Open loop controller performance in the presence of noise or disturbance

In problem $5($c$),$ your robot should track the trajectory perfectly. This is because there is no noise or

disturbance in the system. If noise and disturbance is present, which is the case for real systems, the robot

won't be able to track the trajectory with an open loop controller. We will see this in this exercise.

We can randomly inject noise or disturbances into the system using the Gaussian $($Normal$)$ distribution.

Inject noise in the $V$ and $$ equations in the following way,

$V(t+t)=V(t)+ta(t)+0\mathrm{.}01**$ randn

$(t+t)=(t)+t(t)+0\mathrm{.}001**$ randn

Here $"{0\mathrm{.}01}^{**}$ randn" is a random number generated from a Gaussian distribution with mean $0$ and standard

deviation $0\mathrm{.}01.$ Similarly, $"{0\mathrm{.}001}^{**}$ randn" is a random number generated from a Gaussian distribution with

mean $0$ and standard deviation $0\mathrm{.}001.$

With this noise injection, integrate the unicycle equations using Euler's method and the open loop

controller of problem $5($c$).$ Plot the result for time step $t=0\mathrm{.}01.$ You should be able to see the robot

deviate from the desired trajectory. Submit your code and screenshots.