Good visualization in a car following model in MATLAB

Please I am working on a matlab code for a car-following model and I used ode45 for the solution.

The positions(solution) for each car is good, but the visualization is not correct.

Please, I need help or assistance to make the visualization better.

The code has been attached below.

Thank you.

function xdot = f(t,x)
    N = length(x); % number of vehicles
    umax = 130/3.6; % maximum speed in m/s
    L =1000;
    xdot = zeros(N,1); % initialize derivative vector
    for i = 1:N % loop over all vehicles
        if i < N % use periodic boundary conditions
            si = x(i+1) - x(i); % spacing between cars
        else
            si = (x(1) + L) - x(i);
        end
        if si > 100 % speed is maximum
            xdot(i) = umax;
        elseif si > 5 && si <= 100 % speed decreases linearly
            xdot(i) = ((si - 5)/95)*umax;
        else % speed is zero from 5 downward 
            xdot(i) = 0;
        end
    end
end

N = 50; % number of vehicles
T = 60; % simulation time in seconds
L = 1000;% Total length of the circular track in meters
R = L/(2*pi); %Radius of the circle to be created in meters
x0 = rand(N,1)*L; %Building a random starting point
x0 = sort(x0); %Looking for random starting point

[t,x] = ode45(@f,[0 T],x0); % solve ODEs using ode45

%figure; % create new figure
hold on; % keep previous plots
xlim([-R-5 R+5]) % Calibration of x-axis
ylim([-R-5 R+5]) % Calibration of y-axis

for k = 1:length(t) % loop over time steps
    cla; % clear previous plot
    plot(R*cos(x(k,:)),R*sin(x(k,:)),'.b','MarkerSize',30);% plot current positions
    title(['Time: ' num2str(t(k)) ' s']); % display time
    pause(0.1); % pause for animation speed
end

Answer 1

[albara]

I see that you are using a circular track and plotting the vehicles as points on the circle. One suggestion I have is to improve the visualization by displaying the cars as arrows instead of points. This would provide better visual cues about the car's direction and position on the track. Here's an updated version of your code to achieve this:

function xdot = f(t,x)

% ... (the code remains the same as in the original implementation)

end

N = 50; % number of vehicles

T = 60; % simulation time in seconds

L = 1000;% Total length of the circular track in meters

R = L/(2*pi); %Radius of the circle to be created in meters

x0 = rand(N,1)*L; %Building a random starting point

x0 = sort(x0); %Looking for random starting point

[t,x] = ode45(@f,[0 T],x0); % solve ODEs using ode45

%figure; % create new figure

hold on; % keep previous plots

xlim([-R-5 R+5]) % Calibration of x-axis

ylim([-R-5 R+5]) % Calibration of y-axis

% Plot the circular track

theta_track = linspace(0, 2*pi, 1000);

x_track = R * cos(theta_track);

y_track = R * sin(theta_track);

plot(x_track, y_track, 'k', 'LineWidth', 2);

for k = 1:length(t) % loop over time steps

cla; % clear previous plot

% Plot the circular track again

plot(x_track, y_track, 'k', 'LineWidth', 2);

% Plot the cars as arrows

for i = 1:N

xi = R * cos(x(k,i));

yi = R * sin(x(k,i));

dx = -R * sin(x(k,i));

dy = R * cos(x(k,i));

quiver(xi, yi, dx, dy, 0.05, 'b', 'LineWidth', 2, 'MaxHeadSize', 2);

end

title(['Time: ' num2str(t(k)) ' s']); % display time

pause(0.1); % pause for animation speed

end

This updated code plots the circular track itself and displays the cars as arrows to better represent their positions and directions. The length of the arrows is fixed, but you could potentially adjust them to reflect the speed of the cars if desired. This should make the visualization more informative and easier to understand.

Important: There may be some mistakes in this answer Experts can tell if there are any mistakes and you might find better answer

[Kwasi]

Thank you very much for the assistance, but still the visualization is not good.