PID Controller
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It's surprisingly difficult to drive a wheeled robot in a straight line. No two motors have exactly the same performance, and there may also be differences in the floor surface. If we want a robot to follow a more complicated trajectory or to have some indication of where it has traveled, we need to be able to measure the distance each motor has traveled, that is, how many times the left and right wheels have rotated. This is called odometry.

Besides the distance traveled, we also want to control the motors in such as way that the robot's movements are both accurate and smoothly executed. This means that regardless of whether the robot is traveling in a straight line, a gradual curve, or turning around, we want to set the left and right motors to operate at a specified speed and be able to accurately maintain that speed.

Additionally, we want to gradually change the motor speed rather than make very sudden changes. This reduces the wear and tear on the motor and gear train, and the robot's movements also appear smoother. This is called slewing the speed. We set a slew rate, which is the maximum speed at which the speed of the motor is permitted to change. You can also think of this as a maximum acceleration rate.

To do all this we can measure the speed of the motors themselves using the motor encoders, then use that to determine the difference between the intended and actual motor speeds.

It turns out that we can find such a fancy motor controller in the field of Control Engineering; it's called a PID Controller.

What is a PID Controller?#

A Proportional–Integral–Derivative or PID Controller is a general-purpose mechanism for regulating the output of any kind of system through the use of a feedback loop. The feedback signal provides an indication of the current output of the system and is used to alter the system so that its output matches the desired value. PID Controllers are used in temperature controllers and automobile cruise controls. One of its first industrial uses was as an automated steering system for ships.

A PID Controller uses two numbers, the Set Point (SP) or target value of the system, and the Process Variable (PV), the output value providing the feedback from the system. When the SP and the PV are equal the output from the algorithm is zero and no change is necessary. When there is a difference between SP and PV we consider that the controller's error. Our aim is to reduce that error to zero.

What sets a PID controller apart from simpler controllers is that it combines three types of control terms to quickly reach the desired system output, minimising overcorrection and maximising stability. These three control terms are what forms its acronym: Proportional, Integral, and Derivative.

A Proportional term multiplies the error value by a fixed proportional gain value to determine the corrective value influencing the system output. Because a controller using only a proportional term is using the value of the error to generate its corrective value, it will overshoot its target, then undershoot, with smaller and smaller oscillations until the error approaches zero. Unfortunately, as the oscillation of the system gets closer and closer to its target the amount of correction also approaches zero, so the controller never gets there.

The Integral Term integrates the error value into the correction over time so that it minimises this overshoot and pushes the output towards the target value. This requires that the amount of integral applied to the formula be carefully tuned, otherwise this can create its own form of oscillation. Given this tuning is quite tricky to get right, there is generally some overshoot and therefore oscillation in a PI controller.

A Derivative Term projects the rate of change of the corrective value, and reduces its amount as the system nears the target. This allows the controller to move towards its Set Point as fast as possible, with as little oscillation as possible.

The more I read about PID controllers the more I found that tuning the Integral and Derivative control terms is considered something of a black art. There are a couple of constants in the formula, and tweaking them is done by trial and error, in other words: guessing.

To add another twist to a robot motor controller, we don't want to tell the motors to go from zero to a projected speed immediately, as that would both overly stress the motors and drive system, and cause the robot's movements to be very jerky. I want to slew the value so that it changes at a maximum speed, called a slew rate.

All in all, I've now got requirements for a robot motor control that include a proportional term, integral term, derivative term, and a slew rate.

See: PID Controller on Wikipedia

The rest needs a lot of cleanup, titles, etc.

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