Contact-UAN: Unsupervised Actuator Networks as a Residual World Model for Humanoid Control

Our Team

Nolan Fey^*

Khai Nguyen^*

Yash Prabhu

Gabriel B. Margolis

Pulkit Agrawal

^*Co-first authors

Paper overview

Contact-UAN uses proprioception to align contact forces before learning an actuator residual, making residual world modeling work for floating-base humanoids and improving force/impulse-sensitive hardware behaviors from 6.5 minutes of walking data.

6.5 min

of real-world walking data

43%

lower force-tracking error

20%

more torque efficiency

Abstract

Humanoid policies trained in simulation can transfer qualitatively to hardware while failing to transfer the force interactions learned during training, compromising torque efficiency, load regulation, and robustness to impacts. This failure can arise from actuator sim-to-real gaps because forces depend on actuator torques. We introduce Contact-UAN, a residual world model that preserves a simulator's physics priors while correcting the actuator command channel to align simulated rollouts with recorded hardware rollouts. For humanoid motion with contact, this requires contact-consistent replay: if hardware playback in simulation begins with misaligned contact wrenches, the residual model learns to correct reset artifacts rather than actuator discrepancies. Using only onboard proprioception, Contact-UAN infers the simulator-side stance-foot pose needed to initialize replay with consistent contact forces. We show that a UAN trained on 6.5 minutes of real-world walking data generalizes to tasks that benefit from accurate force and impulse regulation and produces policies that transfer seamlessly to the real world, yielding 20% lower running torque, 43% lower force-tracking error, extreme compliance, accurate impedance control, and dynamic, robust jumps.

Technical Summary

The problem

Actuator gaps become force gaps

Humanoid policies can reproduce qualitative motion on hardware while failing to reproduce the force interactions learned in simulation. Policy optimization can exploit imperfect actuator dynamics, leading to excessive torques, poor commanded-force tracking, or failures during high impulse phases.

The actuator fidelity required for transfer is task-dependent: simple models may be sufficient for quasi-static behavior, while efficient running, force tracking, jumping, and landing depend on accurate actuator response, force generation, and impact absorption. Contact-UAN learns that missing actuator correction from onboard proprioception alone.

Baseline running: excessive torque usage

Baseline jumping: actuator mismatch at takeoff and landing

How can we close the sim-to-real gap with contacts for humanoid control without torque sensors, contact force sensors, or motion capture?

The method

Contact-UAN in three stages

1

Initialize contact-consistent replay

Infer base velocity and simulator-side stance-foot pose from onboard proprioception.
2

Learn the actuator residual

Train the UAN to correct recorded commands so that simulated transitions better match hardware.
3

Train policies, then deploy

Freeze the UAN during downstream training; run only the learned task policy on the robot.

Contact-UAN pipeline showing contact-consistent hardware replay, UAN training, downstream policy training, and policy-only deployment

The Unsupervised Actuator Network (UAN) adds a residual correction δq_t to the base joint-position target:

q_t^cmd = q_t^base + δq_t.

This preserves the simulator's rigid-body dynamics, actuator implementation, contact solver, and numerical integration while correcting only the actuator command channel. During downstream policy training the UAN is deterministic and frozen, forcing high-reward behaviors to remain feasible under the corrected actuator response.

Contact-consistent replay

Infer the simulator state that reproduces contact

Open-loop replay isolates actuator-model error only when simulation starts from a hardware-equivalent state. In a soft-contact simulator, that state is not necessarily the robot's literal absolute height: it is the simulator-side stance-foot pose whose small penetration and tilt reproduce the support wrench implied by the hardware trajectory.

Proprioceptive state-estimation pipeline for contact status, stance-foot height and orientation, and base velocity — Short proprioceptive histories predict contact status, stance-foot pose, and base velocity.

Plot showing strong contact-wrench sensitivity to millimeter-scale height offsets and degree-scale pitch offsets — Soft-contact wrenches are highly sensitive to foot height and orientation.

Contact pose is estimated in two stages: classify contact status, then regress the penetrating foot pose only for feet confidently in stance. Candidate root poses are fused using contact-probability weights. Restricting regression to stance reduces contact-height RMSE by an order of magnitude over direct regression across all gait phases. This precision is essential: in the paper's MuJoCo model, a +2 mm root-height offset reduces normal force by roughly 50%, while a −2° pitch offset changes the support moment by roughly 45%. The estimator omits absolute base height, preventing it from copying a height that may not transfer to hardware.

Model validation

Relabel the reset, then close the actuator gap

Contact-consistent relabeling removes reset artifacts from hardware replay. The UAN then closes the remaining actuator mismatch, reducing 24-step joint-position error and closely matching held-out running trajectories.

Direct estimator baseline

Contact-consistent stance-only estimator

Contact-consistent reset + UAN

Real-world transfer

One residual world model, diverse downstream tasks

A single UAN trained once on walking data supports running, whole-body force control, extreme compliance, proprioceptive impedance control, and dynamic jumping on a 29-DoF Unitree G1. Downstream policies are trained in the frozen UAN-augmented simulator with no robot-specific domain randomization; terrain, ground friction, and pushes are still randomized to encourage robust recovery.

42.8 ± 12.1% lower average force-tracking error

Extreme compliance at zero commanded force

Dynamic jumping, soft landing, and disturbance recovery

Impedance control using onboard sensing alone

3.13 ± 0.06 m/s and 20% lower hardware torque usage

Controlled ablations

Physics priors make the residual data-efficient

In a controlled sim-to-sim transfer experiment, fully learned offline world models struggle even with 33 hours of transitions—approximately 400× more data than the 5-minute UAN dataset.

Adding task-specific running data provides little additional benefit over walking data, indicating that the actuator residual generalizes beyond the behavior used to collect it.

Current scope

Limitations

Contact-UAN models each actuator independently and does not capture inter-joint actuator coupling or motor-temperature-dependent effects. Coupling could be modeled with a whole-body network or cross-attention; temperature effects may require longer datasets, heat modeling, or additional sensing.

Questions & answers

Common questions

Why is it called a residual world model?

A world model predicts the next state from the current state and action. Contact-UAN keeps the simulator's rigid-body dynamics and contact physics, then learns only the actuator-command correction needed for simulated joint transitions to match hardware. It is residual because it corrects an existing physics model instead of replacing it.

How does it compare with fully learned world models?

Fully learned models such as RWM-U must represent the complete robot-environment transition. Contact-UAN retains the simulator as a strong structural prior and learns only the actuator gap. In the controlled sim-to-sim experiment, a UAN trained with 5 minutes of target data reaches expert-level survival, while fully learned offline models struggle with 33 hours of transitions.

Why not rely only on system identification or domain randomization?

System identification is limited by the chosen parameterization, while broad domain randomization can produce conservative policies that under-use the hardware. Contact-UAN learns a reusable actuator correction directly from proprioceptive trajectories and removes robot-specific randomization from downstream policy training.

Why is state estimation necessary for replay?

In a soft-contact simulator, millimeter-scale foot-height and degree-scale orientation errors can substantially change the contact wrench. Without a contact-consistent reset, the UAN may learn to correct an initialization artifact instead of the actuator gap. The proprioceptive estimators infer the simulator-side stance-foot pose that produces the appropriate support interaction.

Does the UAN need to be retrained for every task?

No. The UAN is trained once on walking data and then frozen. Running, force-control, impedance, and jumping policies are trained independently in the same UAN-augmented simulator.

What runs on the robot at deployment?

Only the downstream task policy. The state estimators are used for offline relabeling, and the UAN is used only while training policies in simulation.