# Real-Time Multi-Contact Model Predictive Control via ADMM

arXiv: https://arxiv.org/abs/2109.07076 · HTML: https://mlsanity.com/paper/2109.07076/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2021.

## Built on by (most cited first, 7 of 7)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Jacta: A Versatile Planner for Learning Dexterous and Whole-body Manipulation](https://mlsanity.com/paper/2408.01258/) (2024)
- [Simultaneous Contact-Rich Grasping and Locomotion via Distributed Optimization Enabling Free-Climbing for Multi-Limbed Robots](https://mlsanity.com/paper/2207.01418/) (2022)
- [Learning Linear Complementarity Systems](https://mlsanity.com/paper/2112.13284/) (2021)
- [Diffusion-Based Impedance Learning for Contact-Rich Manipulation Tasks](https://mlsanity.com/paper/2509.19696/) (2025)
- [Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?](https://mlsanity.com/paper/2411.06542/) (2024)
- [Approximately Optimal Global Planning for Contact-Rich SE(2) Manipulation on a Graph of Reachable Sets](https://mlsanity.com/paper/2601.10827/) (2026)

## Abstract (arXiv)

We propose a hybrid model predictive control algorithm, consensus complementarity control (C3), for systems that make and break contact with their environment. Many state-of-the-art controllers for tasks which require initiating contact with the environment, such as locomotion and manipulation, require a priori mode schedules or are so computationally complex that they cannot run at real-time rates. We present a method, based on the alternating direction method of multipliers (ADMM), capable of highspeed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on three numerical examples, including two frictional contact problems, and physical experimentation on an underactuated multi-contact system.