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

2.1 State of the Art 14velocity vector for the extended three dimensional coordinate frame, and v i = [v ix v iy v iz ] Tis the three dimensional vector of the wheel center velocity (Figure 2.2(a)). The vectors d C =[d Cx d Cy d Cz ] T = −[x ICRG y ICRG z ICRG ] T and d i = [d ix d iy d iz ] T , instead, representrespectively the vector from the ICR G to the CoM and to the i th wheel/ground contact pointP i , expressed in the local frame.By considering only planar motion, i.e. d Cz , d iz , v z , v iz , ω x , ω y = 0, equations (2.2) lead to thefollowing relation:ω z = − v ixd iy= − v xd Cy= v iyd ix= v yd Cx, i = 1, . . . , 4 (2.3)Accordingly to the geometrical description in Figure 2.1, the coordinates of vectors d i aredefined as follows:d 1x = d 4x = d Cx − a = −x ICRG − ad 2x = d 3x = d Cx + b = −x ICRG + bd 1y = d 2y = d Cy + c = −y ICRG + c(2.4)d 3x = d 4x = d Cy − c = −y ICRG − c(a)(b)Figure 2.2: (a) Wheel linear and angular velocities; (b) Wheel forces and torques.By combining equation (2.3) and (2.4), the following relations among the wheel velocitiesare obtained:v L v 1x = v 2x , v R v 3x = v 4x(2.5)v F v 2y = v 3y , v B v 1y = v 4y