# Learn to Swim: Data-Driven LSTM Hydrodynamic Model for Quadruped Robot Gait Optimization

arXiv: https://arxiv.org/abs/2505.03146 · HTML: https://mlsanity.com/paper/2505.03146/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 6 May 2025.

## Builds on (most cited first, 3 of 3)

- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Controlling the Solo12 Quadruped Robot with Deep Reinforcement Learning](https://mlsanity.com/paper/2309.16683/) (2023)
- [Online Trajectory Optimization for Dynamic Aerial Motions of a Quadruped Robot](https://mlsanity.com/paper/2110.06330/) (2021)

## Built on by (most cited first, 1 of 1)

- [Swimming Under Constraints: A Safe Reinforcement Learning Framework for Quadrupedal Bio-Inspired Propulsion](https://mlsanity.com/paper/2603.04073/) (2026)

## Abstract (arXiv)

This paper presents a Long Short-Term Memory network-based Fluid Experiment Data-Driven model (FED-LSTM) for predicting unsteady, nonlinear hydrodynamic forces on the underwater quadruped robot we constructed. Trained on experimental data from leg force and body drag tests conducted in both a recirculating water tank and a towing tank, FED-LSTM outperforms traditional Empirical Formulas (EF) commonly used for flow prediction over flat surfaces. The model demonstrates superior accuracy and adaptability in capturing complex fluid dynamics, particularly in straight-line and turning-gait optimizations via the NSGA-II algorithm. FED-LSTM reduces deflection errors during straight-line swimming and improves turn times without increasing the turning radius. Hardware experiments further validate the model's precision and stability over EF. This approach provides a robust framework for enhancing the swimming performance of legged robots, laying the groundwork for future advances in underwater robotic locomotion.