Need help with 6X6 Jacobian Matrix and the derivative of its inverse.

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Abdul Rahman Samewoi 2018-3-7

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https://ww2.mathworks.cn/matlabcentral/answers/386785-need-help-with-6x6-jacobian-matrix-and-the-derivative-of-its-inverse

评论： Abdul Rahman Samewoi 2018-3-7

SlowSubsystem_6mac18_9PM_AssignedTau.zip

Hi, I have a dynamics equation which needs to use 6x6 Matrix Jacobian with many zeros inside the matrix as shown below:

%%JACOBIAN MATRICES
% Manipulator 1
J111 = -L11*sin(q11) - L12*sin(q11 + q12) - L13*sin(q11 + q12 + q13);
J112 = -L12*sin(q11+q12) - L13*sin(q11 + q12 + q13);
J113 = -L13*sin(q11 + q12 + q13);
J121 = L11*cos(q11) + L12*cos(q11 + q12) + L13*cos(q11 + q12 + q13);
J122 = L12*cos(q11+q12) + L13*cos(q11 + q12 + q13);
J123 = L13*cos(q11 + q12 + q13);
% Manipulator 2
J211 = -L21*sin(q21) - L22*sin(q21 + q22) - L23*sin(q21 + q22 + q23);
J212 = -L22*sin(q21+q22) - L23*sin(q21 + q22 + q23);
J213 = -L23*sin(q21 + q22 + q23);
J221 = L21*cos(q21) + L22*cos(q21 + q22) + L23*cos(q21 + q22 + q23);
J222 = L22*cos(q21+q22) + L23*cos(q21 + q22 + q23);
J223 = L23*cos(q21 + q22 + q23);
J= [J111 J112 J113 0 0  0 ; J121 J122 J123 0 0  0 ; 1 1 1 0 0 0 ; 0 0 0  J211 J212 J213; 0 0 0  J221 J222 J223; 0 0 0  1 1 1];

I need to find its inverse,Jinv;its transpose,Jtran; and its transposed inverse,Jtraninv (as shown below) as they all need to be used in dynamics equation inside the Matlab Function Block.

Jinv = pinv(J);
Jtran= transpose(J);
Jtraninv = pinv(Jtran);

The problems arise when I need to find the derivative of Jinv, Jinvdot. I tried to do as shown in figure below (FYI, I have simplified the model for briefly explanation):

I found that the system can be run with value inside the Jinvdot, but there are warnings such that:

I tried to put delay as shown below. As a result, the warnings are eliminated but the values inside the Jinvdot matrix are different.

My questions are: 1. Is this the correct way to find Jinvdot? Any better solution? 2. Should I put the delay or not?

I have also searched similar problems but couldn't find it. I am so appreciated any helps. Thanks.

P.s: I attached my model (constructed using Matlab 2016a) for reference.