Project $2$: Air Traffic Control Simulation

Introduction

One day in $2050,$ you are the air traffic controller sitting at the control tower at ATL, enjoying your

morning coffee. Suddenly, you receive a radio call saying that an airplane, A$1,$ declares an emergency

and needs to land first. Now, you look at the radar map in Figure $1$ and realize that the aircraft is

not the first in the landing queue. Your job is to land and park all three aircrafts in minimal time,

without violating any airspace, runway, and taxiway rule or regulation, with $A1$ being the first to

land and park at $P_3.$ The optimal landing order after A$1$ lands is for you to determine as well.

Objective:

Manage an emergency landing scenario for aircraft A$1,$ prioritizing it for landing and parking at $P_3,$

followed by $A_2$ and $A_3$ or $A_3$ and $A_2.$ Ensure efficient operations without violating airspace rules.

Key Elements:

Aircrafts: A$1,$ A$2,$ A$3.$

Parking: P$1,$ P$2,$ P$3.$

Some Useful Coordinates Information

A$1$: $0\mathrm{.}5$;$0\mathrm{.}1$;$\frac{}{2}.$

A$2$: $0$;$0\mathrm{.}3$;$-0\mathrm{.}2.$

A$3$: $0\mathrm{.}1$;$-0\mathrm{.}3$;$-0\mathrm{.}1.$

P$1$: $[0\mathrm{.}1$; o$].$

P$2$: $0\mathrm{.}2$;$0.$

$P_3$:$[0\mathrm{.}3$;$0].$

Airspace Rules and Regulations

General Rules

R$1$: Minimum separation of aircrafts in the air and on the runway: $0\mathrm{.}25m.$

R$2$: R$1$ does not apply to aircrafts on the taxiway.

R$3$: Do not fly out of the simulation boundary.

R$4$: On the boundary between $2$ areas, the limitations of the faster airspace apply.

R$5$: The center coordinates count as the position of the aircraft. Do not worry about the radius$/$width

of the aircraft.

Class F$($ast$)$ Airspace

$F_1$:$|w{|}_{\text{m}\text{a}\text{x}}=\frac{}{4}ra\frac{d}{s}.$

F$2$: $v_{\text{m}\text{i}\text{n}}=0\mathrm{.}05\frac{m}{s}.$

F$3$: $v_{\text{m}\text{a}\text{x}}=0\mathrm{.}08\frac{m}{s}.$

Class S$($low$)$ Airspace

S$1$: $|w|max=\frac{}{6}ra\frac{d}{s}.$

S$2$: $v_{\text{m}\text{i}\text{n}}=0\mathrm{.}03\frac{m}{s}.$

Ss: $v_{\text{m}\text{a}\text{x}}=0\mathrm{.}04\frac{m}{s}.$

Class X Airspace

$x_1$ : Entry is prohibited at any time.

Runway and Taxiway

T$1$: $|w{|}_{\text{m}\text{a}\text{x}}=\frac{}{2}ra\frac{d}{s}.$

T$2$: $v_{\text{m}\text{i}\text{n}}=0\frac{m}{s}.$

$T_3$:$v_{\text{m}\text{a}\text{x}}=0\mathrm{.}02\frac{m}{s}.$

GOALS:

G$1$: DESIGN ALGORITHM AND WRITE MATLAB CODE TO Park all $3$ aircrafts at the parking spots, with A$1$ at P$3.$ Orientation does not matter.

G$2$: DEVELOP MATLAB CODE TO Achieve G$1$ by a minimal number of iterations, with at most $1750$ iterations.

BASE STRUCTURE MATLAB CODE ON WHICH THE GOALS HAVE TO BE DEVELOPED:

$\%\%$ Simulator Skeleton File $-$ Project $2$

$\%$ This file provides the bare$-$bones requirements for interacting with the

$\%$ Robotarium. Note that this code won't actually run. You'll have to

$\%$ insert your own algorithm! If you want to see some working code, check

$\%$ out the 'examples' folder.

close all

$\%\%$ Get Robotarium object used to communicate with the robots$/$simulator

N $=3$;

r $=$ Robotarium$(\text{'}$NumberOfRobots$\text{'},$ N$,$ 'ShowFigure', true, 'InitialConditions', $[\mathrm{.}50\mathrm{.}1$;$\mathrm{.}1\mathrm{.}3-\mathrm{.}3$;pi$/2$ pi$-0\mathrm{.}2$ pi$-0\mathrm{.}1])$;

data $=[]$;

$\%$ Select the number of iterations for the experiment.

iterations $=1750$; $\%$ Do not change

$\%$ Other important variables

initpos$1=[\mathrm{.}5$; $\mathrm{.}1$; pi$/2]$;

initpos$2=[0$; $\mathrm{.}3$; pi$-0\mathrm{.}2]$;

initpos$3=[\mathrm{.}1$; $-\mathrm{.}3$; pi$-0\mathrm{.}1]$;

target $=[\mathrm{.}3\mathrm{.}2\mathrm{.}1$; $000]$;

targetalt $=[\mathrm{.}3\mathrm{.}1\mathrm{.}2$; $000]$;

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$ Place Static Variables Here $\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%$ Do not modify anything outside this area $\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

$\%$ var $=0$;

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%$ Do not modify anything outside this area $\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

$\%$ Iterate for the previously specified number of iterations

for t $=1$:iterations

$\%$ Retrieve the most recent poses from the Robotarium. The time delay is

$\%$ approximately $0\mathrm{.}033$ seconds

p $=$ r$.$get$\_$poses$()$;

$\%$ Plot the traces every $20$ iterations

if mod$($t$,20)==0$

plot$($p$(1,1),$p$(2,1),\text{'}$k$.\text{'},$p$(1,2),$p$(2,2),\text{'}$m$.\text{'},$p$(1,3),$p$(2,3),\text{'}$b$.\text{'})$;

end

$\%$ Success check with position tolerance embedded

if isequal$($round$($p$(1$:$2,$:$),2),$ target$)||$ isequal$($round$($p$(1$:$2,$:$),2),$ targetalt$)$

fprintf$(\text{'}$Success$!$ The final iteration number is $\%$d$.$

$\text{'},$ t$)$;

break

end

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$ Place Algorithm Here $\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

$\%\%\%\%\%\%\%\%\%\%\%\%\%\%$ Do not modify anything outside this area $\%\%\%\%\%\%\%\%\%\%\%\%\%\%\%$

$\%$ u $=???$;

$\%$ You can try with u $=[0\mathrm{.}030\mathrm{.}020\mathrm{.}01$; $000]$ first. Observe what happens to

$\%$ get a sense of how it works.

$\%\%\%\%\%\%\%\%\%\%$