Linear-Time Contact and Friction Dynamics in Maximal Coordinates using Variational Integrators
This addresses the problem of numerical difficulties in contact interactions for control- and learning-based algorithms in robotics, representing an incremental improvement over existing methods that require constraint stabilization.
The paper tackles the challenge of robust and efficient simulation of contact and friction dynamics by proposing an interior-point algorithm with variational integrators in maximal coordinates, achieving linear-time complexity in both the number of contact points and bodies, as demonstrated theoretically and through implementation.
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.