instantaneous center of rotation). The ground contact speed of the left wheel and the right wheel lead to a rotation of the vehicle by the angular velocity . Following the definition of angular velocity, one obtains:Solving these two equations for and , while the latter is defined as the distance from to the center of the robotUsing the equation for the angular velocity, the instantaneous velocity of the point midway between the robot's wheels is given byThe wheel tangential velocities can also be written aswhere and are the left and the right angular velocities of the wheels around their axes. The robot kinematics in local body coordinates can thus be written asUsing a coordinate transformation (Rotation of axes), the robot's kinematic model in global coordinates can finally be obtainedwhere and are the control variables. Differential Drive Controller One might face a situation where the velocity and the angular velocity are given as inputs, and the angular velocities of the left and right wheels are sought as control variables (see figure above). In this case, the already mentioned equation can be easily reformulated. Using the relations and in one obtains the equation for the angular velocity of the right wheel The same procedure can be applied to the calculation of the angular velocity of the left wheel Examples of differential wheeled robots Pioneer, PeopleBot, PowerBot & PatrolBot- the ActivMedia Robotics mobile robots. Armadillo, Robotican Khepera and e-puck Sbot Alice Roomba RoboMow Shonkbot, a minimal-cost, Arduino-based teaching robot Thymio Edison Giraff Big Trak SCUTTLE An open-source payload-capable robot for hobby and university research. References External links A Tutorial and Elementary Trajectory Model for the Differential Steering System of Robot Wheel Actuators by G.W. Lucas at the open source Rossum Project