# NS

## Kinematics of a Robot Car (Bicycle Model)

While going through the Sebastian Thrun‘s AI for Robotics class, I came across a programming assignment that required implementing basic kinematics of a simple robot in 2D space. The robot uses bicycle model. Here is the underlying geometry that give rise to the basic equations used in the class.

Figure 1: A robot (car) movement in 2D space.

As shown in Fig. 1, the robot lies in a global cartesian coordinate space and is characterized by its  position and heading, $(x, y, \theta)$, where $\theta$ is the heading relative to $x$-axis.  The length of the robot is $L$ and its velocity along heading direction $\theta$ is $v$.

Let’s assume the robot’s origin (center of rear axle in Fig. 1) moves a distance $d$ along the heading direction. We are interested in the turn angle that the robot incurred during the movement.