# Fast Contact-Implicit Model-Predictive Control

arXiv: https://arxiv.org/abs/2107.05616 · HTML: https://mlsanity.com/paper/2107.05616/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2021.

## Built on by (most cited first, 16 of 16)

- [Aligning Cyber Space with Physical World: A Comprehensive Survey on Embodied AI](https://mlsanity.com/paper/2407.06886/) (2024)
- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [Learning coordinated badminton skills for legged manipulators](https://mlsanity.com/paper/2505.22974/) (2025)
- [Jacta: A Versatile Planner for Learning Dexterous and Whole-body Manipulation](https://mlsanity.com/paper/2408.01258/) (2024)
- [Planning-Guided Diffusion Policy Learning for Generalizable Contact-Rich Bimanual Manipulation](https://mlsanity.com/paper/2412.02676/) (2024)
- [CMMLoc: Advancing Text-to-PointCloud Localization with Cauchy-Mixture-Model Based Framework](https://mlsanity.com/paper/2503.02593/) (2025)
- [Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotion](https://mlsanity.com/paper/2403.20001/) (2024)
- [Chasing Stability: Humanoid Running via Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2509.19573/) (2025)
- [MOSAIC: Skill-Centric Manipulation Planning with Physics Simulation](https://mlsanity.com/paper/2504.16738/) (2025)
- [Learning to Walk With Less: A Dyna-Style Approach to Quadrupedal Locomotion](https://mlsanity.com/paper/2509.06296/) (2025)
- [Embedding Classical Balance Control Principles in Reinforcement Learning for Humanoid Recovery](https://mlsanity.com/paper/2603.08619/) (2026)
- [Learning Generic and Dynamic Locomotion of Humanoids Across Discrete Terrains](https://mlsanity.com/paper/2405.17227/) (2024)
- [Reinforcement Learning-Based Model Matching to Reduce the Sim-Real Gap in COBRA](https://mlsanity.com/paper/2406.13700/) (2024)
- [Learning Pivoting Manipulation with Force and Vision Feedback Using Optimization-based Demonstrations](https://mlsanity.com/paper/2508.01082/) (2025)
- [Shooting for Contact: Contact-Implicit Multiple Shooting for Dynamic Motion Retargeting](https://mlsanity.com/paper/2608.03116/) (2026)

## Abstract (arXiv)

We present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by utilizing a bi-level planning formulation with lower-level contact dynamics formulated as time-varying linear complementarity problems (LCPs) computed using strategic Taylor approximations about a reference trajectory. These dynamics enable the upper-level planning problem to reason about contact timing and forces, and generate entirely new contact-mode sequences online. To achieve reliable and fast numerical convergence, we devise a structure-exploiting interior-point solver for these LCP contact dynamics and a custom trajectory optimizer for the tracking problem. We demonstrate real-time solution rates for CI-MPC and the ability to generate and track non-periodic behaviours in hardware experiments on a quadrupedal robot. We also show that the controller is robust to model mismatch and can respond to disturbances by discovering and exploiting new contact modes across a variety of robotic systems in simulation, including a pushbot, planar hopper, planar quadruped, and planar biped.