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

6.2 Simulation Results 876.2 Simulation ResultsIn this section the results of the simulation are presented and further discussed to characterizethe properties of the model, and they are compared with the real data acquired withthe accelerometers in order to check the model reliability. Before running the simulation, weneed to estimate the values for the damping coefficients D x , D y , D z . As explained in Section5.2, it was not possible to analytically compute the values for D x , D y , D z from the identifiedvalues of the angular natural frequency and the damping ratio for the Roll, Pitch and Yawmotion. Conversely, an estimation of the tire damping coefficients can be obtained by settingD x , D y , D z in the simulation to some random values and then changing those values so thatthe Roll and Pitch free responses match with the data presented in Section 5.2. We also recallthe fact that, as the third equation in (5.3) holds for the acquired Yaw free response, theparameters D x and D y are dependent from each other by the second relation on the right sidein (5.10). Thereby, we only need to set the values for D z and either D x or D y .The initial condition for the free response is provided by setting to different values the initialcondition of the integrator for the vertical reaction force. In particular, for the Rollmotion we set the same initial condition for the two left and right-side wheels, while forthe Pitch angle we set the same condition for the two front and rear-side wheels. In orderto provide a free response as close as possible to the acquired one, the initial conditionsare set symmetrically with respect to the tire compression at equilibrium, that is for theRoll case z init1 = z init2 = − mg4Ktire z− 0.001 and z init3 = z init4 = − mg4Ktire z+ 0.001. As the responseis under-damped in the three cases (see Figure 5.4, 5.5), the damping coefficientsare initially set to one fourth of the value corresponding to a critically damped response, i.e.D x = 1 2√ mKx , D y = 1 2√ mKy , D z = 1 2√ mKz , and then they are either increased or decreaseddepending on the simulation results. After several trials, by comparing the results from the¨Accelerometers¨ block with Figure 5.4, 5.5, we obtained the following values:D x = 50, D y = 30, D z = 70 (6.5)Figure 6.5 and 6.6 depict the simulation results respectively for the Roll and Pitch motion,obtained from the ¨Accelerometers¨ block by setting the values in 6.5.It is worth noticing that, although this estimation is not accurate and could not be unique,it provides the needed information to reproduce the real Roll and Pitch oscillation, which is