Calculate Equation of motion matrices

[ZAKARIA BOUZID]

Salam, Hi everyone,

I'm working on apply some control methods on the Arm model, in designing the sliding mode controller I need to get the matrices of equation of motion or state space of the model but I think the getting the matrices is better until now I got the mass matrix using simbody method calcM and the gravity vector using a Matlab script (got it here).

my questions are :
- what is the equation of motion of the model ?
- how I can calculate the Coriolis and the other model matrices ?

I hope to get an answer asap cuz it's related to my thesis work.

Thanks.

[Nicos Haralabidis]

Hello Zakaria,

It is not possible to get a model's underlying equations in symbolic form. Based upon what you have described I think you could work with the individual terms of the equations, to obtain those terms (i.e., coriolis etc) you would have to first set the model's state vector and then extract the necessary terms from the SimbodyMatterSubsystem - https://simbody.github.io/3.7.0/classSi ... 9175f8082a

Hope that helps!

Nicos

[ZAKARIA BOUZID]

Hello Zakaria,

It is not possible to get a model's underlying equations in symbolic form. Based upon what you have described I think you could work with the individual terms of the equations, to obtain those terms (i.e., coriolis etc) you would have to first set the model's state vector and then extract the necessary terms from the SimbodyMatterSubsystem - https://simbody.github.io/3.7.0/classSi ... 9175f8082a

Hope that helps!

Nicos

Hey Nicos,
Thanks for your reply.

I will give you some details to clarify more. I've designed my SMC Controller in general form assuming that the model equation is " Gamma = M*Qdd + C + G, where M mass matrix, C Coriolis vector and G Gravity vector", The controller law now is related to M, C and G, by doing some research I got M, C and G, My issue know How I can verify that the OpenSim model has only these 3 equation, for that I'm looking for the used model in general form (not in programming, but in documentation and if there are other matrices How I can get them ?

Many thanks.

Zakaria.

[Thomas Uchida]

You may find this information in the Simbody Theory Manual (https://github.com/simbody/simbody/tree ... imbody/doc) and/or one of the papers listed on the "Theory and Publications" page in the User's Guide (https://simtk-confluence.stanford.edu:8 ... blications, particularly the papers from IUTAM).

[ZAKARIA BOUZID]

You may find this information in the Simbody Theory Manual (https://github.com/simbody/simbody/tree ... imbody/doc) and/or one of the papers listed on the "Theory and Publications" page in the User's Guide (https://simtk-confluence.stanford.edu:8 ... blications, particularly the papers from IUTAM).

Thanks for your help, I'll check them out.

[yang ming]

Hey Zakaria,

I have met the same problem as you, could you give me some advice on this? I have no idea how to get the matrix.

Thanks!