# Inverse Dynamics Trajectory Optimization for Contact-Implicit Model Predictive Control

arXiv: https://arxiv.org/abs/2309.01813 · HTML: https://mlsanity.com/paper/2309.01813/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2023.

## Built on by (most cited first, 8 of 8)

- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [Equality Constrained Diffusion for Direct Trajectory Optimization](https://mlsanity.com/paper/2410.01939/) (2024)
- [Generative Predictive Control: Flow Matching Policies for Dynamic and Difficult-to-Demonstrate Tasks](https://mlsanity.com/paper/2502.13406/) (2025)
- [Chasing Stability: Humanoid Running via Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2509.19573/) (2025)
- [Diffusing Trajectory Optimization Problems for Recovery During Multi-Finger Manipulation](https://mlsanity.com/paper/2510.07030/) (2025)
- [Approximately Optimal Global Planning for Contact-Rich SE(2) Manipulation on a Graph of Reachable Sets](https://mlsanity.com/paper/2601.10827/) (2026)
- [Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupeds](https://mlsanity.com/paper/2603.14333/) (2026)
- [Shooting for Contact: Contact-Implicit Multiple Shooting for Dynamic Motion Retargeting](https://mlsanity.com/paper/2608.03116/) (2026)

## Abstract (arXiv)

Robots must make and break contact with the environment to perform useful tasks, but planning and control through contact remains a formidable challenge. In this work, we achieve real-time contact-implicit model predictive control with a surprisingly simple method: inverse dynamics trajectory optimization. While trajectory optimization with inverse dynamics is not new, we introduce a series of incremental innovations that collectively enable fast model predictive control on a variety of challenging manipulation and locomotion tasks. We implement these innovations in an open-source solver and present simulation examples to support the effectiveness of the proposed approach. Additionally, we demonstrate contact-implicit model predictive control on hardware at over 100 Hz for a 20-degree-of-freedom bi-manual manipulation task. Video and code are available at https://idto.github.io.