# FACET: Force-Adaptive Control via Impedance Reference Tracking for Legged Robots

arXiv: https://arxiv.org/abs/2505.06883 · HTML: https://mlsanity.com/paper/2505.06883/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 11 May 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [Orbit: A Unified Simulation Framework for Interactive Robot Learning Environments](https://mlsanity.com/paper/2301.04195/) (2023)
- [Extreme Parkour with Legged Robots](https://mlsanity.com/paper/2309.14341/) (2023)
- [ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots](https://mlsanity.com/paper/2306.14874/) (2023)
- [Robot Parkour Learning](https://mlsanity.com/paper/2309.05665/) (2023)
- [Deep Whole-Body Control: Learning a Unified Policy for Manipulation and Locomotion](https://mlsanity.com/paper/2210.10044/) (2022)
- [Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion](https://mlsanity.com/paper/2202.05481/) (2022)
- [UMI on Legs: Making Manipulation Policies Mobile with Manipulation-Centric Whole-body Controllers](https://mlsanity.com/paper/2407.10353/) (2024)
- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [Variable Impedance Control in End-Effector Space: An Action Space for Reinforcement Learning in Contact-Rich Tasks](https://mlsanity.com/paper/1906.08880/) (2019)
- [Visual Whole-Body Control for Legged Loco-Manipulation](https://mlsanity.com/paper/2403.16967/) (2024)
- [Adaptive Compliance Policy: Learning Approximate Compliance for Diffusion Guided Control](https://mlsanity.com/paper/2410.09309/) (2024)
- [Learning Torque Control for Quadrupedal Locomotion](https://mlsanity.com/paper/2203.05194/) (2022)
- [DexForce: Extracting Force-informed Actions from Kinesthetic Demonstrations for Dexterous Manipulation](https://mlsanity.com/paper/2501.10356/) (2025)
- [Torque-based Deep Reinforcement Learning for Task-and-Robot Agnostic Learning on Bipedal Robots Using Sim-to-Real Transfer](https://mlsanity.com/paper/2304.09434/) (2023)
- [Learning Force Control for Legged Manipulation](https://mlsanity.com/paper/2405.01402/) (2024)
- [Learning Visual Quadrupedal Loco-Manipulation from Demonstrations](https://mlsanity.com/paper/2403.20328/) (2024)
- [Robust Quadrupedal Locomotion via Risk-Averse Policy Learning](https://mlsanity.com/paper/2308.09405/) (2023)
- [Rethinking Robustness Assessment: Adversarial Attacks on Learning-based Quadrupedal Locomotion Controllers](https://mlsanity.com/paper/2405.12424/) (2024)
- [Bridging the Sim-to-Real Gap for Athletic Loco-Manipulation](https://mlsanity.com/paper/2502.10894/) (2025)
- [Arm-Constrained Curriculum Learning for Loco-Manipulation of the Wheel-Legged Robot](https://mlsanity.com/paper/2403.16535/) (2024)
- [PA-LOCO: Learning Perturbation-Adaptive Locomotion for Quadruped Robots](https://mlsanity.com/paper/2407.04224/) (2024)
- [DecAP: Decaying Action Priors for Accelerated Imitation Learning of Torque-Based Legged Locomotion Policies](https://mlsanity.com/paper/2310.05714/) (2023)
- [Guardians as You Fall: Active Mode Transition for Safe Falling](https://mlsanity.com/paper/2310.04828/) (2023)
- [Learning Robotic Policy with Imagined Transition: Mitigating the Trade-off between Robustness and Optimality](https://mlsanity.com/paper/2503.10484/) (2025)

## Built on by (most cited first, 11 of 11)

- [SoftMimic: Learning Compliant Whole-body Control from Examples](https://mlsanity.com/paper/2510.17792/) (2025)
- [Learning Human-Humanoid Coordination for Collaborative Object Carrying](https://mlsanity.com/paper/2510.14293/) (2025)
- [GentleHumanoid: Learning Upper-body Compliance for Contact-rich Human and Object Interaction](https://mlsanity.com/paper/2511.04679/) (2025)
- [CHIP: Adaptive Compliance for Humanoid Control through Hindsight Perturbation](https://mlsanity.com/paper/2512.14689/) (2025)
- [CoTaP: Compliant Task Pipeline and Reinforcement Learning of Its Controller with Compliance Modulation](https://mlsanity.com/paper/2509.25443/) (2025)
- [HAFO: A Force-Adaptive Control Framework for Humanoid Robots in Intense Interaction Environments](https://mlsanity.com/paper/2511.20275/) (2025)
- [Task-Specified Compliance Bounds for Humanoids via Lipschitz-Constrained Policies](https://mlsanity.com/paper/2603.16180/) (2026)
- [Force-Aware Reinforcement Learning with Hybrid Sensorless Force Estimation for Wheeled-Legged Loco-Manipulation](https://mlsanity.com/paper/2609.13779/) (2026)
- [Humanoid Rickshaw Pulling: Whole-Body Locomotion under Coupled Wheeled Loads](https://mlsanity.com/paper/2610.04238/) (2026)
- [CoDance: Learning Reactive and Compliant Human-Humanoid Interaction from Video](https://mlsanity.com/paper/2610.05324/) (2026)
- [HULK: Learning Whole-Body Forceful Loco-Manipulation for Humanoids](https://mlsanity.com/paper/2610.08970/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has made significant strides in legged robot control, enabling locomotion across diverse terrains and complex loco-manipulation capabilities. However, the commonly used position or velocity tracking-based objectives are agnostic to forces experienced by the robot, leading to stiff and potentially dangerous behaviors and poor control during forceful interactions. To address this limitation, we present Force-Adaptive Control via Impedance Reference Tracking (FACET). Inspired by impedance control, we use RL to train a control policy to imitate a virtual mass-spring-damper system, allowing fine-grained control under external forces by manipulating the virtual spring. In simulation, we demonstrate that our quadruped robot achieves improved robustness to large impulses (up to 200 Ns) and exhibits controllable compliance, achieving an 80% reduction in collision impulse. The policy is deployed to a physical robot to showcase both compliance and the ability to engage with large forces by kinesthetic control and pulling payloads up to 2/3 of its weight. Further extension to a legged loco-manipulator and a humanoid shows the applicability of our method to more complex settings to enable whole-body compliance control. Project Website: https://facet.pages.dev/