Trajectory tracking using an open loop controller

In this problem, first we will generate a trajectory using the differential flatness technique. Then, we will generate the control inputs for the robot to navigate this desired trajectory using open loop controller techniques.

Consider the equations for the dynamically extended unicycle robot,

$x^{}(t)=V(t)cos(t)$

$y^{}(t)=V(t)sin(t)$

$V^{}(t)=a(t)$

${}^{}(t)=(t)$

The initial conditions are: $x(0)=0,y(0)=0,v(0)=0\mathrm{.}5,(0)=-\frac{}{2}$

$x(t_t)=5,y(t_t)=5,v(t_f)=0\mathrm{.}5,(t_f)=-\frac{}{2}$ where $t_t=15$

Here the controls are $a(t)$ and $(t).$

a$)$ Show this system is differentially flat with flat output $z=(x,y).$