Through The Classroom Door

In most of the Robotics competitions that I have been involved with, there is a need to follow a line. There are many strategies that can be employed to follow a line, but Proportional-Integral-Derivative (PID) control is the most effective. It can also be the most disengaging because of the mathematics involved.

Proportional Control

A good place to start is with Proportional Control and build from there. Proportional Control is where change made to the steering is proportional to, or directly related to, the robot’s distance from the edge of the line or the Target Path.

We control the Bot by changing the value for the turn ratio (or steering value) as the Bot moves forward in a forever loop. The turn ratio is calculated by:

turnRatio = error * gainValue

The error is the difference between where we want the robot to be and where it actually is: targetValue – colourSensor reading

The targetValue is the threshold value on the Target Path. We calculate this by averaging the reading from the colour sensor over white and the reading over the black. ie. targetValue = white reading + black reading / 2.

The gainValue determines how quickly the robot reacts to changes in the error value. A smaller gainValue makes the robot move slowly, which means that it might not react quickly enough for tight turns, but results in less side-to-side motion when the line is fairly straight. A larger gainValue means a quicker reaction but can cause jerkier motion. Selecting the gainValue is called tuning the controller and usually involves some trial and error.

This gives us:

turnRatio = (targetValue – colourSensor) * gainValue

Psuedocode

on start
targetValue = 40
gainValue = 0.7

Repeat forever
turnRatio = (targetValue – colourSensor) * gainValue
Steer motors D + A TurnRatio speed 25

Proportional-Integral-Derivative (PID) controlled Bot

Now we are going to fine tune by incorporating the gain or response to Integral (total errors) and Derivative (rate of) errors. This Proportional-Integral-Derivative (PID) control.

The Proportional part measures the deviation from the Target Path (error), so our turnRatio = (target reflected light – actual reflected light) x Kp. The Kp is a fine tuning value or gain (or how quickly the robot reacts to changes in the Error value) that we can arrive at with some experimentation.

The Derivative is the rate of errors (deviations from the Target Path) and, therefore, we can predict what the next error will be and can fix the steering proactively : derivative = error – last error

The Integral is the sum of all the error (deviations from the Target Path) values and can help determine if the steering fixes from the derivative have helped keep the bot on the Target Path. Looking at the sum of all past errors can detect when steering corrections are not working: integral = integral + errors

Proportional [Error] = How bad is the situation now?
Integral = Have my past fixes helped fix things?
Derivative = How is the situation changing?
PID control = combine the error, integral and derivative values to decide how to steer the robot

The fine tuning is incorporated into the turn ratio (to steer back towards the line) and our aim is to reduce oscillation (rate of turning in and out) as much as possible and achieve smooth line following. The formula for the turn ratio value we need to repeat is:

turnRatio = (error * Kp) + (integral * Ki) + (derivative * Kd)

Where:

error = Target – Ns, where the Target is the threshold value (black+white/2) and Ns is the normalised [turn into a number between 0-100] colour sensor value
Kp = proportional gain or how quickly the robot reacts to changes in the Error value
integral = sum of the errors or sum of how far away from the Target we are
Ki = integral gain
derivative = rate of errors or rate of how far away from target we are
Kd = derivative gain or fine tuning value for derivative or error rate.

So, as the Bot moves along the edge of the line, it will steer into and out of the line based on the value of the turnRatio. Depending on how we adjust the Kp, Ki and Kd values, the steering should be minimal and produce less oscillation.

Pseudocode

on start
Power = 50                           // default speed
Target = 58                         // threshold calculated by white level + black level /2 (theoretically centre of black line)
Kp = 0.7                             // proportional gain. The Gain value determines how quickly the robot reacts to changes in the Error value
Kd = 12                             // gain or response to errors for the derivative. Kd needs to be set at the beginning of the program to a value you arrive at
after some experimentation
Ki = 0.05                       // gain or response to errors for the integral
lastError = 0              //for tracking errors
integral = 0             // add up errors
Direction = -1           //are you left of the line or right of the line
min = 5                  // light reading on black
max = 65           // light reading on white
steer motors Power           // start moving Bot

forever
Ns = 100 * (raw sensor reading – min) / (max – min)       // normalise light sensor reading for calculations
error = Target – Ns                                                                  // calculate error
derivative = error – lastError                                             // calculate the derivative or rate of errors
lastError = error                                                                 // update lastError

integral = 0.5 * integral + error                                // calculate the new integral or total errors
turnRatio = Direction * (Kp * Error + Kd * Derivative + Ki * Integral )            // make final turn ratio calculation
steer motors turnRatio Power                      // turn slightly according to calculations

Tuning Strategy 1
The most common way to tune your PID constants is trial and error. Disable everything but the proportional part (set the other constants to zero). Adjust just the proportional constant until robot follows the line well. Then, enable the integral and adjust until it provides good performance on a range of lines. Finally, enable the derivative and adjust until you are satisfied with the line following.

When enabling each segment, here are some good numbers to start with for the constants:

P: 1.0 adjust by ±0.5 initially and ±0.1 for fine tuning
I: 0.05 adjust by ±0.01 initial and ±0.005 for fine tuning
D: 1.0 adjust by ±0.5 initially and ±0.1 for fine tuning

Tuning Strategy 2
1. Set the Power to 50.
2. Start with Kd and Ki at 0 and Kp at 1. With our target at 60, this will make the Steering value change between -60 and 40 as the normalized sensor reading goes between 0 and 100.
3. Start by testing with just a straight line. A Kp of 1 is likely too large and will cause noticeable oscillation. Progressively reduce Kp by 0.05 until the robot follows a line with no side-to-side movement or only small movement to one side of the edge.
4. Progressively increase Ki by 0.01 until the robot follows the edge of a straight line with no oscillation. If the robot does not constantly drift to one side, you may be able to leave Ki at 0. Be aware that setting Ki too high (above 0.05) will cause the oscillations to grow bigger.
5. Now test the program on a line with curves. Increase the Power variable until the robot is unable to make the turn.
6. Progressively increase Kd by 1 until the robot can traverse the entire path.

The much longer version of this is here: https://wp.me/a8n5jj-fu