CARO: Contact-Agnostic Residual Observation for Zero-Shot Robust Quadruped Locomotion

Zihan Yang; Shixuan Han; Kexin Guo; Xiang Yu

cs.ROAug 25, 2026

CARO: Contact-Agnostic Residual Observation for Zero-Shot Robust Quadruped Locomotion

Authors: Zihan Yang, Shixuan Han, Kexin Guo, Xiang Yu

Organizations: School of Aeronautic Science and Engineering, Beihang University, Beijing 100035, China · School of Automation Science and Electrical Engineering, Beihang University, Beijing 100035, China

Abstract

We propose CARO, a contact-agnostic residual observation framework for policy adaptation. CARO embeds a fixed-base Euler--Lagrange model into the reinforcement learning control loop and constructs a torque-level residual observation without requiring torque sensors, explicit contact estimation, or vision-based measurements of the floating-base position and linear velocity. A disturbance observer extracts a structured signal representing dynamics mismatch, while the policy learns to exploit this feedback for online adaptation. CARO is trained under the same terrain, command, and domain-randomization conditions as the nominal policy, without specialized disturbance curricula or additional adaptation supervision. Nevertheless, it achieves substantially improved zero-shot robustness in simulation and sim-to-real transfer tasks involving out-of-distribution payloads, center-of-mass shifts, terrain geometries, abrupt dynamics changes, and elevated-platform landings.

Figures & tables

Fig. 1: Overview of the CARO framework. The fixed-base Euler–Lagrange internal model is embedded within the RL control loop, and the resulting joint-level residual is provided to the policy as an adaptation signal.

Term	Range	Unit
Added base mass	$[-1.0,\,3.0]$	kg
Friction coefficient	$[0.1,\,1.25]$	-
CoM offset $x$	$[-0.05,\,0.01]$	m
CoM offset $y$	$[-0.03,\,0.03]$	m
CoM offset $z$	$[-0.03,\,0.03]$	m
Motor strength scale	$[0.8,\,1.2]$	-

TABLE I: Domain randomization shared by all methods during training.

Fig. 2: Simulation environments for zero-shot payload-terrain generalization. The robot is evaluated on five terrain types: flat , slope , rough slope , stepping stones , and wave . All terrain difficulty levels are set to $0.7$ .

	Success by Terrain (%) $\uparrow$						Success by Payload (%) $\uparrow$		Aggregate Performance $\uparrow$		Tracking Error $\downarrow$
Method	Flat	Slope	Rough	Stones	Wave	Mean	$2.5\times$	$3.0\times$	Walk Dist. (m)	Reward per Step	Linear (m/s)	Yaw Rate (rad/s)
Vanilla	54.3	54.2	36.4	41.1	50.2	47.2	1.0	0.0	8.224	0.0128	0.138	0.135
CARO	94.9	94.4	65.0	89.4	91.9	87.1	87.4	64.5	13.189	0.0143	0.105	0.080
RMA	92.6	90.0	74.0	76.5	75.6	81.7	84.6	36.4	12.768	0.0145	0.097	0.084
RL2AC	70.3	72.7	34.7	69.4	59.0	61.2	44.9	0.2	9.752	0.0133	0.112	0.122

TABLE II: Zero-shot payload-terrain robustness and tracking performance.

Fig. 4: CARO residual estimates for the hip- $x$ , hip- $y$ , and knee joints of the (a) front-left (FL), (b) front-right (FR), (c) rear-left (RL), and (d) rear-right (RR) legs. Curves show trial means, shaded regions indicate trial-to-trial variability, and the vertical dashed line marks the payload step.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Name	Expression	Weight
Linear-velocity tracking	$\exp\left(-\\|\bm{v}_{xy}^{\mathrm{cmd}}-\bm{v}_{xy}\\|^{2}/\sigma\right)$	$1.0$
Yaw-rate tracking	$\exp\left(-\|\omega_{z}^{\mathrm{cmd}}-\omega_{z}\|^{2}/\sigma\right)$	$0.5$
Vertical velocity	$v_{z}^{2}$	$-2.0$
Roll/pitch angular velocity	$\\|\bm{\omega}_{xy}\\|^{2}$	$-0.05$
Base orientation	$\\|\bm{g}_{xy}\\|^{2}$	$-0.2$
Base height	$(h-0.36)^{2}$	$-1.0$

Appendix

TABLE III: Reward terms used for policy training.

Robot Policy Adaptation

Robot policy adaptation changes or steers learned robot behaviors to handle new tasks, environments, hardware, and user preferences.

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Humanoids deployed in human-centered environments must handle force-interactive tasks, where external contacts introduce unexpected disturbances that disrupt locomotion accuracy and stability. Existing learning-based approaches rely on broad domain randomization, task-specific force objectives, or learning-based force estimators from motion history, each of which compromises accuracy, task transferability, or out-of-distribution (OOD) robustness. We present Analytical Disturbance-Aware Policy Training (ADAPT), a framework that equips humanoid policies with a physically grounded disturbance observer. The core of ADAPT is an analytical whole-body disturbance observer that estimates residual force/torque online with the accessible robot dynamics, without requiring force/torque sensors. Fed directly into the policy, the estimated disturbances give the humanoid an explicit, physics-derived sense of external force/torque that can generalize across diverse unseen scenes. Experiments on a Unitree G1 humanoid show that ADAPT achieves accurate disturbance prediction and stronger robustness than a proprioception-only baseline under torso perturbations, standing pushes, and asymmetric hand payloads, with improved velocity tracking even on OOD disturbances. Moreover, ADAPT enables penalizing inferred disturbances at lower-body joints to encourage lighter locomotion.

Abstract

Robot Policy Adaptation

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