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

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5.2 Identification of the Tire Dynamic Parameters 68tively defined as Roll, Pitch and Yaw motion. Consequently, the robot dynamics can bedescribed by considering planar motion respectively on the y − z, x − z and x − y plane, asdepicted in Figure 5.3.Under the assumption that the wheels are not spinning, the contact points are not movingand some external torques M z , M y , M x are applied to the robot CoM respectively for thethree rotations, we can consider the Roll, Pitch and Yaw motion described by the followingequations:I x ˙ω x =I y ˙ω y =I z ˙ω z =4∑(y i f iz − z i f iy ) + M xi=14∑(−x i f iz + z i f ix ) + M y(5.2)i=14∑(x i f iy − y i f ix ) + M zi=1where x i , y i , z i and f ix , f ix , f ix are respectively the coordinates and the reaction forces ofthe i th contact point. By substituting equations (4.13),(4.9),(4.15) in (5.2) and consideringonly ω x , ω y , ω z 0 respectively for three rotations, we can rewrite the equations describingthe Roll, Pitch and Yaw motion as follows:I x ¨ω x + (4h 2 D y + 4c 2 D z ) ˙ω x + (4h 2 K y + 4c 2 K z )ω x = M xI y ¨ω y + (4h 2 D x + 4a 2 D z ) ˙ω y + (4h 2 K x + 4a 2 K z )ω y = M y(5.3)I z ¨ω z + (4c 2 D x + 4a 2 D y ) ˙ω z + (4c 2 K x + 4a 2 K y )ω z = M zwhere, for a sake of simplicity, it was considered b = a.In order to identify the parameters in (5.3), we consider the free response of a second ordersystem. We can write the free response of equation (5.3) by setting the inputs M x = M y =M z = 0 and dividing by the moment of inertia I x , I y , I z , obtaining the equation:¨ω i + 2ξ i ω ni ˙ω i + ω 2 n iω i = 0 (5.4)where ω ni and ξ i , with i = x, y, z, correspond respectively to the natural angular frequenciesand the damping ratios of the systems in (5.4), and they are related to the parametersK i , D i by the following formulas:
5.2 Identification of the Tire Dynamic Parameters 69(a)(b)(c)Figure 5.3: Scheme of: (a) Roll; (b) Pitch; (c) Yaw.
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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
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Introduction 2boDynamics, VGo Commu
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Introduction 4The robot employed, i
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Chapter 1Hardware and SoftwareIn th
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1.1 The Pioneer 3-AT Robot 8four ho
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1.2 The sensors 10control resolutio
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2.1 State of the Art 12not negligib
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2.1 State of the Art 14velocity vec
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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 80 and 81: 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
Page 112 and 113: Appendixes 10224 Hd = design(h,filt
Page 114 and 115: Appendixes 1043031 % Filter the dat
Page 116 and 117: Appendixes 106(a)(b)(c)Figure 6.10:
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Appendixes 118(a)(b)(c)Figure 6.22:
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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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