$[$For this question submit the following: a $.$m file called runme$\_$q$2.$m$,$ further upload this code separately as a $.$txt file on Canvas $-$ do not combine items into a $.$zip file.$].$ Let the initial co$-$ordinates of your robot be $(x,y)=(1,1),$ and the initial orientation $=0$ radians. The robot is to navigate to point $(5,0\mathrm{.}6).$ Use the feedback linearization technique from class to solve this problem by writing some code in Matlab. Use $h=0\mathrm{.}2,$ let time go from zero to $10$ seconds in steps of $0\mathrm{.}1$ s $.$ Assume $K=\left[\begin{array}{cc}0\mathrm{.}5& 0\\ 0& 0\mathrm{.}5\end{array}\right].$ However, in this case you are also given that you have noisy measurements of the robots $x,y$ position, and the heading angle $.$ The $x,y,$ measurements are corrupted by zero mean i$.$i$.$d$.$ Gaussian noises with variances $0\mathrm{.}05$ each. Use an EKF to estimate the robot's pose, i$.$e$.$ hat$(x),$hat$(y),$hat$(),$ use these estimated states for your controller. Also assume that the 'states' required for you to formulate the EKF based state estimation problem are affected by zero mean i$.$i$.$d$.$ Gaussian noises with variances $0\mathrm{.}05$ each. Produce the following plots $($each plot is required for $4$ separate simulation runs$)$:

a$)$ A plot showing $x$ vs$.y$ and $x_h$ vs$.y_h-$ without the EKF, superimposed on each other using different colors$/$markers$/$ linestyles. Also show the start, and desired end point clearly on this plot. $(10$ Points$)$

b$)$ Above plots $-$ with an EKF. $(10$ Points$)$

c$)$ Plots $($separately$)$ of $$ vs$.t$ with and without the EKF. $(5$ Points$)$

d$)$ What can you observe in general from all the above plots with$/$without the

EKF? $(5$ Points$)$

$[$Hint: See 'manrobot.m$\text{'}$ and 'roboekf.m$\text{'}$ on Canvas, repurpose this code by integrating the required controller and generate the required plots. No ROS$/$Gazebo is needed for this question, this is a simulation that should run entirely in Matlab.$]$