Elliptical trajectory and plot waypoints for robotic arm simulation

How to plot an ellipse on plot3..and also waypoints along the path

I have have a image of circular path.

In same manner how can we plot an ellipse?

final application is simulate a manipulator in in elliptical path.

% LOAD robot into and create rigid tree 
% Specify EndEffector joint position 
gen3 = loadrobot("kinovaGen3");
gen3.DataFormat = 'column';
q_home = [0 15 180 -130 0 55 90]'*pi/180;
eeName = 'EndEffector_Link';
T_home = getTransform(gen3, q_home, eeName);

% Visualize the robot at home configuration
show(gen3,q_home);
axis auto;
view([60,10]); 

% Create Inverse Kinematics Solver and Set Parameters
ik = inverseKinematics('RigidBodyTree', gen3);
ik.SolverParameters.AllowRandomRestart = false;
weights = [1, 1, 1, 1, 1, 1];
q_init = q_home;
%Define Waypoints from the Desired Trajectory
center = [0.5 0 0.4]; %[x y z]
radius = 0.1;

% Define total time and time step, and based on that generate waypoints for the circular trajectory
dt = 0.25;
t = (0:dt:10)';
theta = t*(2*pi/t(end))-(pi/2);
points = center + radius*[0*ones(size(theta)) cos(theta) sin(theta)];

%Plot the waypoints along with the robot at home configuration
hold on;
plot3(points(:,1),points(:,2),points(:,3),'-*g', 'LineWidth', 1.5);
xlabel('x');
ylabel('y');
zlabel('z');
axis auto;
view([60,10]);
grid('minor');

%Solve the Inverse Kinematics for Each Waypoint

numJoints = size(q_home,1);   
numWaypoints = size(points,1);
qs = zeros(numWaypoints,numJoints);
for i = 1:numWaypoints
    T_des = T_home;
    T_des(1:3,4) = points(i,:)';
    [q_sol, q_info] = ik(eeName, T_des, weights, q_init);
    
    % Display status of ik result
    %disp(q_info.Status);
    
    % Store the configuration
    qs(i,:) = q_sol(1:numJoints); 
    
    % Start from prior solution
    q_init = q_sol;
end

%Visualize the Animation of the Solution

figure; set(gcf,'Visible','on');
ax = show(gen3,qs(1,:)');
ax.CameraPositionMode='auto';
hold on;
 
% Plot waypoints
plot3(points(:,1),points(:,2),points(:,3),'b','LineWidth',2);
axis auto;
view([60,10]);
grid('minor');
hold on;
 
title('Simulated Elliptical Movement of the Robot');
% Animate
framesPerSecond = 30;
r = robotics.Rate(framesPerSecond);
for i = 1:numWaypoints
    show(gen3, qs(i,:)','PreservePlot',false);
    drawnow;
    waitfor(r);
end

Answer 1

[Matt J]

Fairly easy to do with this FEX submission,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

gtobj=ellipticalFit.groundtruth([], [0,0],[2,1],90); %Define the ellipe in 2D
xy=gtobj.sample(0:20:360); %Define waypoint coordinates



axis([0 0.6 -0.3 0.3 0 0.6]); grid on
view([-41,-33])

hEllipse=plot(gtobj,{'Color','g'});  %Make plot in xy plane first
hold on
hWayPts=scatter(xy{:},'filled','k','SizeData',50);
hold off
xlabel 'X', ylabel 'Y', zlabel 'Z'

T=makehgtform('translate',[0.4,0,0.4],'yrotate',pi/2); %rototranslate the plot out of xy plane
set([hEllipse,hWayPts],'Parent',hgtransform('Matrix',T))

[Matt J]

RANJITH NAIK's comment moved here:

Thank you for your response sir!

I have a doubt

gtobj=ellipticalFit.groundtruth([], [0,0],[2,1],90);

in the above what value should be assigned here in "[]" ?

And what does "([], [0,0],[2,1],90); " indicate?

[RANJITH NAIK]

thank you once agian

but

gtobj=ellipticalFit.groundtruth([], [0,0],[2,1],90);

in the above code what value should be assigned here in "[]" ?

what does it stand for ?

[Matt J]

It should be left []. Or, you can put your waypoint coordinates (in 2D) instead as a 2xN matrix.

[RANJITH NAIK]

I tried as you directed but i'm getting error... Probably i think i have entered wrong matrix...

How to form a 2*N matrix for this ?

Major axis = 15cm

Minor axis = 7.4 cm

what would be final alteration here gtobj=ellipticalFit.groundtruth([], [0,0],[2,1],90)?

[Matt J]

gtobj=ellipticalFit.groundtruth([], [0,0],[15,7.4]/2,0)

[RANJITH NAIK]

i got same error..

i altered with your value ... what would be the mistake?

[Matt J]

Looks like you didn't download the files. Or, you didn't put them somewhere on the path where Matlab can seee them.