BFM·TTC

Test-Time Compute for Humanoid
Behavior Foundation Models

Weiji Xie1,2,† Junsong Wu1,2,† Zibo Zhou1,2 Yueru Chen1,2 Xingyi Wang1,3 Zhenhua Xiong2 Weinan Zhang2 Chenjia Bai1,4,*
1Institute of Artificial Intelligence (TeleAI), China Telecom 2Shanghai Jiaotong University 3Zhejiang University 4Gamma Robotics

† Equal contribution · * Corresponding author

Paper arXiv Code
Project video3:59 · English narration & captionsChapters

Additional test-time compute can improve motion execution without retraining the humanoid behavior foundation model.

The Command–Execution Gap

Humanoid behavior foundation models (BFMs) can execute diverse motions, but loco-manipulation—walking and manipulating objects—demands high whole-body positional accuracy. Current BFMs show systematic deviations between desired and executed motions: the body drifts from its intended global position, or hands and feet miss intended contacts. This is the command–execution gap.

The same reference motion is sent to a fixed behavior foundation model and robot dynamics. Using the reference as the command leaves errors in left sidestep and backward walking. Adjusted commands produce execution closer to the same reference.
Blue: reference · Orange: command · Gray: execution. Command changes are exaggerated for illustration.

The desired motion need not be supplied directly as the command. Adapting the input to the specific BFM can bring execution closer to the same desired motion.

Test-Time Command Optimization

We introduce Test-Time Command Optimization (TTCO) to improve motion-tracking fidelity in existing humanoid BFMs without further training. TTCO adapts the input command to the specific BFM through sampling-based optimization in closed-loop simulations of the BFM and robot dynamics.

TTCO samples candidate commands, evaluates parallel rollouts through a frozen BFM and physics simulator, updates the proposal from costs, and executes the best command segment before replanning.
  1. Sample commands
  2. Simulate execution
  3. Refine the proposal
  4. Execute and replan

The simulator executes the first segment of the lowest-cost candidate, then replans. For policy learning, command labels are generated offline.

Motion-Tracking Fidelity across Three BFMs

We evaluate TTCO on 12,273 AMASS reference motions using HEFT, SONIC, and TWIST2. Compared with directly using the reference motion as the command, TTCO reduces mean global body-position error by 79–84% across these three BFMs in simulation.

Left sidestep and backward walking. The real robot replays commands optimized in simulation without replanning.
Blue outlines mark the reference motion; all clips play at 1× speed.

Mean global body-position error

Nominal commands Optimized commands
HEFT
27.1
5.7
SONIC
61.5
12.7
TWIST2
109.5
17.3

Simulation means, in centimeters. Lower is better. All bars use the same scale.

Measurements and hardware frames

These simulation results use compute budget ratio K = 640. Joint acceleration increases for all three BFMs, showing a trade-off between tracking precision and motion smoothness.

AMASS means. Each pair reports nominal → optimized performance.
BFM Body-position error (cm) Root-position error (cm) Joint acceleration (rad/s²)
HEFT 27.1 → 5.7 26.4 → 4.8 10.104 → 17.246
SONIC 61.5 → 12.7 60.9 → 11.7 8.832 → 11.999
TWIST2 109.5 → 17.3 107.9 → 16.4 43.280 → 51.574
Real-robot sequences: left sidestep and backward walking, with nominal commands above and optimized commands below. Blue reference outlines show that the final displayed positions are closer after optimization.
Simulation-optimized commands are replayed on the real robot without replanning.
Blue outlines mark the reference motion.

Test-Time Compute Scaling

We analyze test-time compute scaling and derive an approximate compute-optimal allocation strategy. Fitted to limited measurements, our surrogate cost model captures the allocation trade-offs. The resulting strategy sustains performance gains as compute increases and generalizes across motions and BFMs.

On SONIC fitting motions, the proposed strategy follows the empirical optimum as the compute budget grows from 256 to 8192.
4.02%

Mean cost regret

58.0%

Lower cost from K = 256 to 8192

Compute settings and evaluation

The model predicts costs for untested compute configurations from limited measurements. On SONIC and the motions used for fitting, its strategy reaches 4.02% mean regret across six budgets. Regret is the percentage by which cost exceeds the best measured cost at the same budget. Cost falls by 58.0% as K increases from 256 to 8192.

K = I × N × H / E, where I is search iterations, N is candidates per iteration, H is rollout steps, and E is steps executed before replanning. Applied unchanged to SONIC, HEFT, and TWIST2 on five new motions, the strategy reaches 4.60% mean regret across five budgets.

High-Level Policy Learning and Demonstration Reuse

Because of the command–execution gap, recorded robot trajectories may not directly serve as action labels. We apply TTCO offline to generate BFM-specific labels from those trajectories, without requiring the original teleoperation body-motion commands. These labels train high-level loco-manipulation policies and support demonstration reuse across BFMs.

Execution BFM

SONIC demonstrations → SONIC execution

Original commands

TTCO commandsOurs

Recorded robot states

Separate evaluation rollouts · 1× speed

Real-robot success rates

We fine-tune GR00T N1.7 on SONIC demonstrations of four real-robot tasks. For each target BFM, observations and hand labels stay fixed while body-action labels change. Each task and label source is evaluated over 60 rollouts. Values are percentages.

SONIC demonstrations → SONIC execution
Task Original TTCO State
Cup in basket 55.0 55.0 0.0
Parcel bag on shelf 83.3 91.7 10.0
Basket on shelf 53.3 50.0 0.0
Bottle in drawer 50.0 60.0 0.0
Mean 60.4 64.2 2.5

Policies trained on TTCO labels reach 64.2% mean success with SONIC, compared with 60.4% for original-command labels and 2.5% for robot-state labels.