Improving Gradient Computation for Differentiable Physics Simulation with Contacts

TL;DR

This paper improves gradient accuracy in differentiable rigid-body physics simulations with contacts by using continuous collision detection and time-of-impact, enabling better learning and control in simulation-based tasks.

Contribution

It introduces TOI-Velocity, a novel method that enhances gradient computation in contact-rich differentiable simulations, addressing inaccuracies in existing approaches.

Findings

TOI-Velocity produces gradients that match analytical solutions in control tasks.

Existing methods fail to accurately learn control sequences with moving contacts.

The proposed approach improves the reliability of gradient-based learning in physics simulations.

Abstract

Differentiable simulation enables gradients to be back-propagated through physics simulations. In this way, one can learn the dynamics and properties of a physics system by gradient-based optimization or embed the whole differentiable simulation as a layer in a deep learning model for downstream tasks, such as planning and control. However, differentiable simulation at its current stage is not perfect and might provide wrong gradients that deteriorate its performance in learning tasks. In this paper, we study differentiable rigid-body simulation with contacts. We find that existing differentiable simulation methods provide inaccurate gradients when the contact normal direction is not fixed - a general situation when the contacts are between two moving objects. We propose to improve gradient computation by continuous collision detection and leverage the time-of-impact (TOI) to calculate the post-collision velocities. We demonstrate our proposed method, referred to as TOI-Velocity, on two optimal control problems. We show that with TOI-Velocity, we are able to learn an optimal control sequence that matches the analytical solution, while without TOI-Velocity, existing differentiable simulation methods fail to do so.