Forward kinematics of a differential robot

The forward kinematics equations for a robot with a differential drive system are used to solve the following problem:

If a robot is standing in a position (x, y, θ) at time t, determine the pose (x', y', θ') at t + δt given the control parameters V-left and V-right.

This technique can be calculated by the robot to follow a particular trajectory.

Explanations of the forward kinematics equation

We can start by formulating a solution for forward kinematics. The following figure is an illustration of one of the wheels of the robot:

A single wheel of the robot rotating along the local y-axis

The motion around the y-axis is known as the roll; everything else is called the slip. Let's assume that no slip occurs in this case. When the wheel completes one full rotation, it covers a distance of 2π r, where r is the radius of the wheel. We will assume that the movement is two-dimensional. This means that the surface is flat and even.

When the robot is about to perform...