# Adaptive MPC-based quadrupedal robot control under periodic disturbances

arXiv: https://arxiv.org/abs/2505.12361 · HTML: https://mlsanity.com/paper/2505.12361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 16 of 16)

- [Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control](https://mlsanity.com/paper/1909.06586/) (2019)
- [Learning Fast Adaptation with Meta Strategy Optimization](https://mlsanity.com/paper/1909.12995/) (2019)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Adaptive Safety with Control Barrier Functions](https://mlsanity.com/paper/1910.00555/) (2019)
- [Guided Constrained Policy Optimization for Dynamic Quadrupedal Robot Locomotion](https://mlsanity.com/paper/2002.09676/) (2020)
- [Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotion](https://mlsanity.com/paper/2009.10019/) (2020)
- [Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds](https://mlsanity.com/paper/1712.02889/) (2017)
- [Bayesian Learning-Based Adaptive Control for Safety Critical Systems](https://mlsanity.com/paper/1910.02325/) (2019)
- [Imitation Learning from MPC for Quadrupedal Multi-Gait Control](https://mlsanity.com/paper/2103.14331/) (2021)
- [Asynchronous Deep Model Reference Adaptive Control](https://mlsanity.com/paper/2011.02920/) (2020)
- [Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction](https://mlsanity.com/paper/1912.13154/) (2019)
- [Adaptive CLF-MPC With Application To Quadrupedal Robots](https://mlsanity.com/paper/2112.04536/) (2021)
- [Adaptive Force-based Control for Legged Robots](https://mlsanity.com/paper/2011.06236/) (2020)
- [New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases](https://mlsanity.com/paper/1908.05125/) (2019)
- [Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions](https://mlsanity.com/paper/2006.01229/) (2020)
- [Composite Adaptive Disturbance Rejection in Robotics via Instrumental Variables based DREM](https://mlsanity.com/paper/2406.19838/) (2024)

## Abstract (arXiv)

Recent advancements in adaptive control for reference trajectory tracking enable quadrupedal robots to perform locomotion tasks under challenging conditions. There are methods enabling the estimation of the external disturbances in terms of forces and torques. However, a specific case of disturbances that are periodic was not explicitly tackled in application to quadrupeds. This work is devoted to the estimation of the periodic disturbances with a lightweight regressor using simplified robot dynamics and extracting the disturbance properties in terms of the magnitude and frequency. Experimental evidence suggests performance improvement over the baseline static disturbance compensation. All source files, including simulation setups, code, and calculation scripts, are available on GitHub at https://github.com/aidagroup/quad-periodic-mpc.