# Learning Locomotion on Complex Terrain for Quadrupedal Robots with Foot Position Maps and Stability Rewards

arXiv: https://arxiv.org/abs/2604.02744 · HTML: https://mlsanity.com/paper/2604.02744/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2026.

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

- [FootQuery: Future-Touchdown-Guided Retrieval from Depth History for Perceptive Humanoid Locomotion](https://mlsanity.com/paper/2609.21447/) (2026)

## Abstract (arXiv)

Quadrupedal locomotion over complex terrain has been a long-standing research topic in robotics. While recent reinforcement learning-based locomotion methods improve generalizability and foot-placement precision, they rely on implicit inference of foot positions from joint angles, lacking the explicit precision and stability guarantees of optimization-based approaches. To address this, we introduce a foot position map integrated into the heightmap, and a dynamic locomotion-stability reward within an attention-based framework to achieve locomotion on complex terrain. We validate our method extensively on terrains seen during training as well as out-of-domain (OOD) terrains. Our results demonstrate that the proposed method enables precise and stable movement, resulting in improved locomotion success rates on both in-domain and OOD terrains.