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

3.2 Characterization of the Vibrations 39CoM, as the contribution of ω in (3.5) is mainly given by the term ˆp a ˙ω. By substituting thevalues of p a in (3.5), we obtain the following relations:a x = ˙v x + g sin ψa y = ˙v y − p ax ˙ω z − g cos ψ sin θ(3.6)a z = ˙v z + p ax ˙ω y − g cos ψ cos θFigure 3.2: The wood-cube fixed to the robot’s platform at the position p a ≈ [−0.2 0 0] T .We notice that in (3.6) there are all the robot linear and angular accelerations along andaround the three principal axes except for ˙ω x . However, as the robot oscillations around thex and y-axis are constraint by the tire vertical reaction forces, as result of the Roll, Pitch andYaw motion the robot assumes significant values for the linear accelerations along the x andy-axis. In fact, as we will see in the next chapter, the tire reaction forces f ix , f iy , f iz depend onthe wheel center velocities, which depend on the robot angular velocity by relation (2.55).Thereby, the six differential equations defined in (2.65) are strongly coupled even when theCoriolis term is negligible, i.e. for relatively low velocities as in the case of swiveling inplace. Moreover, we notice that, although the real robot angular acceleration can assumerelatively high values because of the vibrations, the angles θ, ψ always assume relativelysmall values if the wheels are not lifting from the floor, which is in general true for ω ∗ z ≤64 deg/s. In such a condition, we can approximate the trigonometric functions by their first