# Proprioceptive External Torque Learning for Floating Base Robot and its Applications to Humanoid Locomotion

arXiv: https://arxiv.org/abs/2309.04138 · HTML: https://mlsanity.com/paper/2309.04138/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 4 of 4)

- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [The MIT Humanoid Robot: Design, Motion Planning, and Control For Acrobatic Behaviors](https://mlsanity.com/paper/2104.09025/) (2021)
- [State Estimation for a Humanoid Robot](https://mlsanity.com/paper/1402.5450/) (2014)

## Built on by (most cited first, 3 of 3)

- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [An Anatomy of Vision-Language-Action Models: From Modules to Milestones and Challenges](https://mlsanity.com/paper/2512.11362/) (2025)
- [Force-Aware Reinforcement Learning with Hybrid Sensorless Force Estimation for Wheeled-Legged Loco-Manipulation](https://mlsanity.com/paper/2609.13779/) (2026)

## Abstract (arXiv)

The estimation of external joint torque and contact wrench is essential for achieving stable locomotion of humanoids and safety-oriented robots. Although the contact wrench on the foot of humanoids can be measured using a force-torque sensor (FTS), FTS increases the cost, inertia, complexity, and failure possibility of the system. This paper introduces a method for learning external joint torque solely using proprioceptive sensors (encoders and IMUs) for a floating base robot. For learning, the GRU network is used and random walking data is collected. Real robot experiments demonstrate that the network can estimate the external torque and contact wrench with significantly smaller errors compared to the model-based method, momentum observer (MOB) with friction modeling. The study also validates that the estimated contact wrench can be utilized for zero moment point (ZMP) feedback control, enabling stable walking. Moreover, even when the robot's feet and the inertia of the upper body are changed, the trained network shows consistent performance with a model-based calibration. This result demonstrates the possibility of removing FTS on the robot, which reduces the disadvantages of hardware sensors. The summary video is available at https://youtu.be/gT1D4tOiKpo.