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

TL;DR

FACET introduces a force-adaptive control framework for legged robots by training a policy to imitate the dynamics of a virtual mass–spring–damper impedance model applied to the CoM. The method uses a temporal-smoothed reference trajectory and a teacher–student RL setup to achieve stable sim-to-real transfer, enabling controllable compliance and robust interaction with large external forces. In simulation, FACET improves robustness to impulses, reduces collision impulses through tunable stiffness, and extends to loco-manipulators; real-world experiments with a Unitree Go2 validate compliant following and payload pulling up to 10 kg. Overall, the work demonstrates a principled way to integrate impedance-based force control with RL for diverse legged morphologies, enabling safer and more versatile forceful interactions in dynamic environments.

Abstract

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 \emph{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/

Figures (6)

• Figure 1: Inspired by impedance control, FACET enables task-space variable compliance and force-adaptive control on legged robots by imitating a reference spring-mass-damper model (b) using reinforcement learning. A high compliance allows the robot to be stopped or kinesthetically guided with ease (a), while a high stiffness allows the robot to exert large forces when pushing/pulling a payload (b). The framework applies to different morphologies and more complex configurations (c).
• Figure 2: Method overview. (a): The policy is trained to imitate the dynamics of an impedance reference model, i.e., a virtual mass-spring-damper system defined on the CoM of the robot (\ref{['sec:ref_model_tracking']}). (b): The reference dynamics is integrated from different starts along the robot trajectory to generate the reference targets, which provides tracking rewards for the policy. (\ref{['sec:temporal_smoothing']}). (c) The policy receives the same set of impedance parameters $(\mathbf{x}_{\rm des}, K_p, K_d)$ and is optimized to produce the same trajectory as that of the reference model (\ref{['sec:rl_setup']}).
• Figure 3: We train a state estimator$\mathcal{E}^{\text{est}}$ to predict the feature extracted by the privileged encoder$\mathcal{E}^{\text{priv}}$. In the second stage, the student actor $\pi^{\rm student}$ is initialized with the teacher's parameters and continues to be finetuned.
• Figure 4: Left: The success rate under varying levels of lateral impulses during locomotion at 1.5 m/s in the x-direction. FACET demonstrates superior robustness to large impulses compared to baseline policies trained with velocity tracking (vanilla) and with random impulse perturbations (robust). Middle: Planar (xy) trajectories of robot CoM under $400N$ peak force. 64 trajectories are shown for each policy. FACET can compliantly follow the impulse, adapting its velocity to keep balance, unlike the stiffer responses or failures of the baselines. Right: Distribution of collision impulse when the robot walks into a virtual wall. FACET achieves a significantly lower collision impulse, and this can be modulated by adjusting the impedance parameter $K_p$, indicating enhanced safety during physical interaction.
• Figure 5: Extension to legged loco-manipulator with two bodies of interest. With a fixed $K_p^{\rm eef}=90$, we increase and then decrease $K^{\rm base}_p$ to examine the relationship between the virtual spring forces and the actual pulling forces produced $f_{\rm pull}$. Similar to portela2024learning, $f_{\rm pull}$ is approximated by a force applied at the end-effector, which counteracts the robot so that it has near-zero velocity.