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

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2.1 State of the Art 22approximates the µ − λ curve obtained by fitting experimental data as it is depicted in Figure2.4 [4]. As provided in [4], the function in (2.29b) includes the instability region, namelyfor λ m < λ i < 1, due to the difference between the static and kinetic friction coefficient, i.e.µ p , µ s . In such a region, in fact, the system described by the skid-steering motion presentsa positive feedback, because of α s < 0, which leads to an undesired increase of the robotvelocity [4]. However, the system is not globally unstable thanks to the constraint |lambda i |
2.1 State of the Art 23(a)(b)Figure 2.4: (a) Relationship between the wheel/ground friction coefficient µ and the longitudinal slip λ undervarious road conditions; (b) A linear piece-wise approximation of the µ − λ relationship.where M r = c(−F 1 − F 2 + F 3 + F 4 ) + b(P 2 + P 3 ) − a(P 1 + P 4 ) is the reaction torque andthe reaction forces F i , P i are provided by (2.32) and (2.27).Finally, we complete the dynamic model defined by (2.19) and (2.23), by adding the reactionforces and torques vector (2.33) and incorporating the non-holonomic constraint (2.13) byusing the Lagrange multiplier ζ:M ¨q + R(q) = B(q)τ + A T (q)ζ. (2.34)To eliminate the unknown ζ, we multiply equation (2.34) by the matrix S T (q) definedin (2.14) and we use the constraint (2.16), obtaining the following dynamic model in thegeneralized coordinates q:¯M ¨q + ¯R = ¯Bτ (2.35)where ¯M = S T M, ¯R = S T R and ¯B = S T B.For control purpose, it is convenient to express the dynamic model of SSMR in terms ofη, ˙η. Thus, by employing the kinematic equations (2.14) and (2.15) in (2.35), we obtainedthe dynamic model:where¯M ˙η + ¯Cη + ¯R = ¯Bτ (2.36)
Page 1 and 2: Università degli Studi di GenovaRo
Page 3 and 4: IINothing great in the World has be
Page 5: 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
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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 (
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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
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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
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5.2 Identification of the Tire Dyna
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Chapter 6SimulationIn this chapter,
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6.1 Simulink Model 80On the right h
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6.1 Simulink Model 82Figure 6.3: Bl
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6.1 Simulink Model 84(a)(b)Figure 6
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6.1 Simulink Model 86that v icx can
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6.2 Simulation Results 88(a)(b)Figu
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6.2 Simulation Results 90enough to
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6.2 Simulation Results 92hand side
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6.2 Simulation Results 94(a)(b)Figu
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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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Advance Modeling of a Skid-Steering Mobile Robot for Remote ...

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