Simulate the differential equations for the unicycle robot model using Euler's method for tin$[0,10]$

and time step $t=0\mathrm{.}1.$ Use the following control input:

$v=1,0t10$

$=\{\begin{array}{cc}3,& 0\mathrm{.}5t1\mathrm{.}5\end{array}$

$-3,2t3$

$-3,4t5$

$3,6t7$

$-3,8t9$

$0$ all other $t$

With initial conditions $x(0)=0,y(0)=0,(0)=1.$

a$)$ Plot $x$ vs $y,x$ vs $t,y$ vs t and $$ vs t$.$ Submit your code and plots.

b$)$ If you plot $x$ vs $y$ for each time step, you'll create a movie of the robot moving in $2$D space.

Feel free to simulate different initial conditions and control input sequences to gain a greater

understanding.