Underwater Robots - Gianluca Antonelli.pdf

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104 5. Experiments Dynamic Control of a6-DOF AUV In Figure 5.11 the 2-norm ofthe linear error isreported. It can be noted that the first fault does not affect the error while for the second there isa small transient that isrecovered. [m] 1.5 1 0.5 0 0 100 200 time [s] 300 400 Fig. 5.11. Experiments of fault tolerant control on ODIN. 2-Norm of the position errors. A, first fault at t =260 satone horizontal thruster. B, second fault at t = 300 satone vertical thruster
6. Kinematic Control of UVMSs “. ..mais de toutes les sciences la plus absurde, à mon avis et celle qui est la plus capable d’é touffer toute espè ce de génie, c’est lagé omé trie. Cette science ridicule apour objet des surfaces, des lignes et des points qui n’existent pas dans la nature. Onfait passer en esprit cent mille lignes courbes entre uncercle et une ligne droite qui le touche, quoique, dans la réalité, on n’ypuisse pas passer un fétu. La géomé trie, en vérité, n’est qu’une mauvaise plaisanterie.” Voltaire, “Jeannot et Colin” 1764. 6.1 Introduction Arobotic system is kinematically redundant when it possesses more degrees of freedom than those required to execute agiven task. Ageneric manipulation task is usually given in terms of position/orientation trajectories for the end effector. In this sense, an Underwater Vehicle-Manipulator System is always kinematically redundant due to the DOFs provided by the vehicle itself. However, it is not always efficient touse vehicle thrusters to move the manipulator end effector because of the difficulty ofcontrolling the vehicle in hovering. Moreover, due to the different inertia between vehicle and manipulator, movement ofthe latter is energetically more efficient. On the other hand, reconfiguration ofthe whole system is required when the manipulator is working at the boundaries ofits workspace or close to akinematic singularity; motion ofthe sole manipulator, thus, is not always possible or efficient. Also, off-line trajectory planning is not always possible in unstructured environments asincase of underwater autonomous missions. Whenamanipulationtask hastobeperformed with an UVMS,the system is usually kept in aconfined space (e.g., underwater structure maintenance). The vehicle is then used to ensure station keeping. However, motion of the vehicle can berequired for specific purposes, e.g., inspection of apipeline, reconfiguration of the system, real-time motioncoordination whileperforming end-effector trajectory tracking. According tothe above, aredundancy resolution technique might beuseful toachieve system coordination insuch away as to guarantee end-effector tracking accuracy and, at the same time, additional control objectives, e.g., G. Antonelli: Underwater Robots, 2nd Edition, STAR 2, pp. 105–140, 2006. © Springer-Verlag Berlin Heidelberg 2006
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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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Page 77 and 78: 3.6 Mixed Earth/Vehicle-Fixed-Frame
Page 79 and 80: 3.7 Jacobian-Transpose-Based Contro
Page 81 and 82: 3.8 Comparison Among Controllers 59
Page 83 and 84: 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: [deg] 120 100 80 60 40 20 0 −20 5
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
Page 167 and 168: 7.4 Nonlinear Control for UVMSs wit
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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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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