HW1

Question 4:

>> R = [0.1729 -0.1468 0.9739 ; 0.9739 0.1729 -0.1468 ; -0.1468 0.9739 0.1729]

R =

0.1729 -0.1468 0.9739

0.9739 0.1729 -0.1468

-0.1468 0.9739 0.1729

>> eig(R)

ans =

-0.2406 + 0.9706i

-0.2406 - 0.9706i

1.0000

>>

>> [V, D] = eig(R)

V =

-0.2887 + 0.5000i -0.2887 - 0.5000i 0.5774

0.5774 0.5774 0.5774

-0.2887 - 0.5000i -0.2887 + 0.5000i 0.5774

D =

-0.2406 + 0.9706i 0 0

0 -0.2406 - 0.9706i 0

0 0 1.0000

The Eigenvector is a unit vector, around which the rotation happens.

Question 5:

Here is the matlab code to simulate:

function [ x, y, theta ] = diffDrive(x0, y0, theta0, v, omega, t, delta)

%diffDrive simulates the movement of a differential driving robot

x = zeros([1, t])

y = zeros([1, t])

theta = zeros([1, t])

for i = 1 : t

if i==1

x(1) = x0 + (v * cos(theta0) * delta)

y(1) = y0 + (v * sin(theta0) * delta)

theta(1) = theta0 + omega * delta

else

x(i) = x(i-1) + (v * cos(theta(i-1)) * delta)

y(i) = y(i-1) + (v * sin(theta(i-1)) * delta)

theta(i) = theta(i-1) + omega*delta

end

plot(x , y)

end

How is the path affected by the choice of δt?

As you can see , increasing the delta, reduces the detail of the plotted image:

To make this image I used: diffDrive(100, 50, 45, 1, 2, 10, 0.5)

To make this image I used: diffDrive(100, 50, 45, 1, 2, 100, 0.25)

To make this image I used: diffDrive(100, 50, 45, 1, 2, 100, 0.5)