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

3.3 Characterization of the Tire Forces 49of the tire stretching is much slower than the releasing, the periodic motion results in a sortof saw-tooth wave as shown from the graphs.Furthermore, from the graphs depicted in Figure 3.6 we can also extract the tire elasticitycoefficient by calculating the slope of the ramps of the saw-tooth shape. In particular, theslope varies from 4 kN mto 6 kN , therefore the measured elasticity coefficient can be estimatedmas K measured = 5 kN . However, such a value of K m measured is not reliable as the rope is extensibleso that the force sensor is also measuring the rope elastic force and therefore the previouslycalculated coefficient includes the rope coefficient too. We can consider our system composedby the robot and the rope as two springs connected in series, so that the elasticitycoefficient the sensor perceives is given by the formula:K measured =K cableK tireK cable + K tire(3.9)Thereby, when K cable is comparable or smaller than K tire , K measured is completely differentfrom K tire and can even be almost equal to K cable .To overcome this problem, the rope was replaced with a steel cable which is not extensible.The force was then measured again for a single wheel touching the ground and also with nowheel touching (Figure 3.3(b)), in order to check whether or not the saw-tooth behavior wasdue only to the rope elasticity. Moreover, the force was measured by pulling only the robotplatform with and without the aluminum frame to check if the weight or the inertia affect themeasurements. Figure 3.7 shows the two cases with one and zero wheel touching.By looking at Figure 3.7, it is easy to notice that, in both cases (with and without thealuminum frame), the saw-tooth shape is not present when all the four wheels are on theplastic pads with some oil underneath, meaning that such a behavior is not due to the ropeelasticity or the robot inertia but only to the tire-spring dynamics. We can also see howthe saw-tooth shape is more regular in these graphs than the ones in Figure 3.5, 3.6, thanksto the high elasticity of the cable. Moreover, as in this case K cable≫ K tire and only onewheel is touching the ground, the value of K measured defined in (3.9) is almost equal to K tire .In particular, the slope of the little ramps varies in the interval 20 − 25 kN mso that we canestimate the tire elasticity coefficient as K tire = 22.5 kN . mAlthough the data presented above clearly show the tire-spring behavior from a qualitativepoint of view, they do not provide reliable values for the identification of the tire elasticitycoefficient. In fact, the measured force is somehow affected also from the other tire forces,