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

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5.1 Identification of the Geometric and Inertial Parameters 66with respect to their CoM for a frame parallel to the robot frame, by using standard formulasfor regular geometric shapes. Then, the tensor of inertia of the robot can be computed byusing the Huygens-Steiner Theorem and Superimposition Principle of moment of inertia fora rigid body, stating respectively:I O = I O ′ + mOO ˆ ′∑I =iI iˆOO ′Twhere m, I are the mass and tensor of inertia of the body, I O , I O ′ are the tensors of inertiacalculated in two generic points O, O ′ ,ˆ OO ′ is the skew-symmetric matrix of the vector OO ′and I i is the tensor of inertia of the i − th component of the body calculated with respect tothe same frame.By using the formulas above and the tensor of inertia of the robot’s components, the tensorof inertia of the whole robot obtained is:⎡⎤1.13 0.001 −0.04I = 0.001 1.52 −0.002⎢⎣−0.04 −0.002 0.91⎥⎦To check the correctness of the above estimation and to have even a better estimation, theideal robot tensor of inertia is calculated by using a Solidworks model of the robot, whichwas already made by Professor M. Stein for a previous project (Figure 5.2). Thereby, thetensor of inertia, automatically calculated by Solidworks, which will be considered in thefollowing is:⎡⎤1.21 0.000355 −0.0655I = 0.000355 1.41 −0.00125⎢⎣−0.0655 −0.00125 0.922⎥⎦(5.1)The data provided by the Solidworks model confirm also the approximated location ofthe robot CoM. In particular, the position of the CoM, with respect to an output coordinatesystem placed at one corner of the rear-right square tube with its axes parallel to the robotprincipal axes (Figure 5.2) (defined by default), is:o p CoM = [0.087 0.139 − 0.041] T
5.2 Identification of the Tire Dynamic Parameters 67Figure 5.2: The Solidworks model of the robot.is:The position of the rear-right contact point with respect to the output coordinate systemo p 4 = [−0.06 − 0.04 − 0.26] T ,Thereby, the position of that contact point with respect to the robot frame is:p 4 = o p 4 − o p CoM = [−0.147 − 0.179 − 0.221] T ,which nearly coincides to the values in the 4 th row in Tab.5.1.5.2 Identification of the Tire Dynamic ParametersIn Section 3.3 the identification of the lateral and vertical tire elasticity coefficient waspresented by analyzing the different data acquired from the force sensor using the testingsystem machine.In this section, the identification of the tire dynamic parameters is completed by analyzingthe free response of the Roll, Pitch and Yaw motion, measured by the three 1-axis accelerometers.Let us consider the robot performing separately pure rotations around the x,y,z-axis, respec-
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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
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 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
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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 116(a)(b)(c)Figure 6.20:
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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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