How to manage the Inverse Kinematics in a Robotic Arm with 3 joints?

The example with 2 joints is given in: http://uk.mathworks.com/help/fuzzy/examples/modeling-inverse-kinematics-in-a-robotic-arm.html?refresh=true; and I've already modified the original code into a 3-joint-robotic arms:

l1 = 10; % length of first arm
l2 = 7; % length of second arm
l3 = 6;
 theta1 = 0:0.1:pi/2;% all possible theta1 values
 theta2 = 0:0.1:pi;% all possible theta2 values
 theta3 = 0:0.1:pi;
[THETA1, THETA2, THETA3] = meshgrid(theta1, theta2,theta3); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3) ; 
X1 = reshape(X, size(X,1), size(X,2)*size(X,3));
Y1 = reshape(Y, size(Y,1), size(Y,2)*size(Y,3));
plot(X1, Y1);
U = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2);
V = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2);
U1 = reshape(U, size(U,1), size(U,2)*size(U,3));
V1 = reshape(V, size(V,1), size(V,2)*size(V,3));

The code is CORRECT and it be can successfully plotted. I am now confused with how to set the data as well as the following steps such as ANFIS network training and the equation of 3-joint-robotic arm. At first I guessed that the angle of the joint theta 1,2,3 as well as the position of the final joint (U,V) and the tip(X,Y) is needed so I typed:

data1 = [X(:) Y(:) U(:) V(:) THETA1(:)]; % create x-y-theta1 dataset
data2 = [X(:) Y(:) U(:) V(:) THETA2(:)]; % create x-y-theta2 dataset
data3 = [X(:) Y(:) U(:) V(:) THETA3(:)]; % create x-y-theta2 dataset

When I tried to train the ANFIS network the system broke down because the data were to large.

Anyone can show me an improved commands?

[Humaira Aslam Mian]

Hey, did you find the soultion??

I m also finding for this...When I had to calculate the value of "phi".

Answer 1

[Junhao Jiang]

if it doesn't solve in mathmatic euqation, neural network maybe a good way to approximate the model