Linear-Time Contact and Friction Dynamics in Maximal Coordinates using Variational Integrators

TL;DR

This paper introduces a linear-time, robust simulation algorithm for contact and friction dynamics in rigid bodies using maximal coordinates and variational integrators, enhancing efficiency and stability.

Contribution

It presents a novel interior-point algorithm combined with variational integrators for maximal-coordinate rigid-body simulation with contact, achieving linear complexity and improved robustness.

Findings

Algorithm achieves linear-time complexity in contact points and bodies.

The method prevents constraint drift through variational discretization.

Demonstrated effectiveness on robotic system simulations.

Abstract

Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A maximal-coordinate representation of the dynamics enables efficient solving algorithms, but current methods in maximal coordinates require constraint stabilization schemes. Therefore, we propose an interior-point algorithm for the numerically robust treatment of rigid-body dynamics with contact interactions in maximal coordinates. Additionally, we discretize the dynamics with a variational integrator to prevent constraint drift. Our algorithm achieves linear-time complexity both in the number of contact points and the number of bodies, which is shown theoretically and demonstrated with an implementation. Furthermore, we simulate two robotic systems to highlight the applicability of the proposed algorithm.