Truck

Control: Truck Backer-Upper

Statement of Problem To back the truck to a loading bay, The truck should approach the bay at 90 degree angle

Fuzzy Systems ToolBox, Mark Beale and Howard Demuth



The truck is making a right turn in backing.



Starting Zone



INPUT Horizontal position Fuzzy Sets

Far left, left, center, right, far right

Far left left

Center

right Far right



INPUT Truck Angle Fuzzy Sets

0, 60, 120, 180, 240, 300, 360

0 60 120 180 240 300 360



OUTPUT Steering Angle Fuzzy Sets

Hard left, left, soft left, center, soft right, right, hard right

centerSoft LLeftr Soft R RightHard L Hard R



Truck backing rules



MATLAB Rule definition A = table(1:5,1:7); C = [5; 6; 6; 7; 7; 3; 5; 6; 7; 7; 3; 3; 6; 6; 7; 2; 2; 4; 6; 6; 1; 2; 2; 5; 5; 1; 1; 2; 3; 3; 1; 1; 2; 2; 3;];



MATLAB Z = group(xposS, xposG, angleS, angleG, SteeringS, SteeringG); S = [xpos; ypos; phi]; Theta = frule(A,C,Z, [S(1);S(3)]);

Note: frule calculates the steering anglebased on the current values of the xposand phi


Assumption: Truck travel at constant velocity V and truck length is L.State Variables: x,y, f = horizontal coordinate/angle of the truck q = steering angle

Control: Simulating the Truck


Nonlinear equationsdescribe the behavior

of truck



function ds=trukmod(s,u) % s(1) =x, s(2)=y,s(3)= f, u = q

L = 1; % Length of truck. (Distance between wheels.) v = 1; % Velocity of truck. % STATES pos = s(1) + sqrt(-1)*s(2); angle = s(3); % DERIVATIVES dpos = v*cos(u)*exp(j*(angle-pi/2)); dangle = v*sin(u)/L; ds = [real(dpos); imag(dpos); dangle];



% assume time step = 0.2 seconddt = 0.2;For I=1:100

if rem(I,5) == 1 % Evaluate controller once a second

% (5 time steps *0.2 seconds) theta = frule(A,C,Z,[s(1);s(3)]);

end s = s + dt * truckmod (s,theta);end

Control: Simulating theControlled Truck


0 20 40 60 80 100-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0



0 10 20 30 40 50 60 70 80 9015

20

25

30

35

40

45

50Horizontal Position Response

Time (Seconds)

Hori

zonta

l Posi

tion (

Mete

rs)



0 10 20 30 40 50 60 70 80 90-70

-60

-50

-40

-30

-20

-10

0

10Vertical Position Response

Time (Seconds)

Vert

ical P

osi

tion (M

ete

rs)



0 10 20 30 40 50 60 70 80 9050

100

150

200

250

300

350

400Truck Angle Response

Time (Seconds)

Tru

ck A

ngle

(D

egre

es)



0 10 20 30 40 50 60 70 80 90-30

-25

-20

-15

-10

-5

0

5

10Steering Angle Response

Time (Seconds)

Ste

eri

ng A

ngle

(D

egre

es)

Control: Improving the truckcontroller


0 20 40 60 80 100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Universe of Discourse for Horizontal Position

Horizontal Position in meters

Gra

de



0 20 40 60 80 100-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0



0 20 40 60 80 100 120 14015

20

25

30

35

40

45

50

55Horizontal Position Response

Time (Seconds)

Hori

zonta

l Posi

tion (M

ete

rs)



0 20 40 60 80 100 120 140-80

-70

-60

-50

-40

-30

-20

-10

0

10Vertical Position Response

Time (Seconds)

Vert

ical P

osi

tion (M

ete

rs)



0 20 40 60 80 100 120 1400

50

100

150

200

250

300

350

400Truck Angle Response

Time (Seconds)

Tru

ck A

ngle

(D

egre

es)



0 20 40 60 80 100 120 140-30

-25

-20

-15

-10

-5

0

5

10Steering Angle Response

Time (Seconds)

Ste

eri

ng Angle

(De

gre

es)

Truck

Documents

Transcript of Truck