roamr Kinematics

Wheel speeds to body twist:

$$v=\frac{v_r+v_l}{2},\omega =\frac{v_r-v_l}{L}$$

Integrate to get $(x,y,\theta )$:

$$\begin{array}{rl}{x}_{k+1}& =x_k+v\Delta t\cos {\theta }_k\\ y_{k+1}& =y_k+v\Delta t\sin {\theta }_k\\ {\theta }_{k+1}& ={\theta }_k+\omega \Delta t\end{array}$$

Odometry from wheel encoders:

$$\begin{array}{rl}& \Delta s_r=2\pi r\frac{n_r}{N},\Delta s_l=2\pi r\frac{n_l}{N}\\ & \Delta s=\frac{\Delta s_r+\Delta s_l}{2},\Delta \theta =\frac{\Delta s_r-\Delta s_l}{L}\end{array}$$