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

5.2 Identification of the Tire Dynamic Parameters 70ω nx =ω ny =ω nz =√4h 2 K y + 4c 2 K zI x, ξ x =√4h 2 K x + 4a 2 K z,I y√ξ y =4c 2 K x + 4a 2 K y,I zξ z =4h 2 D y + 4c 2 D z2 √ I x (4h 2 K y + 4c 2 K z )4h 2 D x + 4a 2 D z2 √ I y (4h 2 K x + 4a 2 K z )4c 2 D x + 4a 2 D y2 √ I z (4c 2 K x + 4a 2 K y )(5.5)It is worth noticing that, in this case, the three angular velocities coincide to the derivativeof the Roll, Pitch and Yaw angles, therefore the equations in (5.4) can be rewritten bysubstituting the ω x = ˙θ, ω y = ˙ψ, ω z = ˙φ and integrating it:¨θ + 2ξ x ω nx ˙θ + ω 2 n xθ = 0¨ψ + 2ξ y ω ny ˙ψ + ω 2 n yψ = 0(5.6)¨φ + 2ξ z ω nz ˙φ + ω 2 n zφ = 0It is well known from automatic control theory [22] that, for under-damped systems (ξ