# An Unconstrained Convex Formulation of Compliant Contact

arXiv: https://arxiv.org/abs/2110.10107 · HTML: https://mlsanity.com/paper/2110.10107/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2021.

## Built on by (most cited first, 3 of 3)

- [Dynamic Handover: Throw and Catch with Bimanual Hands](https://mlsanity.com/paper/2309.05655/) (2023)
- [RoboPianist: Dexterous Piano Playing with Deep Reinforcement Learning](https://mlsanity.com/paper/2304.04150/) (2023)
- [Simultaneous Pick and Place Detection by Combining SE(3) Diffusion Models with Differential Kinematics](https://mlsanity.com/paper/2504.19502/) (2025)

## Abstract (arXiv)

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.