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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3.3 Characterization <strong>of</strong> the Tire Forces 47in place (second part), the <strong>for</strong>ce settles down nearly to a steady value. This steady value dependson the wheel slipping until a certain threshold after which it remains almost constant.In particular, the <strong>for</strong>ce decreases almost linearly <strong>for</strong> ∆v xi < 0.04 m, while <strong>for</strong> ∆v s x i≥ 0.04 m sit remains almost constant around its minimum value between 20 − 30 N depending on thetype <strong>of</strong> the ground. By dividing <strong>for</strong> the weight <strong>of</strong> the robot (gm plat f orm = 225 N), we obtainan estimation <strong>of</strong> the minimum kinetic friction coefficient <strong>for</strong> v y = 1 mm, i.e. µ s k min= 0.1, 0.12.An estimation <strong>of</strong> the static friction coefficient, instead, can be obtained by considering themaximum <strong>for</strong>ce recorded in the first part, which varies between 180 − 200 N <strong>for</strong> the concreteand 200 − 224 N <strong>for</strong> the carpet, and dividing it <strong>for</strong> the weight <strong>of</strong> the robot. In particular,by computing the average value among all the coefficients estimated <strong>for</strong> each trial, we obtaina static friction coefficient µ s = 0.86, 0.98 respectively <strong>for</strong> the concrete floor and carpet.However, as the qualitative behavior <strong>for</strong> both the static and kinetic <strong>for</strong>ce does not change<strong>for</strong> different types <strong>of</strong> ground, only the data acquired on the concrete floor will be consideredin the following. Another consideration is that the irregular structure <strong>of</strong> the carpet causesa significant variation on the <strong>for</strong>ce recorded during different tests, especially <strong>for</strong> the static<strong>for</strong>ce (see the first part <strong>of</strong> Figure 3.5(b)), providing not very accurate and reliable data.In order to better understand and analyze the saw-tooth behavior resulting when the wheelsare stopped, the robot was also pulled laterally but placing some oil and a piece <strong>of</strong> smoothplastic underneath two and three wheels, allowing respectively only two and one wheeltouching with the ground while the others slide upon the floor nearly without friction. Thegraphs in Figure 3.6 depict the <strong>for</strong>ce measured in the two cases, using as touching wheelsboth the ones further and closer to the pulling side.Figure 3.6 shows very well the saw-tooth shape <strong>of</strong> the <strong>for</strong>ce even when only one wheelis touching, meaning that such a behavior is not due to the complex interaction among thefour wheels but it is due to some tire properties. By looking carefully at the wheels whilepulling the robot, it can be noticed that such a behavior is due to the rubber <strong>of</strong> the tire andcan be explained by thinking about the tire as a spring-mass-damper system. In fact, whenthe robot is pulled sidewards and the wheels are not slipping, the contact point <strong>of</strong> each wheelstays fixed to the ground, allowing the rubber <strong>of</strong> the tire to be stretched as a spring, untilthe spring <strong>for</strong>ce overcome the static friction <strong>for</strong>ce. Then, the contact point moves due to thetire-spring releasing and then it stops allowing the rubber to stretch again 1 . As the dynamics1 See Section 4 <strong>for</strong> further details.