As you may know, robot kinematics is the study of motion without considering the forces that affect the motion, and robot dynamics is the study of the forces acting on a robot. In this section, we will discuss the kinematics of a differential robot.

Typically, a mobile robot or vehicle can have six degrees of freedom (DOF), which are represented as x, y, z, roll, pitch, and yaw. The x, y, and z degrees are translation, and roll, pitch, and yaw are rotation values. The roll movement of robot is sideways rotation, pitch is forward and backward rotation, and yaw is the heading and orientation of the robot. A differential robot moves along a 2D plane, so we can say it will have only three DOF, such as x, y, and theta, where theta is the heading of the robot and points along the forward direction of the robot.

The following figure shows the coordinate system of a differential-drive robot:

Figure 8: The coordinate system representation of a differential...