# Consensus Complementarity Control for Multi-Contact MPC

arXiv: https://arxiv.org/abs/2304.11259 · HTML: https://mlsanity.com/paper/2304.11259/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2023.

## Built on by (most cited first, 6 of 6)

- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [Empirical Analysis of Sim-and-Real Cotraining of Diffusion Policies for Planar Pushing from Pixels](https://mlsanity.com/paper/2503.22634/) (2025)
- [Planning-Guided Diffusion Policy Learning for Generalizable Contact-Rich Bimanual Manipulation](https://mlsanity.com/paper/2412.02676/) (2024)
- [Generative Predictive Control: Flow Matching Policies for Dynamic and Difficult-to-Demonstrate Tasks](https://mlsanity.com/paper/2502.13406/) (2025)
- [Combined Constrained Sampling and Reinforcement Learning for Robotic Manipulation](https://mlsanity.com/paper/2602.08557/) (2026)
- [Learning Pivoting Manipulation with Force and Vision Feedback Using Optimization-based Demonstrations](https://mlsanity.com/paper/2508.01082/) (2025)

## 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 too computationally complex to run at real-time rates. We present a method based on the alternating direction method of multipliers (ADMM) that is capable of high-speed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on five numerical examples, including four high-dimensional frictional contact problems, and a physical experimentation on an underactuated multi-contact system. We further demonstrate the effectiveness of our method on a physical experiment accomplishing a high-dimensional, multi-contact manipulation task with a robot arm.