HAC-LOCO: Learning Hierarchical Active Compliance Control for Quadruped Locomotion under Continuous External Disturbances

Despite recent remarkable achievements in quadruped control, it remains challenging to ensure robust and compliant locomotion in the presence of unforeseen external disturbances. Existing methods prioritize locomotion robustness over compliance, often leading to stiff, high-frequency motions, and energy inefficiency. This paper, therefore, presents a two-stage hierarchical learning framework that can learn to take active reactions to external force disturbances based on force estimation. In the first stage, a velocity-tracking policy is trained alongside an auto-encoder to distill historical proprioceptive features. A neural network-based estimator is learned through supervised learning, which estimates body velocity and external forces based on proprioceptive measurements. In the second stage, a compliance action module, inspired by impedance control, is learned based on the pre-trained encoder and policy. This module is employed to actively adjust velocity commands in response to external forces based on real-time force estimates. With the compliance action module, a quadruped robot can robustly handle minor disturbances while appropriately yielding to significant forces, thus striking a balance between robustness and compliance. Simulations and real-world experiments have demonstrated that our method has superior performance in terms of robustness, energy efficiency, and safety. Experiment comparison shows that our method outperforms the state-of-the-art RL-based locomotion controllers. Ablation studies are given to show the critical roles of the compliance action module.

@article{zhou2025_2507.02447,
  title={ HAC-LOCO: Learning Hierarchical Active Compliance Control for Quadruped Locomotion under Continuous External Disturbances },
  author={ Xiang Zhou and Xinyu Zhang and Qingrui Zhang },
  journal={arXiv preprint arXiv:2507.02447},
  year={ 2025 }
}