Another dynamically consistent way to account for dissipative forces in Mujoco physics engine

[DjoleMNE]

Hi,
just wanted to share an idea/suggestion :)

From documentation of Mujoco library [1] and from reference [2], I have seen that dynamics computations are largely based on Gauss principle of least constraints. But when it comes to adding dissipative (e.g. some frictional) forces in those computations, I noticed that Mujoco's formulation at this point deviates from a bit from Gauss' principle, and it takes a different (but still valid) direction. I.e. those forces are still added in Gauss' formulation, but they are not modelled using the same way that extended Gauss' principle considers those additional aspects of dynamics [5].

I was wondering if it would make sense to instead continue with Gauss' principle all the way when it comes to adding dissipative forces. I.e. to take another dynamical-consistent way of modeling the dissipative forces and improve the accuracy of Mujoco engine even more. More specifically, for dissipative forces such as static (zero velocity) and load-dependent parts of dynamic (non-zero velocity) friction forces (in joints, contacts, etc.), reaction-forces from position limits (since these limits dissipate energy from the system when the system reaches them), etc. @emotodorov, @yuvaltassa.

References to this different approach are [3][4][5]. The idea is to use extended Gauss' principle that considers dissipative forces in its original acceleration energy cost (i.e. 2nd order change of kinetic/potential energy). More specially, Gauss' and Maximum-Dissipation principles can be combined to produce a dynamically consistent formulation to account for dissipative forces.

Looking forward to your feedback. And I apologize in advance if some of my explanations here, or my understanding of these aspects, are incorrect in any way.

Thank you in advance for you feedback and please correct me if I got something wrong in here. :)

P.S. Recently there has been some new developments around Gauss-based solvers in State of the Art that contribute to advancing physics-related computations in terms of efficiency [6]. I see a lot of similarity between that work and Mujoco's solvers. They have also referenced Mujoco work in their publication.

[1] https://mujoco.readthedocs.io/en/stable/overview.html (Computation and Modelling sections)
[2] E. Todorov, "Convex and analytically-invertible dynamics with contacts and constraints: Theory and implementation in MuJoCo," 2014 IEEE International Conference on Robotics and Automation (ICRA).
[3] Vukcevic, Djordje, "Extending a constrained hybrid dynamics solver for energy-optimal robot motions in the presence of static friction", Technical Report, 2018. (chapter 5)
[4] A. F. Vereshchagin, “Modelling and control of motion of manipulation robots”, Soviet Journal of Computer and Systems Sciences, vol. 27, pp. 29–38, 1989. (unfortunately, access to this publication is not available anywere (neither paid or free access), but I have access to a scanned copy if requred for referencing)
[5] G. Pozharitskii, “Extension of the principle of gauss to systems with dry (coulomb) friction”, Journal of Applied Mathematics and mechanics, vol. 25, pp. 586 –607, 1961.
[6] A. S. Sathya, H. Bruyninckx, W. Decré and G. Pipeleers, "Efficient Constrained Dynamics Algorithms Based on an Equivalent LQR Formulation Using Gauss' Principle of Least Constraint," in IEEE Transactions on Robotics, vol. 40, pp. 729-749, 2024

Best regards,
Djordje