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.
As shown in Fig. 1, the robot lies in a global cartesian coordinate space and is characterized by its position and heading, , where is the heading relative to -axis. The length of the robot is and its velocity along heading direction is .
Let’s assume the robot’s origin (center of rear axle in Fig. 1) moves a distance along the heading direction. We are interested in the turn angle that the robot incurred during the movement.