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

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3.1 The accelerometer 36(a)(b)Figure 3.1: (a) A spring-mass-damper 1-axis accelerometer scheme; (b) Bode diagram of the transfer functiona spring-mass-damper 1-axis accelerometer system.
3.2 Characterization of the Vibrations 37its acceleration along its axis.3.2 Characterization of the VibrationsThe aim of this section is to provide a qualitative and quantitative idea about the vibrationswhich occur while the robot is turning (ω L ω R ). First of all, different qualitativetests has been done by running the robot at different angular velocities on different types ofground. The tests has been also done by modifying the robot’s structure, therefore changingits dynamics configuration. In particular, the robot has been run with and without the aluminumframe and the laptop, with different types of tire and even with two cubes of woodreplacing two wheels on the same side. Moreover, to check the importance of the robot inertia,a long plastic pale with two weights attached to its extremes was fixed to the robot alongits principal axes. After several tests, we could clearly claim that the main cause of the robotvibrations is the complex behavior of the lateral reaction forces, due to the tire dynamics andthe complex tire/ground interaction, and their interaction with each other. In fact, when wereplace two wheels with cubes of wood, large vibrations never appear independently fromthe robot’s structure. Conversely, when the four wheels are mounted on the robot, the vibrationsdo not appear while running the robot’s platform, but they become relevant when thealuminum frame is fastened on it and they increase when increasing the robot weight andinertia along the x and y axis.In order to have also a quantitative idea, the vibrations are measured by acquiring the datafrom the accelerometers fixing the wood-cube to the robot in different locations, whileswiveling the robot in place with different angular velocities (v ∗ x = 0, ω ∗ z 0). The dataare also acquired by running the robot on all the types of floor in the School of Engineeringat RWU, i.e. carpet for the rooms, tile for the corridors and concrete for the laboratories.The relation between the acceleration a = [a x a y a z ] T measured from the three accelerometersand the robot acceleration ˙V, when the wood-cube is fixed to the robot at the positionp a with respect to the robot CoM, can be obtained by computing the linear velocity of thewood-cube from the robot velocity, differentiating it with respect to time and adding the gravitycontribution. The linear velocity v a can be computed by applying the Plücker transformfor spatial velocity vectors [18], [19] to the robot twist V:
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
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 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
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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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