Advance Modeling of a Skid-Steering Mobile Robot for Remote ...

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3.3 Characterization of the Tire Forces 52(a)(b)Figure 3.9: Static lateral force by dragging a single wheel upon a piece of wood: (a) without the ability to moveperpendicularly to the drag surface; (b) with the ability to move perpendicularly to the drag surface.
3.3 Characterization of the Tire Forces 53as expected. However, by calculating the slope for relatively small intervals, the nonlineardynamics can be reasonably approximated by two linear pieces, the first one from 0 N to90 N with K tire = 15 kN and the second one from 90 N to 150 N with K m tire = 21 kN , thereforemwe can estimate the tire elasticity coefficient as K tire = 18 kN . mThe last parameter we want to identify is the tire vertical force due to the tire-spring dynamics.In order to measure the tire vertical force, a single wheel was fixed to the forcesensor by a steel tube with a ’L’ shape (see Figure 3.8). The testing machine pushed thewheel downwards for few centimeters, so that a vertical load was applied on the wheel andthe vertical force due to the tire compression could be measured with respect to distance(see Figure 3.10(a)). Then, the piece of wood was pulled sidewards, so that the wheel wasdragged upon the wood surface and the vertical force was measured with respect to time (seeFigure 3.10(b)).The graph in Figure 3.10(a) shows that also the tire-spring dynamics during vertical compressionis approximatively linear and by calculating its slope we obtain a tire vertical elasticitycoefficient K tirez = 80 kN . mThe graph in Figure 3.10(b), instead, seems to confirm the results obtained for the graphs inFigure 3.9. When the wheel has no capability to move vertically, i.e. when wheel is draggedtowards the right hand side, the force stays around a steady value meaning that the tire isnot releasing. Conversely, when it has such a capability, i.e. when wheel is dragged towardsthe left hand side, the force presents a saw-tooth shape meaning that the tire always releasesafter stretching. The reason why the vertical force increases when the tire is stretching anddecreases when releasing (left hand side), is probably due to ’L’ shape tube since, when thetire stretches, the contact point moves a little closer to the sensor vertical axis and thereforethe steel rod is pushed a little upwards increasing the measured force. Conversely, whenthe tire releases, the contact point moves a little further from the sensor vertical axis andtherefore the steel rod is allowed to move a little downwards resulting in a decrease of theperceived force.
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Università degli Studi di GenovaRo
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IINothing great in the World has be
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CONTENTSIV6 Simulation 786.1 Simuli
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LIST OF FIGURESVII6.4 (a) Block sch
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List of Tables5.1 Table of the geom
Page 12 and 13: Introduction 2boDynamics, VGo Commu
Page 14 and 15: Introduction 4The robot employed, i
Page 16 and 17: Chapter 1Hardware and SoftwareIn th
Page 18 and 19: 1.1 The Pioneer 3-AT Robot 8four ho
Page 20 and 21: 1.2 The sensors 10control resolutio
Page 22 and 23: 2.1 State of the Art 12not negligib
Page 24 and 25: 2.1 State of the Art 14velocity vec
Page 26 and 27: 2.1 State of the Art 16Figure 2.3:
Page 28 and 29: 2.1 State of the Art 18Finally, by
Page 30 and 31: 2.1 State of the Art 20constraint (
Page 32 and 33: 2.1 State of the Art 22approximates
Page 34 and 35: 2.2 Generalized Modeling 24⎡1 0¯
Page 36 and 37: 2.2 Generalized Modeling 26V = [v T
Page 38 and 39: 2.2 Generalized Modeling 28where T(
Page 40 and 41: 2.2 Generalized Modeling 30⎡g R(J
Page 42 and 43: 2.2 Generalized Modeling 32where we
Page 44 and 45: Chapter 3Experimental DataIn this c
Page 46 and 47: 3.1 The accelerometer 36(a)(b)Figur
Page 48 and 49: 3.2 Characterization of the Vibrati
Page 54 and 55: 3.3 Characterization of the Tire Fo
Page 66 and 67: 4.1 Tire Lateral Force 56Figure 4.1
Page 68 and 69: 4.1 Tire Lateral Force 58velocity b
Page 70 and 71: 4.1 Tire Lateral Force 600 ≤ µ i
Page 72 and 73: 4.3 Tire Vertical Force 62f ix (t)
Page 74 and 75: Chapter 5Identification of the Robo
Page 76 and 77: 5.1 Identification of the Geometric
Page 78 and 79: 5.2 Identification of the Tire Dyna
Page 88 and 89: Chapter 6SimulationIn this chapter,
Page 90 and 91: 6.1 Simulink Model 80On the right h
Page 92 and 93: 6.1 Simulink Model 82Figure 6.3: Bl
Page 94 and 95: 6.1 Simulink Model 84(a)(b)Figure 6
Page 96 and 97: 6.1 Simulink Model 86that v icx can
Page 98 and 99: 6.2 Simulation Results 88(a)(b)Figu
Page 100 and 101: 6.2 Simulation Results 90enough to
Page 102 and 103: 6.2 Simulation Results 92hand side
Page 104 and 105: 6.2 Simulation Results 94(a)(b)Figu
Page 106 and 107: 6.2 Simulation Results 96• For λ
Page 108 and 109: AppendixesAppendix A1 %% Main progr
Page 110 and 111: Appendixes 10080 title([conf,’; A
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Appendixes 10224 Hd = design(h,filt
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Appendixes 1043031 % Filter the dat
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Appendixes 106(a)(b)(c)Figure 6.10:
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Appendixes 120(a)(b)Figure 6.24: Pe
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Bibliography[1] G. Oriolo, A. De Lu
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