An Unconstrained Convex Formulation of Compliant Contact

TL;DR

This paper introduces a convex, unconstrained formulation for compliant frictional contact that enables fast, accurate, and robust simulation of robotic manipulation tasks, including complex contact patches and transitions.

Contribution

The authors develop a novel convex formulation that analytically eliminates contact constraints, allowing for efficient, globally convergent simulation of compliant contact with detailed physical modeling.

Findings

Solver achieves global convergence and fast warm-starts

Method outperforms existing commercial and open source simulators in accuracy

Robust simulation of robotic tasks with realistic contact transitions

Abstract

We present a convex formulation of compliant frictional contact and a robust, performant method to solve it in practice. By analytically eliminating contact constraints, we obtain an unconstrained convex problem. Our solver has proven global convergence and warm-starts effectively, enabling simulation at interactive rates. We develop compact analytical expressions of contact forces allowing us to describe our model in clear physical terms and to rigorously characterize our approximations. Moreover, this enables us not only to model point contact, but also to incorporate sophisticated models of compliant contact patches. Our time stepping scheme includes the midpoint rule, which we demonstrate achieves second order accuracy even with frictional contact. We introduce a number of accuracy metrics and show our method outperforms existing commercial and open source alternatives without sacrificing accuracy. Finally, we demonstrate robust simulation of robotic manipulation tasks at interactive rates, with accurately resolved stiction and contact transitions, as required for meaningful sim-to-real transfer. Our method is implemented in the open source robotics toolkit Drake.