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

3.3 Characterization of the Tire Forces 47in place (second part), the force 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 force decreases almost linearly for ∆v xi < 0.04 m, while for ∆v s x i≥ 0.04 m sit remains almost constant around its minimum value between 20 − 30 N depending on thetype of the ground. By dividing for the weight of the robot (gm plat f orm = 225 N), we obtainan estimation of the minimum kinetic friction coefficient for v y = 1 mm, i.e. µ s k min= 0.1, 0.12.An estimation of the static friction coefficient, instead, can be obtained by considering themaximum force recorded in the first part, which varies between 180 − 200 N for the concreteand 200 − 224 N for the carpet, and dividing it for the weight of the robot. In particular,by computing the average value among all the coefficients estimated for each trial, we obtaina static friction coefficient µ s = 0.86, 0.98 respectively for the concrete floor and carpet.However, as the qualitative behavior for both the static and kinetic force does not changefor different types of ground, only the data acquired on the concrete floor will be consideredin the following. Another consideration is that the irregular structure of the carpet causesa significant variation on the force recorded during different tests, especially for the staticforce (see the first part of 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 of 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 force 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 of the force 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 of 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 of each wheelstays fixed to the ground, allowing the rubber of the tire to be stretched as a spring, untilthe spring force overcome the static friction force. 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 for further details.