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

2.1 State of the Art 16Figure 2.3: Wheel/ground contact point velocities with slipping.According to the geometrical description in Figure 2.3 and to the given definition ofICR l , ICR r , we can write the longitudinal slip velocities as:∆v Lx = ∆v 1x = ∆v 2x = (y ICRl − c)ω z∆v Rx = ∆v 3x = ∆v 4x = (y ICRr + c)ω z(2.9)By combining equation (2.9) and the expressions of v L , v R from equation (2.6), we obtainthe following definitions for the y-coordinates of the ICRs:y ICRl = v x − rω Lω z, y ICRr = v x − rω Rω z, y ICRG = v xω z(2.10)It must be noticed that the coordinate y ICRG can reach infinite values if the vehicle angularvelocity ω z = 0, namely when the robot moves along a perfect straight line under ω L = ω R .Conversely, the other coordinates y ICRl , y ICRrand the s value are bounded. This observationcan be explained by the fact that both the numerators and the denominators in (2.8) and (2.10)are infinitesimals of the same order when the ω z → 0. Therefore, the values for y ICRl , y ICRrand s are well defined at a finite distance when the vehicle is not rotating.Let ω L , ω R be the control inputs at the kinematic level, from the definition of the longitudinalwheel slip in (2.7) we know that v Lx = r(1 − λ L )ω L and v Rx = r(1 − λ R )ω R . By substituting