# TAMOLS: Terrain-Aware Motion Optimization for Legged Systems

arXiv: https://arxiv.org/abs/2206.14049 · HTML: https://mlsanity.com/paper/2206.14049/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2022.

## Built on by (most cited first, 14 of 14)

- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [DTC: Deep Tracking Control](https://mlsanity.com/paper/2309.15462/) (2023)
- [Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion](https://mlsanity.com/paper/2308.12517/) (2023)
- [RL + Model-based Control: Using On-demand Optimal Control to Learn Versatile Legged Locomotion](https://mlsanity.com/paper/2305.17842/) (2023)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Visual CPG-RL: Learning Central Pattern Generators for Visually-Guided Quadruped Locomotion](https://mlsanity.com/paper/2212.14400/) (2022)
- [Rethinking Robustness Assessment: Adversarial Attacks on Learning-based Quadrupedal Locomotion Controllers](https://mlsanity.com/paper/2405.12424/) (2024)
- [Deep Reinforcement Learning for Bipedal Locomotion: A Brief Survey](https://mlsanity.com/paper/2404.17070/) (2024)
- [DreamWaQ++: Obstacle-Aware Quadrupedal Locomotion With Resilient Multi-Modal Reinforcement Learning](https://mlsanity.com/paper/2409.19709/) (2024)
- [Guided Reinforcement Learning for Omnidirectional 3D Jumping in Quadruped Robots](https://mlsanity.com/paper/2507.16481/) (2025)
- [Generating a Terrain-Robustness Benchmark for Legged Locomotion: A Prototype via Terrain Authoring and Active Learning](https://mlsanity.com/paper/2208.07681/) (2022)
- [Efficient Reinforcement Learning for Jumping Monopods](https://mlsanity.com/paper/2309.07038/) (2023)
- [Global-Local Attention Decomposition for Terrain Encoding in Humanoid Perceptive Locomotion](https://mlsanity.com/paper/2606.00637/) (2026)
- [Mind Your Steps: A General Learning Framework for Accurate Humanoid Foothold Tracking](https://mlsanity.com/paper/2606.08253/) (2026)

## Abstract (arXiv)

Terrain geometry is, in general, non-smooth, non-linear, non-convex, and, if perceived through a robot-centric visual unit, appears partially occluded and noisy. This work presents the complete control pipeline capable of handling the aforementioned problems in real-time. We formulate a trajectory optimization problem that jointly optimizes over the base pose and footholds, subject to a heightmap. To avoid converging into undesirable local optima, we deploy a graduated optimization technique. We embed a compact, contact-force free stability criterion that is compatible with the non-flat ground formulation. Direct collocation is used as transcription method, resulting in a non-linear optimization problem that can be solved online in less than ten milliseconds. To increase robustness in the presence of external disturbances, we close the tracking loop with a momentum observer. Our experiments demonstrate stair climbing, walking on stepping stones, and over gaps, utilizing various dynamic gaits.