# Momentum Control with Hierarchical Inverse Dynamics on a Torque-Controlled Humanoid

arXiv: https://arxiv.org/abs/1410.7284 · HTML: https://mlsanity.com/paper/1410.7284/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2014.

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

- [BeyondMimic: From Motion Tracking to Versatile Humanoid Control via Guided Diffusion](https://mlsanity.com/paper/2508.08241/) (2025)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Embedding Classical Balance Control Principles in Reinforcement Learning for Humanoid Recovery](https://mlsanity.com/paper/2603.08619/) (2026)
- [Robust Contact State Estimation in Humanoid Walking Gaits](https://mlsanity.com/paper/2208.00278/) (2022)
- [STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching](https://mlsanity.com/paper/2603.08478/) (2026)
- [Model-Informed Safe Reinforcement Learning for Bipedal Locomotion via Step-to-Step Prediction](https://mlsanity.com/paper/2609.34486/) (2026)
- [Exploiting Hierarchical Controller Structure in Contextual Parameter Learning for Humanoid Loco-Manipulation](https://mlsanity.com/paper/2610.04609/) (2026)

## Abstract (arXiv)

Hierarchical inverse dynamics based on cascades of quadratic programs have been proposed for the control of legged robots. They have important benefits but to the best of our knowledge have never been implemented on a torque controlled humanoid where model inaccuracies, sensor noise and real-time computation requirements can be problematic. Using a reformulation of existing algorithms, we propose a simplification of the problem that allows to achieve real-time control. Momentum-based control is integrated in the task hierarchy and a LQR design approach is used to compute the desired associated closed-loop behavior and improve performance. Extensive experiments on various balancing and tracking tasks show very robust performance in the face of unknown disturbances, even when the humanoid is standing on one foot. Our results demonstrate that hierarchical inverse dynamics together with momentum control can be efficiently used for feedback control under real robot conditions.