$\%\%$ Define the artificial potential field parameters $\%$ Points of attraction xa $=70$; ya $=50$; $\%$ Location of obstacles nobs $=5$; xo $=[2030355065]$; yo $=[1325353845]$; $\%$ Size of obstacles $($rho$\_0)$ rho$\_0=[74534]$; $\%$ Constants. Ka $=1$; Kv $=20$; Kr $=[500350500250250]*1000$; mass $=5$; $\%\%$ Integration step. $\%$ initial conditions x$0=5$; y$0=5$; $\%$ Initialise simulation parameters x $=$ x$0$; y $=$ y$0$; vx $=0$; vy $=0$; terminate $=$ false; t $=0$; dt $=0\mathrm{.}01$; $\%$ Store variables for later assessment traj $=[]$; Fac $=[]$; Frc $=[]$; Fdc $=[]$; Fc $=[]$; while$($~terminate$)\%\%$ Check if reached destination rho $=$ sqrt$(($xa$-$x$)^2+($ya$-$y$)^2)$; if$($rho $<0\mathrm{.}1)$ terminate $=$ true; end $\%\%\%$ Calculate the conservative forces $\%$ Attractive force $($Fa$)$ Fa $=$ zeros$(2,1)$; $\%------$ INSERT YOUR CODE HERE $------$ Fac $=[$Fac Fa$]$; $\%$ Repulsive force $($Fr$)$ Fr $=$ zeros$(2,1)$; $\%------$ INSERT YOUR CODE HERE $------$ Frc $=[$Frc Fr$]$; $\%$ Damping force $($Fd$)$ Fd $=$ zeros$(2,1)$; $\%------$ INSERT YOUR CODE HERE $------$ Fdc $=[$Fdc Fd$]$; $\%$ Total force $($F$)\%------$ INSERT YOUR CODE HERE $------$ Fc $=[$Fc F$]$; $\%$ Velocity and Position $($vx$,$ vy$,$ x$,$ y$)$ through integrating the equations $\%------$ INSERT YOUR CODE HERE $------$ traj $=[$traj $[$x;y$]]$; $\%$plot the trajectory end $\%\%$ Display the results $\%$ Plot the trajectory figure$(1)$; $\%$ Now the attractive potential contour xmin $=0$; xmax $=80$; ymin $=0$; ymax $=60$; $[$X$,$Y$]=$ meshgrid$($xmin:$5$:xmax,ymin:$5$:ymax$)$; Z $=1\mathrm{.}0*(0\mathrm{.}5*$Ka$*$sqrt$(($X$-$xa$).^2+($Y$-$ya$).^2))$; Zmax $=$ max$($max$($Z$))$; Z $=10*$Z$/$Zmax; contour$($X$,$Y$,$Z$,50)$;hold on; plot$($traj$(1,1),$traj$(2,1),\text{'}$bo$\text{'},$'LineWidth',$6)$; plot$($xa$,$ya$,\text{'}$bx$\text{'},$'LineWidth',$10)$; xlabel$(\text{'}$x$($m$)\text{'})$; ylabel$(\text{'}$y$($m$)\text{'})$; axis$(\text{'}$equal$\text{'})$; $\%$ The obstacle contours for kk $=1$:nobs r $=0$:$0\mathrm{.}01$:rho$\_0($kk$)$; tht $=0$:$0\mathrm{.}1$:$2*$pi$+0\mathrm{.}1$; $[$THT$,$R$]=$ meshgrid$($tht$,$r$)$; Z $=0\mathrm{.}5*$Kr$($kk$)*(($sqrt$(($R$.*$cos$($THT$)).^2+($R$.*$sin$($THT$)).^2))-($rho$\_0($kk$))).^2$; Zmax $=$ max$($max$($Z$))$; Z $=10*$Z$/$Zmax; contour$($xo$($kk$)+$R$.*$cos$($THT$),$yo$($kk$)+$R$.*$sin$($THT$),$Z$,50)$; end $\%$ Draw the obstacle boundaries for jj $=1$:nobs tht $=0$:$0\mathrm{.}01$:$2*$pi; xobs $=$ xo$($jj$)+$rho$\_0($jj$)*$cos$($tht$)$; yobs $=$ yo$($jj$)+$rho$\_0($jj$)*$sin$($tht$)$; plot$($xobs$,$yobs,$\text{'}$:r$\text{'},$'LineWidth',$2\mathrm{.}0)$; end $\%\%$ Finally, plot the trajectory plot$($traj$(1,$:$),$traj$(2,$:$),\text{'}$g$\text{'},$'LineWidth',$2\mathrm{.}0)$; hold off; axis equal; axis tight; $$ Insert code in required space The task in term project $1$ is to implement the artificial potential function path planning algorithm for the drone scenario shown in figure TP$1.$ x $0504030201$ Figure TP$1$: Drone path scenario.The obstacles in the path of the drone have the size, coordinates and repulsive gain given in table TP$1$ below, Kr Obstacle Position $1(20,13)2(30,25)3(35,35)4(50,385(65,45$ Radius $74534.500000350000500000250000250000$ Table TP$1$: Obstacle parameters. Furthermore, the initial drone position is $(5,5)$ and the location of the desired target point is $(70,50).$ Your task is to complete the code template provided and to show that a feasible path can be generated using the artificial potential function method. The drone equations of motion can be represented by a simple double$-$integrator model in $2$ dimensions $($x$,$y$).$ Assume the vehicle has a mass of $5$kg$.$ The Potential functions should take the following form,Furthermore, the initial drone position is $(5,5)$ and the location of the desired target point is $(70,50).$ Your task is to complete the code template provided and to show that a feasible path can be generated using the artificial potential function method. The drone equations of motion can be represented by a simple double$-$integrator model in $2$ dimensions $($x$,$y$).$ Assume the vehicle has a mass of $5$kg$.$ The Potential functions should take the following form, Attractive: Ua Kap? $0\backslash$rho $>\backslash$Rho $\backslash$omicron $2$ Repulsive: U$,=$ K$,$ p $<$ PO Pr Pol where Pa $=($x $$ xa$)2+($y $$ ya$)2$ and Por $($x $$ Xobs$)2+($y $$ Yobs$).$ When developing the appropriate APF control law, you should also include an additional force proportional to the drone velocity as follows, Fx$,=-$K$,$ Vx$)$ F yy $=-$K$,$ Vy Remember to use the variable names specified in the template code for each of the simulation terms. Failure to do so will result in failure of the Matlab Grader tests. Once your code have passed all of the MATLAB Grader tests, you MUST press SUBMIT for marking.