Spring-Rod System Identification via Differentiable Physics Engine

Reviewer 1

The paper introduces a system identification architecture for spring-rod systems where the simulation step is split up into separate, low-dimensional building blocks: force generation implementing Hooke’s law, acceleration generation which converts forces to accelerations given inertia matrices and masses, and an Euler integrator that computes the next state. These modules have a very small number of parameters thanks to changing the frames in which they are used, e.g. by representing angular acceleration in the local frame to only have diagonal inertia matrices. In the experiments, given trajectories from a tensegrity system simulated in MuJoCo with varying initial conditions, the parameters of the spring-rod system are fitted to match the states of the reference system. Compared to a Koopman-augmented interaction network baseline, the presented linear regression model achieves significantly higher accuracy, and can find good parameters within few training samples. The presented work is currently very limited as it only allows to model the dynamics for systems with a known topology consisting of linear springs connected to rods. Such systems can be learned via linear regression since, following Hooke’s law, the force response of a spring is linear w.r.t. displacement. Compared to more general physics-based, data-driven models, such as interaction networks, which can learn the topology and dynamics between the parts of any system, it remains to be shown how the approach can be extended to more complex systems involving discontinuities (contacts), non-linear force responses, or interactions with rigid / soft bodies, etc.” “Related work which needs to be cited that also combines data-driven functions with a physics engine, is for example [1].

Line 80 should read ““Hooke’s law””.

[1] Sim-to-Real Transfer with Neural-Augmented Robot Simulation Florian Golemo, Adrien Ali Taiga, Aaron Courville, Pierre-Yves Oudeyer. Proceedings of The 2nd Conference on Robot Learning, 2018.

Reviewer 2

The authors present a differentiable physics engine for spring-rod assemblies, as commonly found in tensegrity robots. Through application of Hooke’s law to spring-damped constraints between endpoints of rods, the system is able to simulate and identify complicated systems such as the NASA Icosahedron.

The paper discusses experiments on system identification against the MuJoCo physics simulator, simulating the NASA Icosahedron, and shows that they perform favorably against a baseline of interaction networks augmented with Koopman operators.

The discussion of the importance of moving from 3D to 1D representations does not appear novel, many existing engines represent spring-damped constraints in a single dimension. The paper also lacks a description of its novelty when compared to existing differentiable physics engines.

Finally, the approach as presented is quite limited, since it lacks a collision mechanism or a contact model.” “This paper has many, many typos. On line 80, Hooke’s law is referred to as ““Hulk’s law””.

In Figure 2, more exposition on p, v, q, w could be given in the caption.

There is no discussion of the parameters of the baseline interaction net, nor a description of its interaction with the Koopman operator. It is not clear which reference, if any, is relevant.

The engine as presented lacks a contact and friction model, yet the authors report extremely accurate results against MuJoCo over long time periods. Is the NASA Icosahedron in freefall? If so, that should be highlighted in the paper.

Reviewer 3

The paper presents a set of regression units that learn to compute forces and accelerations given some system states that are reduced to 1D inputs in a model-reduction pre-pass. The regression units are trained in a supervised manner, and a comparison is performed between using single and multiple regressors, and methods that try to learn the full 3D dynamics update.

I like the idea of using data-driven physical models to define force interactions, but I was a little disappointed, because it seems the learned models are limited to linear springs. I think where this approach would become more interesting is when the internal dynamics is some complex nonlinear function for which the underlying model is unknown (not just the parameters). I think the paper could touch on this by mentioning that the use of some e.g.: MLP model could be used to learn more complex functions.

Overall I think this is promising and interesting work, I would be happy to see it published at the workshop.

I would like to see a more thorough discussion of the relation to previous work. It is true that systems like DiffTaichi focus on MPM, but they are not restricted to this, and could quite easily simulate mass-spring systems. It would be helpful to more clearly contrast the presented work with these previous methods to know which are the most similar.

If I understand correctly, the regressors are essentially learning how to solve the Newton-Euler equations for accelerations. I wonder why not just regress the inertia matrix and mass directly, rather than the whole acceleration computation. Does the proposed approach gain anything by outputing accelerations rather than the parameters that can then be plugged into a regular Newton-Euler update? I’m also wondering if the regressor also computes e.g.: coriolis / gyroscopic terms?

I have the same question with regard to the force regressor, why not regress the stiffness k, and damping value c directly? Or is this in fact what is done? I found it a little confusing that the output of the regressor is that actual force magnitude instead of the parameters themselves (which can then just be plugged into a known force model).

A few minor typos:

Ln 46, ““researchers extends”” -> ““researchers extended”” Ln 80, ““Hulk’s law””, is this a typo of Hooke’s law? Ln 116, ““for each a rod and spring”” -> ““for each rod and spring””