Advance Modeling of a Skid-Steering Mobile Robot for Remote ...
Advance Modeling of a Skid-Steering Mobile Robot for Remote ...
Advance Modeling of a Skid-Steering Mobile Robot for Remote ...
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6.2 Simulation Results 90enough to qualitatively reproducing the real robot jerky motion. In fact, if we slightly changethose values, the overall system behavior nearly does not change.After the tire damping coefficients are estimated, we still need to identify/estimate two parametersto complete our model: the effective mass <strong>of</strong> the tire m t , determining the contactpoint dynamics in (6.4), and the maximum wheel slip λ max , determining the characteristic<strong>of</strong> the dynamic friction coefficient µ x in (4.12a). Un<strong>for</strong>tunately, because <strong>of</strong> lack <strong>of</strong> adequatelaboratory instrumentation and the presence <strong>of</strong> time constraints, we could neither identifynor estimate such parameters. However, we can provide an idea about their order <strong>of</strong> magnitudeby qualitatively and quantitatively analyzing the simulation results obtained by settingthem to some values from different ranges. Moreover, we notice that, as the mass <strong>of</strong> onewheel is 0.07 kg, it is reasonable to think that the effective tire mass should assume values<strong>of</strong> the order <strong>of</strong> 10 −2 kg. After changing different values in the range [0.001, 0.07], we foundout that the value <strong>of</strong> the tire mass nearly does not affect the system behavior. Thereby, wedecided to set the tire mass as half <strong>of</strong> the wheel mass, i.e m t = 0.035 kg.The Simulink model is first tested by running the simulation with the wheels stopped, i.e.v x , ω z= 0, and the testing machine activated so that it provides a cable <strong>for</strong>ce pulling therobot along the y-axis, i.e. K cable = 10 6 [0 1 0 0 0 0] T . In order to compare the resultsobtained in the simulation with the ones provided in Section 3.3, the simulations aredone by moving the testing machine at v y = 0.001 m sand by setting the applications pointp cable at different heights.We notice that, as the wheels are not spinning and no external <strong>for</strong>ce is provided along thex-axis, the value <strong>of</strong> λ max is not affecting the system behavior. In fact, independently fromλ max , we have λ i = 0 < λ max , there<strong>for</strong>e µ iy = v iyrω i= 1 because <strong>of</strong> the saturation block due tothe constraint provided in Section 4.1. Thereby, we can set, <strong>for</strong> instance, λ max = 1.Figure 6.7(a) depicts the simulation results representing the <strong>for</strong>ce measured by the testingmachine when pulling the robot plat<strong>for</strong>m sidewards, <strong>for</strong> different applications points p cable .By comparing the graphs in Figure 6.7(a) with the graphs in Section 3.3 both from aqualitative and quantitative point <strong>of</strong> view, the following considerations can be done:• The model qualitatively reproduces the real saw-tooth shape <strong>of</strong> the static lateral <strong>for</strong>ceas measured by the testing machine.• The exact shape <strong>of</strong> the cable <strong>for</strong>ce depends on the height <strong>of</strong> the application point. Thehigher from the ground the application point is the more weight is perceived on right