Heres the inverse kinematics. It started off pretty nice but blew up when trying to solve for thi1.
I put the MATLAB code in dropbox that I used to calculate T1e. The matrix was really big and I couldn't figure out how to print a proper copy so take a look on dropbox if you want to see the entire matrix.
Awesome work. Looks great. I think there is one error on page 4 of 4, fifth line down, when you substitute c1 into Y you dropped the alpha*s1 term. Is that correct? One question: how do we account for the multiple solutions to the inverse tan, sin, and cos functions which the joint angles are evaluated with?
You're talking about the +/- angle orientations for inverse tan/sin/cos right?
The numerical value of the inverse of sine won't be an issue since it's an odd function, but we would have to worry about inverse tan and cosine.
Using a program could allow the use of an 'atan2' function, so our problem would boil down to cosine. The only solution I can think of is an 'sgn(distance)' term in front of the inverse cosine term, where 'sgn(distance)' would be positive or negative depending on the distance variable.
Belaye: if I understand your question correctly as: "For different values of thetap, thetay, x, y, z (different orientations of the end effector) we should have multiple solutions for each end effector orientation. How does this manifest in the equations I derived?”
My answer to that is that if you plug in the given values, you will get multiple solutions to thi1, thi2 etc.
Looks really good. We'll go over it in more detail today to double check the work but it looks great. Very simple to read and follow.
ReplyDeleteAwesome work. Looks great. I think there is one error on page 4 of 4, fifth line down, when you substitute c1 into Y you dropped the alpha*s1 term. Is that correct? One question: how do we account for the multiple solutions to the inverse tan, sin, and cos functions which the joint angles are evaluated with?
ReplyDeleteThis comment has been removed by the author.
DeleteYou're talking about the +/- angle orientations for inverse tan/sin/cos right?
DeleteThe numerical value of the inverse of sine won't be an issue since it's an odd function, but we would have to worry about inverse tan and cosine.
Using a program could allow the use of an 'atan2' function, so our problem would boil down to cosine. The only solution I can think of is an 'sgn(distance)' term in front of the inverse cosine term, where 'sgn(distance)' would be positive or negative depending on the distance variable.
Belaye: if I understand your question correctly as: "For different values of thetap, thetay, x, y, z (different orientations of the end effector) we should have multiple solutions for each end effector orientation. How does this manifest in the equations I derived?”
DeleteMy answer to that is that if you plug in the given values, you will get multiple solutions to thi1, thi2 etc.
also the alpha is fine. I can show you when you get here.
Delete