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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