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

3.3 Characterization of the Tire Forces 53as expected. However, by calculating the slope for relatively small intervals, the nonlineardynamics can be reasonably approximated by two linear pieces, the first one from 0 N to90 N with K tire = 15 kN and the second one from 90 N to 150 N with K m tire = 21 kN , thereforemwe can estimate the tire elasticity coefficient as K tire = 18 kN . mThe last parameter we want to identify is the tire vertical force due to the tire-spring dynamics.In order to measure the tire vertical force, a single wheel was fixed to the forcesensor by a steel tube with a ’L’ shape (see Figure 3.8). The testing machine pushed thewheel downwards for few centimeters, so that a vertical load was applied on the wheel andthe vertical force due to the tire compression could be measured with respect to distance(see Figure 3.10(a)). Then, the piece of wood was pulled sidewards, so that the wheel wasdragged upon the wood surface and the vertical force was measured with respect to time (seeFigure 3.10(b)).The graph in Figure 3.10(a) shows that also the tire-spring dynamics during vertical compressionis approximatively linear and by calculating its slope we obtain a tire vertical elasticitycoefficient K tirez = 80 kN . mThe graph in Figure 3.10(b), instead, seems to confirm the results obtained for the graphs inFigure 3.9. When the wheel has no capability to move vertically, i.e. when wheel is draggedtowards the right hand side, the force stays around a steady value meaning that the tire isnot releasing. Conversely, when it has such a capability, i.e. when wheel is dragged towardsthe left hand side, the force presents a saw-tooth shape meaning that the tire always releasesafter stretching. The reason why the vertical force increases when the tire is stretching anddecreases when releasing (left hand side), is probably due to ’L’ shape tube since, when thetire stretches, the contact point moves a little closer to the sensor vertical axis and thereforethe steel rod is pushed a little upwards increasing the measured force. Conversely, whenthe tire releases, the contact point moves a little further from the sensor vertical axis andtherefore the steel rod is allowed to move a little downwards resulting in a decrease of theperceived force.