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

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Chapter 6SimulationIn this chapter, the Simulink implementing the simulation of the three-dimensionalSSMR motion is first presented. The model includes the generalized dynamic model providedin Section 2.2 and the model of the tire reaction forces provided in Section 4. Acomplete description of the main blocks of the model is provided. Then, the results of thesimulation, performed by using the identified robot parameters presented in the previoussections, are presented and further discussed to characterize the properties of the model. Finally,the obtained results are compared with the real data acquired with the accelerometersin order to check the adherence of the model to the real system. In particular, the followingobjectives will be considered as benchmark:• To validate the tire reaction force model by qualitatively reproducing the real staticand kinetic lateral force measured by the force sensor when pulling the robot platformsidewards (Section 3.3).• To validate qualitatively the overall three-dimensional SSMR model by performing thetwo basic motion commands from an odometry point of view, i.e. moving along astraight line and swiveling in place.• To reproduce qualitatively and quantitatively the robot jerky motion when swivelingin place, from a point of view of the amplitude and the frequency of the vibrationsmeasured by the accelerometers (Section 3.2).
6.1 Simulink Model 796.1 Simulink ModelThe overall block scheme developed in Simulink for the simulation of three-dimensionalSSMR motion is depicted in Figure 6.1. The block scheme can be divided in three mainparts: the left hand side part represents the high level velocity controller, the central partrepresents the tire reaction force dynamics, and the right hand side part represents the threedimensionalrigid-body motion dynamics. In our case, as the robot is not equipped with anysensor measuring its velocity or the position, the controller provides the left and right-sideangular velocities as feed-forward control input to each wheel, given the desired robot linearand angular velocity as reference signals, by inverting the kinematic relation in (2.11) andwithout considering the wheel slip. The reason why we do not consider the wheel slip isbecause we can not have any information on the wheel center velocities, due to the absenceof velocity sensors.Figure 6.1: Block scheme of the Simulink model.The block for the three-dimensional rigid-body motion dynamics simply implements thegeneralized dynamic model in (2.65) and provides the robot position q, velocity V and acceleration˙V given the resultant force and torque vector F, as depicted in Figure 6.2(a). Asthe simulation is mainly performed for the robot swiveling in place, i.e. v x = 0, ω z 0, theproduct between the linear and angular velocities of the robot is relatively low with respectto its linear and angular accelerations, so that the Coriolis term M ˆVV is negligible. Thereby,in order to simplify the model and reduce the computational time, the Coriolis term was notincluded in the Simulink block.
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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:
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2.1 State of the Art 18Finally, by
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2.1 State of the Art 20constraint (
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2.1 State of the Art 22approximates
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2.2 Generalized Modeling 24⎡1 0¯
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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 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:
Page 130 and 131: Appendixes 120(a)(b)Figure 6.24: Pe
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Appendixes 128(a)(b)(c)Figure 6.31:
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Bibliography[1] G. Oriolo, A. De Lu
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