Derivatives (sensitivities) of mj_step with respect to model parameters

[antalpeter1]

Intro

Hi!

I am a doctoral student currently on exchange at ETH Zurich, and I use MuJoCo for my research on nonlinear robust MPC.

My setup

I use the MuJoCo C API to predict the future states of a robot and obtain the gradients of the dynamics.

My question

I would also like to propagate the effect of uncertain parameters through the dynamics, which would require the derivatives of the dynamics (mj_step) with respect to certain model parameters (e.g. mass). I have two questions regarding this:

1. Is there an existing implementation for this problem?
2. If not, do you think it is possible to implement this similar to mjd_transitionFD? Meaning, I would perturb the model parameters by setting the value of m->body_mass, call mj_stepSkip, and mj_stateDiff.

Minimal model and/or code that explain my question

No response

Confirmations

• I searched the latest documentation thoroughly before posting.
• I searched previous Issues and Discussions, I am certain this has not been raised before.

[yuvaltassa]

1. @kevinzakka is working on a system identification toolbox that does exactly this. It will be made public in April.
2. It would be very hard to do this in a general way in C, like mjd_transitionFD, how would you define the the vector of possible modifications? Moreover, some changes can be made directly to mjModel, while some changes require recompilation (using mjSpec).