From: Passivity-based control of an omnidirectional mobile robot
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 |