World coordinate frame $${\mathbf {q}} = \left[ {\begin{array}{lll} x &\quad y &\quad \theta \\ \end{array} } \right] ^{\mathrm{T}}$$ Robot position and orientation angle $${\mathbf{V}}_{\mathrm{M}} = \left[ {\begin{array}{lll} {V_x } &\quad {V_y } &\quad {\dot{\theta } } \\ \end{array}} \right] ^{\mathrm{T}}$$ Robot translational velocity and rotational angular rate Mechanical constants m Robot mass $$I_\mathrm{v}$$ Robot moment of inertia around the mass center of the robot $$I_\mathrm{w}$$ Wheel moment of inertia around the wheel shaft r Wheel radius $$D_{\mathrm{in}}$$ Inner contact radius $$D_{\mathrm{out}}$$ Outer contact radius $$L_{0}$$ Average contact radius $$I_0$$ Combined moment of inertia of motor, gear train and wheel referred to the motor shaft $$b_0$$ Combined viscous friction coefficient of the motor, gear and wheel shaft. $$k_{\mathrm{b}}$$ Motor back EMF constant $$k_{\mathrm{t}}$$ Motor torque constant $$R_{\mathrm{a}}$$ Motor armature resistance n Gear reduction ratio 