problem in making Two link manipulator used inverse kinematics(jacobian)
Show older comments
i dont know what is wrong...
i used jacobian driven DHtable
i think animation part is not wrong
but find jacobian part has matter but i cant find that...
clc, clear, close all;
syms theta1 theta2 t
%% init
l1 = 1 ; l2 = 1;
d1 = 0; a1 = l1 ;alpha1 = 0; home1 = -60;
d2 = 0; a2 = l2 ;alpha2 = 0; home2 = 120;
%% find jacobian
A01 = DHtheta(theta1, d1, a1, alpha1,home1);
A12 = DHtheta(theta2, d2, a2, alpha2,home2);
T01 = A01;
T02 = simplify(A01*A12);
O02 = T02(1:3,4);
O01 = T01(1:3,4);
z = [0;0;1];
Jv1 = simplify(cross(z,O02));
Jv2 = simplify(cross(z,(O02-O01)));
J = [Jv1,Jv2;z,z];
%% trajectory planning
x0 = cosd(home1)+cosd(home1+home2);
y0 = sind(home1)+sind(home1+home2);
ax = amat(x0,0,0,x0,0,0,0,1);
ay = amat(y0,0,0,1,0,0,0,1);
xtraj = ax(1)*t.^5+ax(2)*t.^4+ax(3)*t.^3+ax(4)*t.^2+ax(5)*t+ax(6);
ytraj = ay(1)*t.^5+ay(2)*t.^4+ay(3)*t.^3+ay(4)*t.^2+ay(5)*t+ay(6);
xdottmp = diff(xtraj,t);
ydottmp = diff(ytraj,t);
treal = linspace(0,1,1000);
xd= double(subs(xtraj,t,treal));
yd= double(subs(ytraj,t,treal));
xdot= double(subs(xdottmp,t,treal));
ydot= double(subs(ydottmp,t,treal));
%% cal theta value
th1 = zeros(1000);
th2 = zeros(1000);
th1(1) = home1;
th2(1) = home2;
dotmat = zeros(2,1);
for k=1:1:1000
tmpJ1 = subs(J,[theta1 theta2],[th1(k) th2(k)]);
Ja = double(tmpJ1(1:2,1:2));
dotmat(1,1) = xdot(k);
dotmat(2,1) = ydot(k);
thdottmp = Ja\dotmat;
th1(k+1) = th1(k) + thdottmp(1)*0.001;
th2(k+1) = th2(k) + thdottmp(2)*0.001;
end
%% animation
figure;
h = plot(0,0,0,0);
axis([-0.5 1.5 -1 1]);axis equal;
for k=1:1:1000
Xcoord1 = [0 cosd(th1(k))];
Ycoord1 = [0, sind(th1(k))];
Xcoord2 = [cosd(th1(k)), cosd(th1(k))+cosd(th1(k)+th2(k))];
Ycoord2 = [sind(th1(k)), sind(th1(k))+sind(th1(k)+th2(k))];
h(1).XData = Xcoord1;
h(1).YData = Ycoord1;
h(2).XData = Xcoord2;
h(2).YData = Ycoord2;
drawnow;
if k==1
pause;
end
end
function A = DHtheta(theta, d, a, alpha,home)
thetaMat = [cosd(theta+home), -sind(theta+home), 0 , 0;
sind(theta+home), cosd(theta+home), 0 , 0;
0 0 1 0;
0 0 0 1];
dMat = [ 1 0 0 0;
0 1 0 0;
0 0 1 d;
0 0 0 1];
alphaMat = [ 1 0 0 0;
0 cosd(alpha) -sind(alpha) 0;
0 sind(alpha) cosd(alpha) 0;
0 0 0 1];
aMat = [ 1 0 0 a;
0 1 0 0;
0 0 1 0;
0 0 0 1];
A = thetaMat*dMat*aMat*alphaMat;
end
function a = amat(q0,q0dot,q02dot,qf,qfdot,qf2dot,t0,tf)
trjmat = [t0^5, t0^4, t0^3, t0^2, t0, 1;
5*t0^4, 4*t0^3, 3*t0^2, 2*t0, 1, 0;
20*t0^3, 12*t0^2 6*t0, 2 , 0, 0 ;
tf^5, tf^4, tf^3, tf^2, tf, 1;
5*tf^4, 4*tf^3, 3*tf^2, 2*tf, 1, 0;
20*tf^3, 12*tf^2 6*tf, 2 , 0, 0 ];
qmat = [q0;q0dot;q02dot;qf;qfdot;qf2dot];
a = trjmat\qmat;
end
1 Comment
Sachin Meena
on 8 Jan 2019
Could you please tell what is the expected output?
Answers (1)
Francisco J. Triveno Vargas
on 11 Sep 2024
0 votes
Hi my friend, you can check the functions here.
Regards
Francisco
Categories
Find more on Mathematics and Optimization in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!