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MetricsExample.m
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MetricsExample.m
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%Author: Iryna Borshchova;
%Date: Nov 29, 2021
%Organization: FRL NRC Ottawa
% Copyright (c) 2022 National Research Council Canada
clear all;
%Rounding alpha
Ndecimals = 2 ;
f = 10.^Ndecimals ;
% Own UAS with the following characteristics
nz = 1.4; % 1.5g turn considered reasonable for a UAS
time_resol=0.1; %time resolution for approximation
ground_speed_h_vect = [60]; %m/s
ground_int_speed = 30; %Intruder ground speed m/s
sigma_al=0; %assume perfect position information for now
sigma_cross=0;
DMOD=152; %collision bubble
t_sim=190;
post_col=5; % 5 sec post-collision
% wind
wind_speed=5; % in M/s
mission_length=0;
blind_zone=100;
sensor_unc=150;
own_unc=10;
maxBank = 45;
maxRollRate = 10; % 10 Deg/s roll rate
wind_dir=90; % Is direction wind is coming from
azimuth_vect =[-179.75:0.25:179.75];
sensor_rate=2.5; %sec, rate of revisit
scans_track=5; % scans needed to establish the track after detection
t_track=sensor_rate*scans_track; %sec required for a sensor to establish a track on the intruder target
t_warn=15; %sec, to give to a pilot upon execution of CA maneuver ; 0 means automatic
t_link=3;
t_delta=t_track+t_warn+t_link;
% figure for polar plot
figure(1);
rng = polaraxes;
figure(2);
d_hdg = polaraxes;
figure(3);
closvel = polaraxes;
% Find wind velocity components
vx_w=wind_speed*sin(wind_dir/180*pi);
vy_w=wind_speed*cos(wind_dir/180*pi);
R_min_m = NaN(1, length(azimuth_vect));
R_min_m_over = NaN(1, length(azimuth_vect));
%loop through UAV speeds
for ii=1:length(ground_speed_h_vect)
ground_speed_h = ground_speed_h_vect(ii);
% Loop through each azimuth:
for k=1:length(azimuth_vect)
% initialize arrays
arraySize = (t_sim+post_col)/time_resol;
y_h = zeros(1, arraySize);
y_i = zeros(1, arraySize);
x_h = zeros(1, arraySize);
x_i = zeros(1, arraySize);
vy_h = zeros(1, arraySize);
vy_i = zeros(1, arraySize);
vx_h = zeros(1, arraySize);
vx_i = zeros(1, arraySize);
% calculate the collision Alpha using intruder and ownship ground
% speeds
[alpha]=round(calculate_alpha(ground_speed_h, ground_int_speed, azimuth_vect(k))*f)/f;
if (alpha ~=0 && alpha ~=180 && alpha ~=-180)
%calculate the Beta angle (wrap to 180)
beta = 180-alpha;
if (beta) > 180
beta = beta - 360;
elseif beta < -180
beta = beta + 360;
end
psi_i= mod((360-alpha)*pi/180, 2*pi); % intruder heading in rads
psi_h = 0; % ownship heading north initially;
beta_rad = beta*pi/180;
% origin at Tcpa, ownship heading north for simplicity
% let's calculate ownship initial conditions
% i) positions (earth referenced)
% ii) Velocities (earth referenced)
vx_h(1)=ground_speed_h*sin(psi_h);
vy_h(1)=ground_speed_h*cos(psi_h);
x_h(1) = 0;
y_h(1) = -ground_speed_h*t_sim;
% let's calculate intruder initial conditions;
% have ground speed info
% i) positions (earth referenced)
% ii) Velocities (earth referenced)
%offset from CPA
vx_i(1)=ground_int_speed*sin(psi_i);
vy_i(1)=ground_int_speed*cos(psi_i);
x_i(1) = ground_int_speed*t_sim*sin(beta_rad);
y_i(1) = ground_int_speed*t_sim*cos(beta_rad);
% calculate avoidance options
[turn_angles, cutoff, t2, t2_miss_dist, azimuth, infov]=avoidSimplified(x_h(1), y_h(1),vx_h(1), vy_h(1),...
x_i(1),y_i(1), vx_i(1), vy_i(1), sigma_al,...
sigma_cross, time_resol,nz,DMOD, vx_w, vy_w, maxBank, maxRollRate);
% pref manuevre turn and time is the first element in the array
pref_man_time=t2(1);
pref_man_turn=turn_angles(1);
% the next block is needed to establish minimim range
% requirements
host_vel = [vx_h(1);vy_h(1)];
intr_vel = [vx_i(1);vy_i(1)];
vel_rel = (host_vel-intr_vel);
host_pos = [x_h(1);y_h(1)];
intr_pos = [x_i(1);y_i(1)];
pos_rel = (host_pos-intr_pos);
vvel = dot(vel_rel,vel_rel);
posvel = dot(pos_rel,vel_rel);
if vvel > 0
Tcpa = -posvel/vvel; % time to closest point of approach
else
Tcpa= 0;
end
posvel = dot(pos_rel,vel_rel);
if posvel < 0 % posvel < 0 iff aircraft are converging in horizontal plane
Taumod = (DMOD^2-dot(pos_rel,pos_rel))/dot(pos_rel,vel_rel); % modified tau
else
Taumod = -1;
end
if Taumod < 0
Taumod=-1;
end
tm(k)=Taumod-pref_man_time+t_delta;
% calculate min sensor range
R_min_m(k)=tm(k)*sqrt(vvel)+blind_zone+mission_length+sensor_unc+own_unc;
if pref_man_turn>=0
Delta_hdg_r(k)=pref_man_turn;
azim_r(k)=azimuth_vect(k);
Delta_hdg_l(k)=NaN;
azim_l(k)=NaN;
else
Delta_hdg_l(k)=pref_man_turn;
azim_l(k)=azimuth_vect(k);
Delta_hdg_r(k)=NaN;
azim_r(k)=NaN;
end
%those are needed to plot a mesh
clos_vel(k)=sqrt(vvel);
% calculate avoidance turns with wind
for time=2:(t_sim+post_col)/time_resol
% this block is for the straight line before the turn
if(time<(pref_man_time)/time_resol)
x_h(time)=x_h(time-1) + vx_h(time-1)*time_resol;
y_h(time)=y_h(time-1) + vy_h(time-1)*time_resol;
vx_h(time)=vx_h(time-1);
vy_h(time)=vy_h(time-1);
%update intruder info
y_i(time) = y_i(time-1) +ground_int_speed*cos(psi_i)*time_resol;
x_i(time) = x_i(time-1) + ground_int_speed*sin(psi_i)*time_resol;
else
%calculate track to know when to stop turning
track=wrapTo180(atan2(vx_h(time-1),vy_h(time-1))*180/pi);
if (abs(track)<abs(wrapTo180(pref_man_turn+psi_h)))
g=9.80665;
air_speed_h=sqrt((vx_h(time-1)+vx_w)*(vx_h(time-1)+vx_w)+(vy_h(time-1)+vy_w)*(vy_h(time-1)+vy_w));
R = air_speed_h*air_speed_h/g/sqrt(nz*nz-1.0);
omega = -sign(pref_man_turn)*air_speed_h/R;
%use coordinated turn model
x_h(time)=x_h(time-1) + time_resol*vx_h(time-1)-omega*time_resol*time_resol/2*vy_h(time-1);
vx_h(time)=vx_h(time-1)*(1-omega*time_resol*omega*time_resol/2) -omega*time_resol*vy_h(time-1);
y_h(time)=vx_h(time-1)*omega*time_resol*time_resol/2+y_h(time-1)+time_resol*vy_h(time-1);
vy_h(time)=vx_h(time-1)*omega*time_resol+(1-omega*time_resol*omega*time_resol/2)*vy_h(time-1);
%update intruder info
y_i(time) = y_i(time-1) +ground_int_speed*cos(psi_i)*time_resol;
x_i(time) = x_i(time-1) + ground_int_speed*sin(psi_i)*time_resol;
else %end of turn; back to straight line
vx_h(time)=vx_h(time-1);
vy_h(time)=vy_h(time-1);
x_h(time)=x_h(time-1) + vx_h(time-1)*time_resol;
y_h(time)=y_h(time-1) + vy_h(time-1)*time_resol;
%update intruder info
y_i(time) = y_i(time-1) +ground_int_speed*cos(psi_i)*time_resol;
x_i(time) = x_i(time-1) + ground_int_speed*sin(psi_i)*time_resol;
end
end
end
else
R_min_m(k)=NaN;
tm(k)=NaN;
Delta_hdg_r(k)=NaN;
azim_r(k)=NaN;
Delta_hdg_l(k)=NaN;
azim_l(k)=NaN;
az(ii,k)=NaN;
clos_vel(k)=NaN;
end % end for alpha
% calculate the collision Alpha using intruder and ownship ground
% speeds for overtake
[alpha]=round(calculate_alpha_ov(ground_speed_h, ground_int_speed, azimuth_vect(k))*f)/f;
if (alpha ~=0 && alpha ~=180 && alpha ~=-180)
%calculate the Beta angle (wrap to 180)
beta = 180-alpha;
if (beta) > 180
beta = beta - 360;
elseif beta < -180
beta = beta + 360;
end
psi_i= mod((360-alpha)*pi/180, 2*pi); % intruder heading in rads
psi_h = 0; % ownship heading north initially;
beta_rad = beta*pi/180;
% origin at Tcpa, ownship heading north for simplicity
% let's calculate ownship initial conditions
% i) positions (earth referenced)
% ii) Velocities (earth referenced)
vx_h(1)=ground_speed_h*sin(psi_h);
vy_h(1)=ground_speed_h*cos(psi_h);
x_h(1) = 0;
y_h(1) = -ground_speed_h*t_sim;
% let's calculate intruder initial conditions;
% have ground speed info
% i) positions (earth referenced)
% ii) Velocities (earth referenced)
%offset from CPA
vx_i(1)=ground_int_speed*sin(psi_i);
vy_i(1)=ground_int_speed*cos(psi_i);
x_i(1) = ground_int_speed*t_sim*sin(beta_rad);
y_i(1) = ground_int_speed*t_sim*cos(beta_rad);
% calculate avoidance options
[turn_angles, cutoff, t2, t2_miss_dist, azimuth, infov]=avoidSimplified(x_h(1), y_h(1),vx_h(1), vy_h(1),...
x_i(1),y_i(1), vx_i(1), vy_i(1), sigma_al,...
sigma_cross, time_resol,nz,DMOD, vx_w, vy_w, maxBank, maxRollRate);
% pref manuevre turn and time is the first element in the array
pref_man_time=t2(1);
pref_man_turn=turn_angles(1);
% the next block is needed to establish minimim range
% requirements
host_vel = [vx_h(1);vy_h(1)];
intr_vel = [vx_i(1);vy_i(1)];
vel_rel = (host_vel-intr_vel);
host_pos = [x_h(1);y_h(1)];
intr_pos = [x_i(1);y_i(1)];
pos_rel = (host_pos-intr_pos);
vvel = dot(vel_rel,vel_rel);
posvel = dot(pos_rel,vel_rel);
if vvel > 0
Tcpa = -posvel/vvel; % time to closest point of approach
else
Tcpa= 0;
end
posvel = dot(pos_rel,vel_rel);
if posvel < 0 % posvel < 0 iff aircraft are converging in horizontal plane
Taumod = (DMOD^2-dot(pos_rel,pos_rel))/dot(pos_rel,vel_rel); % modified tau
else
Taumod = -1;
end
if Taumod < 0
Taumod=-1;
end
tm(k)=Taumod-pref_man_time+t_delta;
% calculate min sensor range
R_min_m_over(k)=tm(k)*sqrt(vvel)+blind_zone+mission_length+own_unc+sensor_unc;
if pref_man_turn>=0
Delta_hdg_r(k)=pref_man_turn;
azim_r(k)=azimuth_vect(k);
Delta_hdg_l(k)=NaN;
azim_l(k)=NaN;
else
Delta_hdg_l(k)=pref_man_turn;
azim_l(k)=azimuth_vect(k);
Delta_hdg_r(k)=NaN;
azim_r(k)=NaN;
end
%those are needed to plot a mesh
clos_vel_over(k)=sqrt(vvel);
% calculate avoidance turns with wind
for time=2:(t_sim+post_col)/time_resol
% this block is for the straight line before the turn
if(time<(pref_man_time)/time_resol)
x_h(time)=x_h(time-1) + vx_h(time-1)*time_resol;
y_h(time)=y_h(time-1) + vy_h(time-1)*time_resol;
vx_h(time)=vx_h(time-1);
vy_h(time)=vy_h(time-1);
%update intruder info
y_i(time) = y_i(time-1) +ground_int_speed*cos(psi_i)*time_resol;
x_i(time) = x_i(time-1) + ground_int_speed*sin(psi_i)*time_resol;
else
%calculate track to know when to stop turning
track=wrapTo180(atan2(vx_h(time-1),vy_h(time-1))*180/pi);
if (abs(track)<abs(wrapTo180(pref_man_turn+psi_h)))
g=9.80665;
air_speed_h=sqrt((vx_h(time-1)+vx_w)*(vx_h(time-1)+vx_w)+(vy_h(time-1)+vy_w)*(vy_h(time-1)+vy_w));
R = air_speed_h*air_speed_h/g/sqrt(nz*nz-1.0);
omega = -sign(pref_man_turn)*air_speed_h/R;
%use coordinated turn model
x_h(time)=x_h(time-1) + time_resol*vx_h(time-1)-omega*time_resol*time_resol/2*vy_h(time-1);
vx_h(time)=vx_h(time-1)*(1-omega*time_resol*omega*time_resol/2) -omega*time_resol*vy_h(time-1);
y_h(time)=vx_h(time-1)*omega*time_resol*time_resol/2+y_h(time-1)+time_resol*vy_h(time-1);
vy_h(time)=vx_h(time-1)*omega*time_resol+(1-omega*time_resol*omega*time_resol/2)*vy_h(time-1);
%update intruder info
y_i(time) = y_i(time-1) +ground_int_speed*cos(psi_i)*time_resol;
x_i(time) = x_i(time-1) + ground_int_speed*sin(psi_i)*time_resol;
else %end of turn; back to straight line
vx_h(time)=vx_h(time-1);
vy_h(time)=vy_h(time-1);
x_h(time)=x_h(time-1) + vx_h(time-1)*time_resol;
y_h(time)=y_h(time-1) + vy_h(time-1)*time_resol;
%update intruder info
y_i(time) = y_i(time-1) +ground_int_speed*cos(psi_i)*time_resol;
x_i(time) = x_i(time-1) + ground_int_speed*sin(psi_i)*time_resol;
end
end
end
else
R_min_m_over(k)=NaN;
tm(k)=NaN;
Delta_hdg_r(k)=NaN;
azim_r(k)=NaN;
Delta_hdg_l(k)=NaN;
azim_l(k)=NaN;
az(ii,k)=NaN;
clos_vel_over(k)=NaN;
end % end for alpha
end %for azimuth
polarplot(d_hdg,azim_r'*pi/180, Delta_hdg_r, 'LineWidth', 0.5, 'Color', 'g');
d_hdg.ThetaDir = 'clockwise';
d_hdg.ThetaZeroLocation = 'top';
grid on
hold (d_hdg, 'on')
polarplot(d_hdg,azim_l'*pi/180, abs(Delta_hdg_l), 'LineWidth', 0.5, 'Color', 'r');
d_hdg.ThetaDir = 'clockwise';
d_hdg.ThetaZeroLocation = 'top';
grid on
hold (d_hdg, 'on')
polarplot(rng,azimuth_vect'*pi/180, R_min_m'/1000, 'LineWidth', 0.5);
rng.ThetaDir = 'clockwise';
rng.ThetaZeroLocation = 'top';
grid on
hold (rng, 'on')
polarplot(rng,azimuth_vect'*pi/180, R_min_m_over'/1000, 'LineWidth', 0.5);
rng.ThetaDir = 'clockwise';
rng.ThetaZeroLocation = 'top';
grid on
hold (rng, 'on')
polarplot(closvel,azimuth_vect'*pi/180, clos_vel', 'LineWidth', 0.5);
closvel.ThetaDir = 'clockwise';
closvel.ThetaZeroLocation = 'top';
grid on
hold (closvel, 'on')
polarplot(closvel,azimuth_vect'*pi/180, clos_vel_over', 'LineWidth', 0.5);
closvel.ThetaDir = 'clockwise';
closvel.ThetaZeroLocation = 'top';
grid on
hold (closvel, 'on')
end% for loop ground speed vector
legend(d_hdg,'Right turn','Left turn', 'Location', 'northeastoutside');
title(d_hdg,['Delta Hdg (deg), Load Factor ' num2str(nz) ', Intruder Speed ' num2str(ground_int_speed) ' (mps)'])
hold (d_hdg, 'off')
%
legend(rng,[num2str(ground_speed_h_vect),repmat(' mps',[length(ground_speed_h_vect'),1])], 'Location', 'northeastoutside');
title(rng,['Rmin (km), Load Factor ' num2str(nz) ', Intruder Speed ' num2str(ground_int_speed) ' (mps)'])
hold (rng, 'off')
legend(closvel,[num2str(ground_speed_h_vect),repmat(' mps',[length(ground_speed_h_vect'),1])], 'Location', 'northeastoutside');
title(closvel,['Closing Vel(m/s), Load Factor ' num2str(nz) ', Intruder Speed ' num2str(ground_int_speed) ' (mps)'])
hold (closvel, 'off')
function h = circle2(x,y,r)
d = r*2;
px = x-r;
py = y-r;
h = rectangle('Position',[px py d d],'Curvature',[1,1], 'EdgeColor', 'r');
% daspect([1,1,1])
end