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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.

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