# Adaptive CLF-MPC With Application To Quadrupedal Robots

arXiv: https://arxiv.org/abs/2112.04536 · HTML: https://mlsanity.com/paper/2112.04536/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2021.

## Built on by (most cited first, 7 of 7)

- [Online Damage Recovery for Physical Robots with Hierarchical Quality-Diversity](https://mlsanity.com/paper/2210.09918/) (2022)
- [Hierarchical Quality-Diversity for Online Damage Recovery](https://mlsanity.com/paper/2204.05726/) (2022)
- [Collaborative Navigation and Manipulation of a Cable-towed Load by Multiple Quadrupedal Robots](https://mlsanity.com/paper/2206.14424/) (2022)
- [MULE: Multi-terrain and Unknown Load Adaptation for Effective Quadrupedal Locomotion](https://mlsanity.com/paper/2505.00488/) (2025)
- [A stabilizing reinforcement learning approach for sampled systems with partially unknown models](https://mlsanity.com/paper/2208.14714/) (2022)
- [Combining model-predictive control and predictive reinforcement learning for stable quadrupedal robot locomotion](https://mlsanity.com/paper/2307.07752/) (2023)
- [Adaptive MPC-based quadrupedal robot control under periodic disturbances](https://mlsanity.com/paper/2505.12361/) (2025)

## Abstract (arXiv)

Modern robotic systems are endowed with superior mobility and mechanical skills that make them suited to be employed in real-world scenarios, where interactions with heavy objects and precise manipulation capabilities are required. For instance, legged robots with high payload capacity can be used in disaster scenarios to remove dangerous material or carry injured people. It is thus essential to develop planning algorithms that can enable complex robots to perform motion and manipulation tasks accurately. In addition, online adaptation mechanisms with respect to new, unknown environments are needed. In this work, we impose that the optimal state-input trajectories generated by Model Predictive Control (MPC) satisfy the Lyapunov function criterion derived in adaptive control for robotic systems. As a result, we combine the stability guarantees provided by Control Lyapunov Functions (CLFs) and the optimality offered by MPC in a unified adaptive framework, yielding an improved performance during the robot's interaction with unknown objects. We validate the proposed approach in simulation and hardware tests on a quadrupedal robot carrying un-modeled payloads and pulling heavy boxes.