Underwater Robots - Gianluca Antonelli.pdf

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94 5. Experiments Dynamic Control of a6-DOF AUV of 0 . 63 mand vertical diameter of 0 . 61 m, made ofanodizied Aluminum (AL 6061-T6). Its dry weight isabout 125 kg. It is, thus, slightly positive buoyant. The processor is aMotorola 68040/33 MHz working with VxWorks 5.2 operating system. The power supply is furnished by 24 Lead Gel batteries, 20 for the thrusters and 4for the CPU, which provide about 2hours of autonomous operations. The actuating system is made of 8marine propellers built at ASL; they are actuated by brushless motors. Each motor weighs about 1kgand can provide amaximum thrust force of about 27N.The sensory system is composed of: apressure sensor for depth measuring, with an accuracy of 3cm; 8sonars for position reconstruction and navigation, each with arange 0 . 1 ÷ 14. 4m;anInertial System for attitude and velocity measures. Fig. 5.1. ODIN, the AUV used to experimentally test adaptive and fault tolerant control strategies 5.3 Experiments of Dynamic Control Despite the closed environment inwhich the experiments have been conducted, the pool of the University ofHawaii, it is necessary to take into account
5.3 Experiments of Dynamic Control 95 the presence ofacurrent asanirrotational, constant disturbance [127]. The modeling aspects of including the current in the dynamic model hav ebeen discussed in Section2.4.3. Since the measure of the current isnot available in ODIN, ithas been taken into account asadisturbance τ v,C acting atthe force/moment level on the vehicle-fixed frame. Moreover, since the number of dynamic parameters could be very large (n θ,v > 100, see [127]) it was implemented areduced version of the regressor matrix in order to adapt only with respect to the restoring force/moments and tothe current. Inother words, the control law implemented was the reduced controller of the one discussed in Section 3.2. The experiment was conceived in the following way: the vehicle had to follow adesired trajectory with trapezoidal profile. Since the sonars need to be under the surface of the water towork properly the first movement planned was inthe z direction (see Figure 5.2 for the relevant frames). The vehicle planned to move 2m in the y direction and 2m in the x direction. 23 m x O diving pool ODIN y y b x b arm 23 m magnetic north Fig. 5.2. Sketch ofthe pool used for experiments with relevant frames The control law has been designed using quaternions, however the specifications ofthe desired trajectory and the output results are given in Euler angles because of their immediate comprehension. Notice that the transformation from Euler angles toquaternions is free from representation singularities. The attitude must be kept constant atthe value of η d,2 =[0 0 90] T deg . Since the vehicle is not perfectly balanced, atrest, i.e., with the thrusters off, its position is φ ≈ 5 ◦ and θ ≈ 15 ◦ with the yaw depending on the current. The desired orientation, thus, is aset-point for the control task.
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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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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 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: 5. Experiments of Dynamic Control o
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
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
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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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