# Stabilizing Humanoid Robot Trajectory Generation via Physics-Informed Learning and Control-Informed Steering

arXiv: https://arxiv.org/abs/2509.24697 · HTML: https://mlsanity.com/paper/2509.24697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Real-world robot offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- Offline RL and imitation learning from data / [Real-world robot offline RL](https://mlsanity.com/offlinerl/real-world-robot-offline-rl/)

## Builds on (most cited first, 17 of 17)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [Synthesizing Physical Character-Scene Interactions](https://mlsanity.com/paper/2302.00883/) (2023)
- [Humanoid-Gym: Reinforcement Learning for Humanoid Robot with Zero-Shot Sim2Real Transfer](https://mlsanity.com/paper/2404.05695/) (2024)
- [DeepGait: Planning and Control of Quadrupedal Gaits using Deep Reinforcement Learning](https://mlsanity.com/paper/1909.08399/) (2019)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [Sim-to-Real Learning for Humanoid Box Loco-Manipulation](https://mlsanity.com/paper/2310.03191/) (2023)
- [HumanMimic: Learning Natural Locomotion and Transitions for Humanoid Robot via Wasserstein Adversarial Imitation](https://mlsanity.com/paper/2309.14225/) (2023)
- [Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policies](https://mlsanity.com/paper/2410.11825/) (2024)
- [Deep Learning Models for Global Coordinate Transformations that Linearize PDEs](https://mlsanity.com/paper/1911.02710/) (2019)
- [Learning natural locomotion behaviors for humanoid robots using human knowledge](https://mlsanity.com/paper/2005.10195/) (2020)
- [A Benchmarking of DCM Based Architectures for Position, Velocity and Torque Controlled Humanoid Robots](https://mlsanity.com/paper/1911.13233/) (2019)
- [Momentum Control of an Underactuated Flying Humanoid Robot](https://mlsanity.com/paper/1702.06075/) (2017)
- [A Benchmarking of DCM Based Architectures for Position and Velocity Controlled Walking of Humanoid Robots](https://mlsanity.com/paper/1809.02167/) (2018)
- [Online DNN-driven Nonlinear MPC for Stylistic Humanoid Robot Walking with Step Adjustment](https://mlsanity.com/paper/2410.07849/) (2024)

## Abstract (arXiv)

Recent trends in humanoid robot control have successfully employed imitation learning to enable the learned generation of smooth, human-like trajectories from human data. While these approaches make more realistic motions possible, they are limited by the amount of available motion data, and do not incorporate prior knowledge about the physical laws governing the system and its interactions with the environment. Thus they may violate such laws, leading to divergent trajectories and sliding contacts which limit real-world stability. We address such limitations via a two-pronged learning strategy which leverages the known physics of the system and fundamental control principles. First, we encode physics priors during supervised imitation learning to promote trajectory feasibility. Second, we minimize drift at inference time by applying a proportional-integral controller directly to the generated output state. We validate our method on various locomotion behaviors for the ergoCub humanoid robot, where a physics-informed loss encourages zero contact foot velocity. Our experiments demonstrate that the proposed approach is compatible with multiple controllers on a real robot and significantly improves the accuracy and physical constraint conformity of generated trajectories.