Key Engineering Takeaways
- •Given robot linear velocity v and angular velocity w, individual wheel velocities are: v_R = v + (w · L / 2) and v_L = v - (w · L / 2).
- •Wheel encoder odometry drifts over time due to wheel slippage, tire deformation, and uneven terrain—requiring sensor fusion with IMU and LiDAR.
- •Using 2nd-order Runge-Kutta integration reduces orientation heading truncation error during tight turns.
Prerequisites
- • Basic 2D geometry and trigonometry
Forward & Inverse Velocity Kinematics Equations
Let $r$ be the wheel radius and $L$ be the track width (distance between wheels):
### Forward Kinematics (Wheel velocities $\to$ Robot velocity):
$$v = \frac{r}{2} (\omega_R + \omega_L)$$
$$\omega = \frac{r}{L} (\omega_R - \omega_L)$$
### Inverse Kinematics (Desired robot $[v, \omega]^T \to$ Wheel velocities):
$$\omega_R = \frac{2v + \omega L}{2r}$$
$$\omega_L = \frac{2v - \omega L}{2r}$$
Tags:#Differential Drive#Mobile Robots#Odometry#Dead Reckoning#Kinematics#Unicycle Model