How to get the input control matrix from SOFA

[xlsufo]

Hello everyone！
I have read the paper FEM Based Workspace Estimation for Soft Robots: a Forward-Backward Interval Analysis Approach, which studies a soft robot driven by cables, as shown below.

The Euler-Lagrange equation are constructed

I want to reproduce the content of the paper. But I don't know how to get the H matrice from SOFA.
The paper mentions the reference "The finite element method in engineering", but I don't have the license for this book.
Can anyone help?

[alxbilger]

The matrix you want to get is not available through Python in SOFA. There is a work in progress so it becomes available. Stay tune, it may come in the next days/weeks (but you will have to compile SOFA or wait the next release in december).

The very short term solution would be to get it in C++

[xlsufo]

Thank you, may I ask if there is some reference for implementation in C++.

[alxbilger]

Actually, I realized that the matrix is already available in the Data constraint of a MechanicalObject. The problem is that it will be a string, and you will have to parse it (making the simulation ultra-slow). Here is an example of what you would get:

[xlsufo]

Hello!
I extracted this data from the DiamondRobot in softrobot tutorials.

I reduced the number of cables to one and got the following result:

 Constraint ID : 0  
dof ID : 444  value : 0.0004578 -0.0500435 -0.0167298
dof ID : 483  value : 0.00613595 -0.670739 -0.224232
dof ID : 1237  value : 0.00355964 -0.389115 -0.130083
dof ID : 1445  value : -0.00147765 0.161526 0.0539992

Is this the H matrix I need? I noticed that my “dof ID” number is 4, while your example is 3. What is the reason for this difference? Maybe because the DiamondRobot is composed of tetrahedral units?

[alxbilger]

you're right. The cables are defined in a different space than the main DoFs. The BarycentricMapping maps values from this space to the main DoFs using the topology. In this case, a point in a tetrahedron. This point is distributed to the main DoFs using the barycentric coordinates.

[xlsufo]

I'm very sorry that I haven't studied these theories. Based on your explanation, I think that when the tension of the cable is u, the values ​​of above points are a1, a2, a3, and a4. If I want to get the actual force distributed on the four points, can I follow the following formula?

[alxbilger]

A Pull Request has been submitted sofa-framework/SofaPython3#459. If you build SOFA yourself, you can already checkout the branch (but changes may still occur), or you wait that it is merged into master. If you use the binaries, you will have to wait for the next release.