Variable Mass System Dynamics simulations

[angadhn]

After Friday's workshops (2/3/2023), @yuvaltassa and I had a chat about simulating 6-DoF rocket-type systems in Mujoco, i.e. systems that are characterised by variable mass and variable geometry that then impact the moments of inertia. Yuval also recommended opening a discussion here- after duly going through the tutorials- about the system I wish to simulate that could potentially be added as an example to MuJoCo, which I am happy to do.

The System

The baseline example I am looking to simulate is described in this paper, which investigates the attitude dynamics of torque-free variable mass cylinders subjected to four propellant "burns". One of the burns assumes the cylinder's mass is lost uniformly without altering its overall dimensions (i.e., there is only an $\dot{m}$ term which influences the time rates of changes of the moments of inertia); the other three account for geometry changes, as well (e.g., a rocket motor might consume propellant burning from one end of a cylinder to the other so the length of the cylinder reduces along with the mass). The paper assumes there is no gravity ($g=0$) but there are interesting enough behaviours seen across these burn patterns (which we don't need to get into for now). As a result, the governing equations resemble the Euler equations of a single rigid body with some corrective terms for mass variation (Equations 11-13 from said paper are below, for reference).

Having read through the MuJoCo tutorial, I am circling back to the discussion on Friday and seeking guidance on how one might simulate a variable mass cylinder as described above. I imagine defining the mass, geometry, and (subsequently) the inertias within a simulation is one part of the problem but not sufficient as the governing equations might also need massaging.

However, any advice to get started on this would be much appreciated.

[saran-t]

At first glance, I'd say that this can be mostly implemented as a passive force plugin without any need to modify MuJoCo code. However, the variable inertia side of the story might mean that you have to write back into mjModel which is supposed to be const.

Maybe @yuvaltassa has a better idea, but this might end up being one of those situations where there's no better alternative than just dropping the const qualifier.

[yuvaltassa]

Yes, I think this would be a case where you should just overwrite the mass and inertia. It should be easy to write a test for this along the lines of: have 2 XMLs, one with full fuel cylinder, one with say half of the fuel is gone, then check that the mass/inertia modification that you're doing to mjModel is actually the correct one.

Try this and see if you get stuck. The fields you want to change are mjModel.{body_mass, body inertia}, and you probably want the fuel cylinder to be a seperate body, kinematically "welded" (no DoFs) to its parent.