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Table 1 Nomenclature

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