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

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3.3 Characterization of the Tire Forces 48(a)(b)Figure 3.6: Static lateral force by pulling the robot’s platform sidewards with a rope at v y = 1 mm sconcrete on: (a) Two wheels; (b) One wheel., sliding on
3.3 Characterization of the Tire Forces 49of the tire stretching is much slower than the releasing, the periodic motion results in a sortof saw-tooth wave as shown from the graphs.Furthermore, from the graphs depicted in Figure 3.6 we can also extract the tire elasticitycoefficient by calculating the slope of the ramps of the saw-tooth shape. In particular, theslope varies from 4 kN mto 6 kN , therefore the measured elasticity coefficient can be estimatedmas K measured = 5 kN . However, such a value of K m measured is not reliable as the rope is extensibleso that the force sensor is also measuring the rope elastic force and therefore the previouslycalculated coefficient includes the rope coefficient too. We can consider our system composedby the robot and the rope as two springs connected in series, so that the elasticitycoefficient the sensor perceives is given by the formula:K measured =K cableK tireK cable + K tire(3.9)Thereby, when K cable is comparable or smaller than K tire , K measured is completely differentfrom K tire and can even be almost equal to K cable .To overcome this problem, the rope was replaced with a steel cable which is not extensible.The force was then measured again for a single wheel touching the ground and also with nowheel touching (Figure 3.3(b)), in order to check whether or not the saw-tooth behavior wasdue only to the rope elasticity. Moreover, the force was measured by pulling only the robotplatform with and without the aluminum frame to check if the weight or the inertia affect themeasurements. Figure 3.7 shows the two cases with one and zero wheel touching.By looking at Figure 3.7, it is easy to notice that, in both cases (with and without thealuminum frame), the saw-tooth shape is not present when all the four wheels are on theplastic pads with some oil underneath, meaning that such a behavior is not due to the ropeelasticity or the robot inertia but only to the tire-spring dynamics. We can also see howthe saw-tooth shape is more regular in these graphs than the ones in Figure 3.5, 3.6, thanksto the high elasticity of the cable. Moreover, as in this case K cable≫ K tire and only onewheel is touching the ground, the value of K measured defined in (3.9) is almost equal to K tire .In particular, the slope of the little ramps varies in the interval 20 − 25 kN mso that we canestimate the tire elasticity coefficient as K tire = 22.5 kN . mAlthough the data presented above clearly show the tire-spring behavior from a qualitativepoint of view, they do not provide reliable values for the identification of the tire elasticitycoefficient. In fact, the measured force is somehow affected also from the other tire forces,
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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
Page 8 and 9: LIST OF FIGURESVII6.4 (a) Block sch
Page 10 and 11: 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
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AppendixesAppendix A1 %% Main progr
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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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