The strategy we have just described for pulse-width modulating motors is known as an open-loop control scheme. In open-loop control, there is no feedback from the motors, telling the robot's program how fast the wheels are turning or how far the robot has gone. Rather, the motors are just given different commanded voltages. But depending on terrain, surface obstacles, slippage in wheel contacts, or load on the robot, the commanded voltages do not necessarily imply particular speeds.
To implement a true velocity or position control algorithm, the robot needs sensors on the wheels, such as the shaft encoders. Such feedback enables what are known as closed-loop control algorithms. A typical control system will look like this:
The basic idea of a control loop is to take the desired velocity command, send that command to the motors, see how fast the motors actually spin, and then measure that speed and compare it to the commanded speed. The difference is called the error signal and it can be either positive or negative. The type of controller determines what computation the control system performs on the error signal. One type of controllers is the PID controller.
In a PID controller, the output, T, is related to the error signal, e, by the following relation:
Let's see how the stead state output (output at time equal to infinity) as the proportional constants k are varied: