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Thanks for going through the paper and finding the discrepancies with matrix t01 and t12. It helped me a lot as I was looking through this. I found one typo I think in the comments of your code, where the paper t01 matrix i see here https://www.ijstr.org/final-print/sep2017/Inverse-Kinematic-Analysis-Of-A-Quadruped-Robot.pdf in row index 1 col index 1 has positive cos(theta1).
image

The matrix in the paper still has weird stuff going on in the row index 2. I only threw this PR out as the comments confused me slightly as I was comparing the matrices in your comments to the paper.

I agree with you, and did out the matrix math using their DH parameters and arrive at the same thing you got.
https://wikimedia.org/api/rest_v1/media/math/render/svg/6963d0c47a3a894ff0719c8df348d188b996074e

joint i theta i (degree) alpha i (degree) r i (meters) d i (meters)
0-1 theta1 0 l1 0

Looking at t01:

cos(theta1) -sin(theta1)*cos(0) sin(theta1) * sin(0) -l1 * cos(theta1)
sin(theta1) cos(theta1) * cos(0) -cos(theta1) * sin(0) -l1 * sin(theta1)
0 sin(0) cos(0) 0
0 0 0 1

so that is:

cos(theta1) -sin(theta1)* 1 sin(theta1) * 0 -l1 * cos(theta1)
sin(theta1) cos(theta1) * 1 -cos(theta1) * 0 -l1 * sin(theta1)
0 0 1 0
0 0 0 1

so that is:

cos(theta1) -sin(theta1) 0 -l1 * cos(theta1)
sin(theta1) cos(theta1) 0 -l1 * sin(theta1)
0 0 1 0
0 0 0 1

I did the same thing for matrix t12, and also got something that agrees with you, just with a different sign on the 1 in row index 2. This is probably do to spot micro doing legs pointing back, and alpha being positive pi/2 instead of -pi/2 as in the paper model.

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