: 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 and 120: 5.3 Experiments of Dynamic Control
Page 121 and 122: 5.4 Experiments of Fault Tolerance
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
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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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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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