Moving a dot at a constant velocity in a circular path in MATLAB

Hello, I want to present a dot in a rectangular field and make it move in the field at a constant velocity in a circular path (the position of the dot has to be known with respect to time). Additionally I want to manipulate the initial position in which it will be presented. Can anyone help me ?

[James Tursa]

Have you written any code so far? A simple formulation something like the following would get you the position of the dot for time t:

pos = [x0,y0] + r*[cos(theta0 + thetadot*t),sin(theta0 + thetadot*t)];

[VINAY KUMAR REDDY MEDAPATI]

I tried with the following code so far. Here the dot is moving in the direction of x-axis. I want to make the dot move in a circular path.

 x0 = 0;
 y = 0;
 v = 2;                   %Velocity of 2
 for time=1:100
 x = x0(1,:) + v*time; 
 plot(x, y,'r*');         %Plot the red dot
 axis([0 100 0 160])
 drawnow();
 pause(0.1)
 end

Answer 1

[Star Strider]

See if this does what you want:

crc = @(r,p,a) [r*cosd(a + p);  r*sind(a + p)];

t = linspace(0, 360, 361);                              % Time
init_pos = 25;                                          % Initial Position (°)
radius = 1.2;
locus = crc(radius, init_pos, t);

figure(1)
for k1 = 2:length(t)
    plot(locus(1,k1),  locus(2,k1), 'gp')
    axis([-1.5  1.5    -1.5  1.5])
    grid
    axis square
    drawnow    
end

[VINAY KUMAR REDDY MEDAPATI]

This is the model. Can the circle be plotted along it's path, so that the coordinate at different time for suppose t0 to t1 can be known. Can the same be implemented for a square path and a circular path? Can we define a particular velocity for the movement?

[Star Strider]

I am not certain what you want to do.

See if this works for you:

crc = @(r,p,a) [r*cosd(a + p);  r*sind(a + p)];

t = linspace(0, 360, 361);                              % Time
init_pos = 25;                                          % Initial Position (°)
radius = 1.2;
locus = crc(radius, init_pos, t);

figure(1)
for k1 = 2:length(t)
    plot(locus(1,k1),  locus(2,k1), 'gp', 'MarkerFaceColor','g')
    hold on
    plot(locus(1,1:k1),  locus(2,1:k1), '-b')
    hold off
    axis([-1.5  1.5    -1.5  1.5])
    grid
    axis square
    drawnow
end

[VINAY KUMAR REDDY MEDAPATI]

Yes. This is required. Do you define any particular velocity of the dot while moving? Can we make the point move from a certain point supposing (15,90) in the axis [0 60 0 120] in a clockwise direction?

[Star Strider]

The radial velocity is constant in my code. The angular velocity is also constant, and is hypot(dx,dy) where ‘dx’ is the change in the x-position with respect to time, and ‘dy’ the y-position.

I don’t know how you want to define the centre of the circle, but if you define it as the centre of the grid (that being (30,60), and you want the circle to start at (15,90), the radius has to be 33.541, so it will plot outside the horizontal limits of the axis you want. That’s just how the maths work.

It is necessary to use axis equal or the circle plots as an ellipse.

The new code:

crc = @(r,p,a) [r*cosd(a + p);  r*sind(a + p)];

t = linspace(0, 360, 361);                                  % Time
centre = [30; 60];                                          % Circle Centre
init_pos = atan2d(90-centre(2), 15-centre(1));              % Initial Position (°)
radius = hypot(15-centre(1), 90-centre(2));                 % Circle Radius
locus = bsxfun(@plus, crc(radius, init_pos, t), centre);    % Calculate Circle Locus

figure(1)
for k1 = 2:length(t)
    plot(locus(1,k1),  locus(2,k1), 'gp', 'MarkerFaceColor','g')
    hold on
    plot(locus(1,1:k1),  locus(2,1:k1), '-b')
    hold off
    axis([0  60    0  120])
    grid
    axis equal
    drawnow
end

[VINAY KUMAR REDDY MEDAPATI]

Thank you, it works. Instead of constant velocity you have considered, can we define a velocity and make the dot move with that velocity suppose 1 m/sec? And after plotting the circle can we store the (x,y) positions on the circle for different time samples for suppose 30 time samples.

[Star Strider]

My pleasure.

The units in my initial code are arbitrary. I used your units and coordinate system for my second code. You can make the units whatever you want, by defining them appropriately with respect to the coordinate system you choose.

The (x,y) positions already exist in the ‘locus’ matrix. The x-coordinates are ‘locus(1,:)’ and the y-coordinates are ‘locus(2,:)’.

You can define the sampling interval in the ‘t’ vector to be whatever you choose. In my code, I chose 1-degree (or second, or day, or year) increments for the the time parameter vector ‘t’, so you can define ‘t’ to be whatever you wish. Some simple trigonometry and calculus will give you the distance and angular and radial velocities in the corresponding units.

[VINAY KUMAR REDDY MEDAPATI]

Thank you very much. It was very helpful. Can the same be done in a square path and zig-zag path. Do we need to just change crc in the above code or will it be entirely different?

[Star Strider]

My pleasure.

It would be entirely different for square and zig-zag paths. Plotting a square and zig-zag paths I will leave to you. You may be able to adapt the circle-plotting algorithm to the square by using the cotangent function to change the radius to a straight line, considering your ‘requirements’ and constraints. A sawtooth function would be relatively easy to program, but a true zig-zag more difficult, especially if you wanted the radius of the circle to be a zig-zag.

sawtooth = @(a,p) rem(a,p).*(rem(a,p)<p);

figure(2)
plot(t, sawtooth(t,45))
grid

[Maryam Naveed]

Can you further explain me this code?Actually i want 100 points that are arranged in 10 rows ans 10 columns.and each points moves in a circular path?how to do this?i will be thankful to you if u find ou=ut a solution for me.