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

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 of the tire m t , determining the contactpoint dynamics in (6.4), and the maximum wheel slip λ max , determining the characteristicof the dynamic friction coefficient µ x in (4.12a). Unfortunately, because of lack of adequatelaboratory instrumentation and the presence of time constraints, we could neither identifynor estimate such parameters. However, we can provide an idea about their order of magnitudeby qualitatively and quantitatively analyzing the simulation results obtained by settingthem to some values from different ranges. Moreover, we notice that, as the mass of onewheel is 0.07 kg, it is reasonable to think that the effective tire mass should assume valuesof the order of 10 −2 kg. After changing different values in the range [0.001, 0.07], we foundout that the value of the tire mass nearly does not affect the system behavior. Thereby, wedecided to set the tire mass as half of 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 force 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 force is provided along thex-axis, the value of λ max is not affecting the system behavior. In fact, independently fromλ max , we have λ i = 0 < λ max , therefore µ iy = v iyrω i= 1 because of the saturation block due tothe constraint provided in Section 4.1. Thereby, we can set, for instance, λ max = 1.Figure 6.7(a) depicts the simulation results representing the force measured by the testingmachine when pulling the robot platform sidewards, for 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 of view, the following considerations can be done:• The model qualitatively reproduces the real saw-tooth shape of the static lateral forceas measured by the testing machine.• The exact shape of the cable force depends on the height of the application point. Thehigher from the ground the application point is the more weight is perceived on right