The velocity motion model assumes that the robot is controlled through 2 velocities: rotational and translational velocity:

\begin{equation} u_{t}=\left(\begin{array}{l}{v_{t}} \ {\omega_{t}}\end{array}\right) \end{equation}

A sampling algorithm generates a random pose according to the distribution \(p(x_t| u_t, x_{t-1})\), and perturbs it with the noise, drawn from the error parameters of the kinematic motion model.

\begin{equation} \left(\begin{array}{c}{\hat{v}} \ {\hat{\omega}}\end{array}\right)=\left(\begin{array}{c}{v} \ {\omega}\end{array}\right)+\left(\begin{array}{c}{\varepsilon_{\alpha_{1}|v|+\alpha_{2}|\omega|}} \ {\varepsilon_{\alpha_{3}|v|+\alpha_{4}|\omega|}}\end{array}\right) \end{equation}