# Model Predictive Control with Environment Adaptation for Legged Locomotion

arXiv: https://arxiv.org/abs/2105.05998 · HTML: https://mlsanity.com/paper/2105.05998/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2021.

## Built on by (most cited first, 5 of 5)

- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Learning Perceptual Locomotion on Uneven Terrains using Sparse Visual Observations](https://mlsanity.com/paper/2109.14026/) (2021)
- [Benchmarking Model Predictive Control and Reinforcement Learning Based Control for Legged Robot Locomotion in MuJoCo Simulation](https://mlsanity.com/paper/2501.16590/) (2025)
- [VAE-Loco: Versatile Quadruped Locomotion by Learning a Disentangled Gait Representation](https://mlsanity.com/paper/2205.01179/) (2022)
- [PALo: Learning Posture-Aware Locomotion for Quadruped Robots](https://mlsanity.com/paper/2503.04462/) (2025)

## Abstract (arXiv)

Re-planning in legged locomotion is crucial to track the desired user velocity while adapting to the terrain and rejecting external disturbances. In this work, we propose and test in experiments a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot for achieving dynamic locomotion on a variety of terrains. We introduce a mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and improves adaptation to the terrain features. Our NMPC is based on the real-time iteration scheme that allows us to re-plan online at 25,Hz with a prediction horizon of 2 seconds. We use the single rigid body dynamic model defined in the center of mass frame in order to increase the computational efficiency. In simulations, the NMPC is tested to traverse a set of pallets of different sizes, to walk into a V-shaped chimney,and to locomote over rough terrain. In real experiments, we demonstrate the effectiveness of our NMPC with the mobility feature that allowed IIT's 87, kg quadruped robot HyQ to achieve an omni-directional walk on flat terrain, to traverse a static pallet, and to adapt to a repositioned pallet during a walk.