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

5.2 Identification of the Tire Dynamic Parameters 75data f peakx f peaky f peakz1 5.8594 2.9297 7.81252 5.8594 2.9297 7.32423 5.8594 2.9297 7.32424 6.3477 2.9297 6.83595 5.8594 2.9297 7.81256 6.3477 3.4180 7.81257 5.8594 2.9297 7.32428 6.3477 3.4180 7.8125mean 6.0425 3.0518 7.5073std 0.2527 0.2260 0.3633Table 5.2: Peak frequencies of the Roll, Pitch and Yaw free response for random initial conditions.the exponential function always envelops the data when λ assumes values relatively close toλ = 2, 3.5, 4.5 respectively for the Roll, Pitch and Yaw. In conclusion, we can consider thefrequencies of the oscillations and the rates of decay estimated as:f peakx = 6.04, λ x = 2f peaky = 3.05, λ y = 3.5f peakz = 7.51, λ z = 4.5By looking at the free response functions defined in (5.7), the following relations betweenf peaki , λ i and the corresponding ω ni , ξ i can be easily derived:2π f peaki =√1 − ξ 2 i ω n iλ i = ξ i ω niThereby, the angular natural frequencies and the damping ratios are estimated as follows:ω in =ξ i =√4π 2 f 2 peak i+ λ 2 iλ i√4π 2 f 2 peak i+ λ 2 i(5.9)leading to the values: