October 5, 2013
Proportional, Integral,
Derivative Line Following
Welcome and Introductions
Page 2
Line Following
•Why is line following useful in FLL?
•Wide black lines with surrounding white area can be used for
successful navigation.
•Light sensor is preferable to color sensor due to: (a) higher
resolution, and (b) ability to calibrate.
•As with all line following, steering the robot is accomplished by
independently controlling the power of the left and right
motors. The motors work to keep the light sensor at the
edge of the line.
Page 3
PID
What is PID?
A PID (Proportional, Integral, Derivative) controller is a common technique used to control
a wide variety of machinery including vehicles, robots, and rockets.
A PID controller compared to a standard 2 and 3 level line follower. The x-axis is the light sensor reading. The y-axis is the
amount of turn. Note that the threshold for the 2 level and 3 level line following is 50.
Page 4
We will construct a PID line follower which…
• Moves the robot forward.
• Uses light sensor in port 2 to follow the line.
• Follows the left-hand-side edge of the line.
2
B
C
Page 5
PID Pseudocode – Initial variables to be used
Let “Kp” = some number
Let “Ki” = some number
Let “Kd” = some number
Let “Tp” (target power) = some power level
Let “Integral” = 0
Let “Derivative” = 0
Let “Last Error” = 0
Page 6
Pseudocode – some calculations to perform
Reset rotation sensor B
Begin Loop
Let “Error” = light sensor intensity reading – (minus) 50
Let “Integral” = “Error” + (plus) “Integral”
Let “Derivative” = “Error” – (minus) “Last Error”
Let “PTerm” = “Kp” x (times) “Error”
Let “ITerm” = “Ki” x (times) “Integral”
Let “DTerm” = “Kd” x (times) “Derivative”
Let “Turn” = “PTerm” + “ITerm” + “DTerm”
Let “Turn” = Turn / (divided by) 100
Let “PowerB” = “Tp” + (plus) “Turn”
Let “PowerC” = “Tp” - (minus) “Turn”
Let “LastError” = “Error”
Page 7
Pseudocode – establish power levels
If “Power B” > 0, then motor block B forward unlimited at “Power B”
power level,
else motor block B reverse unlimited at negative “Power B”
power level but with direction or movement reversed
(We want a negative number to mean that the motor should
reverse direction. But the data port on a NXT-G MOTOR block
does not understand that. The power level is always a number
between 0 and +100. The motor's direction is controlled by a
different input port. Negative motor power needs to be made
into a positive number and the motor direction needs to be
reversed on the control panel
If “Power C” > 0, then motor block C forward unlimited at “Power C”
power level,
else motor block CB reverse unlimited at negative “Power C” power
level but with direction or movement reversed
End Loop
Stop Motors C and B
Page 8
PID Calculations for “P”
PID - Illustration of Power Levels for Each Motor
Error
Kp
-50
-49
-48
-47
-46
-45
-44
-43
-42
-41
-40
-39
-38
-37
-36
-35
-34
-33
-32
-31
-30
-29
-28
-27
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Trunc
Kp*Error (Kp*Erro
Kp*Error /100
r/100)
-2000
-1960
-1920
-1880
-1840
-1800
-1760
-1720
-1680
-1640
-1600
-1560
-1520
-1480
-1440
-1400
-1360
-1320
-1280
-1240
-1200
-1160
-1120
-1080
-1040
-1000
-960
-920
-880
-840
-800
-760
-720
-680
-20.0
-19.6
-19.2
-18.8
-18.4
-18.0
-17.6
-17.2
-16.8
-16.4
-16.0
-15.6
-15.2
-14.8
-14.4
-14.0
-13.6
-13.2
-12.8
-12.4
-12.0
-11.6
-11.2
-10.8
-10.4
-10.0
-9.6
-9.2
-8.8
-8.4
-8.0
-7.6
-7.2
-6.8
-20
-19
-19
-18
-18
-18
-17
-17
-16
-16
-16
-15
-15
-14
-14
-14
-13
-13
-12
-12
-12
-11
-11
-10
-10
-10
-9
-9
-8
-8
-8
-7
-7
-6
TP
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
PID - Illustration of Power Levels for Each Motor
Power
Power
Motor B Motor C Error
20
21
21
22
22
22
23
23
24
24
24
25
25
26
26
26
27
27
28
28
28
29
29
30
30
30
31
31
32
32
32
33
33
34
60
59
59
58
58
58
57
57
56
56
56
55
55
54
54
54
53
53
52
52
52
51
51
50
50
50
49
49
48
48
48
47
47
46
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Kp
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Trunc
Kp*Error (Kp*Erro
Kp*Error /100
r/100)
-640
-600
-560
-520
-480
-440
-400
-360
-320
-280
-240
-200
-160
-120
-80
-40
0
40
80
120
160
200
240
280
320
360
400
440
480
520
560
600
640
-6.4
-6.0
-5.6
-5.2
-4.8
-4.4
-4.0
-3.6
-3.2
-2.8
-2.4
-2.0
-1.6
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
6.0
6.4
-6
-6
-5
-5
-4
-4
-4
-3
-3
-2
-2
-2
-1
-1
0
0
0
0
0
1
1
2
2
2
3
3
4
4
4
5
5
6
6
TP
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Page 9
PID - Illustration of Power Levels for Each Motor
Power
Power
Motor B Motor C
34
34
35
35
36
36
36
37
37
38
38
38
39
39
40
40
40
40
40
41
41
42
42
42
43
43
44
44
44
45
45
46
46
46
46
45
45
44
44
44
43
43
42
42
42
41
41
40
40
40
40
40
39
39
38
38
38
37
37
36
36
36
35
35
34
34
Error
Kp
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Trunc
Kp*Error (Kp*Erro
Kp*Error /100
r/100)
720
760
800
840
880
920
960
1000
1040
1080
1120
1160
1200
1240
1280
1320
1360
1400
1440
1480
1520
1560
1600
1640
1680
1720
1760
1800
1840
1880
1920
1960
2000
7.2
7.6
8.0
8.4
8.8
9.2
9.6
10.0
10.4
10.8
11.2
11.6
12.0
12.4
12.8
13.2
13.6
14.0
14.4
14.8
15.2
15.6
16.0
16.4
16.8
17.2
17.6
18.0
18.4
18.8
19.2
19.6
20.0
7
7
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
14
14
14
15
15
16
16
16
17
17
18
18
18
19
19
20
TP
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
Power
Power
Motor B Motor C
47
47
48
48
48
49
49
50
50
50
51
51
52
52
52
53
53
54
54
54
55
55
56
56
56
57
57
58
58
58
59
59
60
33
33
32
32
32
31
31
30
30
30
29
29
28
28
28
27
27
26
26
26
25
25
24
24
24
23
23
22
22
22
21
21
20
Questions?
Page 10