P-BFM: Perceptive Behavioral Foundation Models for Humanoid Control via Unsupervised Reinforcement Learning

Xue Wang; Yitang Li; Yiming Zhang; Siqin Wang; Junhan Sun; Zhihao Liu; Yaojie Shen; Jingbo Yuan

cs.ROOct 11, 2026

P-BFM: Perceptive Behavioral Foundation Models for Humanoid Control via Unsupervised Reinforcement Learning

Authors: Xue Wang, Yitang Li, Yiming Zhang, Siqin Wang, Junhan Sun, Zhihao Liu, Yaojie Shen, Jingbo Yuan,

Organizations: University of Shanghai for Science and Technology · RoboPartyLab · Tsinghua University · Zhejiang University ·

Abstract

Behavioral foundation models (BFMs) provide humanoids with reusable repertoires of whole-body behaviors; in real-world humanoid control, the same behavioral intent may require fundamentally different motions under different terrain constraints. Covering such variation with terrain-matched demonstrations requires enumerating a combinatorial space of behaviors and terrain geometries. We introduce P-BFM, a perceptive behavioral foundation model that factorizes humanoid control into terrain-invariant intent and terrain-conditioned realization. A forward-backward representation maps motion references, target states, and reward functions into a shared intent space without terrain information, while a perceptive policy learns how to realize each intent under the surrounding terrain geometry. We further identify a complementary limitation of purely latent control: behavioral latents can preserve local motion patterns while losing precise global progress. We therefore introduce Explicit Root Instructions (ERI), which separates global transport (e.g., heading and planar velocity) from behavioral intent, while leaving local whole-body adaptation to the perceptive policy. This decomposition leads to a characteristic capability absent from conventional BFMs: one fixed intent induces different, terrain-appropriate behaviors, including changes in step height, stride, posture, foothold placement, and contacts, without terrain-specific demonstrations. Across challenging terrains, P-BFM improves motion fidelity, root-control precision, and perturbation recovery over strong baselines. A single frozen policy further supports motion tracking, goal reaching, reward inference, teleoperation, and terrain-aware recovery, and transfers zero-shot to a Unitree G1 using onboard depth sensing.

Figures & tables

Figure 1: Unified intent representation in P-BFM . Motion references, teleoperation inputs, target states, and reward functions are mapped into a shared terrain-agnostic intent space. A single perceptive policy realizes the same intent through distinct behaviors adapted to different terrains. Videos: https://roboparty.github.io/P-BFM/

Figure 2: Overview of P-BFM . During pretraining, we learn a terrain-agnostic intent space through FB learning and a perceptive actor that interprets the intent latent into terrain-adaptive behavior. At inference, different task specifications are encoded into latents, and the same actor executes them across terrains without task-specific training. Orange arrows denote inputs to the actor.

Method	Seen motions					Unseen motions
Method	$E_{\mathrm{jpos}}\;(\mathrm{rad})\downarrow$	$E_{\mathrm{vel}}^{\mathrm{root}}\;(\mathrm{m/s})\downarrow$	$E_{\mathrm{head}}^{\mathrm{root}}\;({}^{\circ})\downarrow$	$\mathrm{FS}\;(\mathrm{cm})\downarrow$	$\mathrm{RR}\;(\%)\uparrow$	$E_{\mathrm{jpos}}\;(\mathrm{rad})\downarrow$	$E_{\mathrm{vel}}^{\mathrm{root}}\;(\mathrm{m/s})\downarrow$	$E_{\mathrm{head}}^{\mathrm{root}}\;({}^{\circ})\downarrow$	$\mathrm{FS}\;(\mathrm{cm})\downarrow$	$\mathrm{RR}\;(\%)\uparrow$
UFO	$0.15{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.06}$	$0.65{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.46}$	$49.6{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,29.3}$	$0.092{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.050}$	$3.4$	$0.16{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.06}$	$0.37{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.27}$	$28.9{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,23.9}$	$0.066{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.047}$	$16.6$
PMT	$0.21{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.04}$	$\mathbf{0.20}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.08}$	$8.8{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,7.7}$	$0.078{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.029}$	$2.4$	$0.46{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.09}$	$0.86{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.27}$	$84.4{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,22.5}$	$0.205{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.103}$	$0.5$
P-BFM	$\mathbf{0.11}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.04}$	${0.25}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.12}$	$\mathbf{6.9}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,5.4}$	$\mathbf{0.043}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.026}$	$\mathbf{41.2}$	$\mathbf{0.13}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.06}$	$\mathbf{0.21}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.12}$	$\mathbf{6.7}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,4.7}$	$\mathbf{0.026}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.016}$	$\mathbf{61.4}$

Table 1: Comparison with existing perception-based general-purpose humanoid controllers on seen motions and a subset of 994 unseen SOMA motions.

Figure 3: Terrain-adaptive behavior from a single forward-walking intent. Given the same reference-derived intent, P-BFM produces distinct locomotion patterns across terrains, including stair ascent/descent, slope traversal, discrete foothold selection, and rough-terrain stepping.

Method	Seen motions					Unseen motions
Method	$E_{\mathrm{jpos}}\;(\mathrm{rad})\downarrow$	$E_{\mathrm{vel}}^{\mathrm{root}}\;(\mathrm{m/s})\downarrow$	$E_{\mathrm{head}}^{\mathrm{root}}\;({}^{\circ})\downarrow$	$\mathrm{FS}\;(\mathrm{cm})\downarrow$	$\mathrm{RR}\;(\%)\uparrow$	$E_{\mathrm{jpos}}\;(\mathrm{rad})\downarrow$	$E_{\mathrm{vel}}^{\mathrm{root}}\;(\mathrm{m/s})\downarrow$	$E_{\mathrm{head}}^{\mathrm{root}}\;({}^{\circ})\downarrow$	$\mathrm{FS}\;(\mathrm{cm})\downarrow$	$\mathrm{RR}\;(\%)\uparrow$
w/o head	$0.12{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.04}$	$0.28{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.14}$	$19.3{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,14.2}$	$0.045{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.026}$	$20.7$	$\mathbf{0.13}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.06}$	$0.22{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.12}$	$14.6{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,14.3}$	$0.026{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.018}$	$39.5$
w/o vel	$0.12{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.04}$	$0.41{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.26}$	$7.7{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,6.9}$	$\mathbf{0.032}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.018}$	$22.4$	$\mathbf{0.13}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.06}$	$0.32{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.19}$	$\mathbf{6.3}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,4.9}$	$\mathbf{0.020}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.012}$	$42.9$
P-BFM	$\mathbf{0.11}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.04}$	$\mathbf{0.25}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.12}$	$\mathbf{6.9}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,5.4}$	$0.043{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.026}$	$\mathbf{41.2}$	$\mathbf{0.13}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.06}$	$\mathbf{0.21}{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.12}$	$6.7{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,4.7}$	$0.026{\color[rgb]{0.5,0.5,0.5}\scriptstyle\,\pm\,0.016}$	$\mathbf{61.4}$

Table 2: Ablation study of global instructions on seen and unseen motions. “w/o head” removes the global heading instruction, while “w/o vel” removes the global base-velocity instruction.

Figure 4: Qualitative ablation. Without heading instructions, the robot exhibits heading drift; without velocity instructions, it steps in place. P-BFM maintains the intended heading and progress.

Figure 5: Real-world teleoperation with perception-driven terrain adaptation.

Figure 6: Real-world demonstrations of goal reaching and terrain-aware recovery.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Observation group	Dimension
Proprioceptive state	64
Previous action	29
Four-step proprioception–action history	372
Heading instruction	2
Horizontal-velocity instruction and validity flag	3
Estimated current root velocity	3

Appendix

Table 3: Observation groups used by the full model. Privileged inputs are used during training and are excluded from the deployed actor.

Network	Width $w$	Branch blocks $k$	Trunk blocks $r$	Output $m$	Members
$F$	2048	4	6	256	2
$Q_{D}$	1024	2	4	1	2
$Q_{A}$	2048	2	4	1	2
$Q_{H}$	1024	1	3	1	2
$Q_{V}$	1024	1	3	1	2

Appendix

Table 4: Forward and critic architectures. Each branch includes two affine projections in addition to its listed residual blocks. Each trunk includes an additional output projection. Each ensemble member is a complete, independently parameterized network.

Layer	Parameters	Output shape
Input	Normalized depth	$1\times 18\times 32$
Conv + ReLU	$1\to 16,\ k=3,\ s=1,\ p=1$	$16\times 18\times 32$
Conv + ReLU	$16\to 32,\ k=3,\ s=2,\ p=1$	$32\times 9\times 16$
Conv + ReLU	$32\to 64,\ k=3,\ s=1,\ p=1$	$64\times 9\times 16$
Adaptive average pooling	Output size $2\times 4$	$64\times 2\times 4$
Flatten	—	$512$

Appendix

Table 5: Shared single-frame depth encoder. Shapes are channels

\times

height

\times

width before flattening.

Value term	Role	Base coefficient
$Q_{\mathrm{FB}}$	Behavioral intent	1
$Q_{D}$	Conditional motion prior	0.01
$Q_{A}$	Physical auxiliary objectives	0.02
$Q_{H}$	Heading tracking	0.002
$Q_{V}$	Horizontal-velocity tracking	0.002

Appendix

Table 6: Coefficients in the actor objective. The four auxiliary value terms are additionally multiplied by the detached scale

\alpha

Cost	Coefficient
Action change	$-0.1$
Joint-position limit violation	$-10$
Body-impact severity	$-1$
Loaded-foot tangential speed	$-4$
Ankle-roll magnitude	$-1$
Foot stumbling	$-2$

Appendix

Table 7: Physical costs and their coefficients inside

r_{A}^{\mathrm{raw}}

. These coefficients are separate from the actor coefficient

0.02

for

Q_{A}

Parameter	Value
Latent dimension	256
Discount factor	0.98
Minibatch size per GPU	1,024
Effective minibatch size across eight GPUs	8,192
Forward-network learning rate	$3\times 10^{-4}$
Backward-network learning rate	$1\times 10^{-5}$

Appendix

Table 8: Optimization settings of the evaluated full model.

ID	Terrain family	Geometry parameters
0	Flat terrain	Planar surface; geometry is independent of difficulty.
1	Perlin-noise rough terrain	Target height range $0$ to $H_{\mathrm{rough}}(d)=0.02+0.04d\,\mathrm{m}$ before border resampling.
2	Pyramid stairs (outward descent)	Riser height $h(d)=0.10+0.10d\,\mathrm{m}$ ; tread depth $0.30\,\mathrm{m}$ ; central platform $1.6\times 1.6\,\mathrm{m}$ .
3	Inverted pyramid stairs (outward ascent)	Same riser heights, tread depth, and central-platform dimensions as the pyramid stairs, with inverted elevation.
4	Low platforms	Grid-cell width $0.80\,\mathrm{m}$ ; cell heights sampled from $[-H_{\mathrm{plat}}(d),H_{\mathrm{plat}}(d)]$ , where $H_{\mathrm{plat}}(d)=0.03+0.07d\,\mathrm{m}$ , before height quantization.
5	Inverted pyramid slope	Configured slope parameter $s(d)=0.20d$ ; nominal angle envelope $0$ to $\arctan(0.20)\approx 11.31^{\circ}$ .

Appendix

Table 9: Terrain families and difficulty-dependent geometry. IDs follow the terrain generator’s column order. Here

d

denotes normalized tile difficulty. Stair traversal directions are defined for motion from the central platform toward the tile boundary.

Evaluation	Continuous metrics		Recovery
	Motions/segments	Episodes	Segments	Episodes
LaFAN comparison	902	315,700	862	241,360
LaFAN ablation	862	301,700	862	241,360
SOMA	994	347,900	281	78,680
PMT references	297	103,950	297	83,160

Appendix

Table 10: Main evaluation coverage per model. Continuous metrics use five trials per motion–terrain–row condition. Recovery uses one trial at each of four force magnitudes.

Three-method comparison
Method	RR@3s (%)	RR@5s (%)	Pre-push violation (%)
UFO	22.50	28.38	31.70
PMT	0.87	1.07	98.98
P-BFM	56.99	69.50	20.30
Ablation
w/o Heading Instr.	35.15	45.44	21.52

Appendix

Table 11: Category-balanced SOMA recovery results. Rates are recording- and category-macro averages. Each condition uses one trial per force magnitude. Pre-push violation denotes failure to remain within the tracking tolerances throughout the one-second pre-push interval.

Parameter	Setting
Automatic exposure	Disabled
Exposure time	$1600\,\mu\mathrm{s}$
Gain	16
Infrared emitter power	240
Depth-stream resolution	$480\times 270$ pixels
Depth-stream frame rate	$60\,\mathrm{Hz}$

Appendix

Table 12: Recorded camera and depth-processing settings for the final real-world deployment. Gain and infrared emitter power are reported as device setting values.

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Building Behavioral Foundation Models (BFMs) for humanoid robots has the potential to unify diverse control tasks under a single, promptable generalist policy. However, existing approaches are either exclusively deployed on simulated humanoid characters, or specialized to specific tasks such as tracking. We propose BFM-Zero, a framework that learns an effective shared latent representation that embeds motions, goals, and rewards into a common space, enabling a single policy to be prompted for multiple downstream tasks without retraining. This well-structured latent space in BFM-Zero enables versatile and robust whole-body skills on a Unitree G1 humanoid in the real world, via diverse inference methods, including zero-shot motion tracking, goal reaching, and reward optimization, and few-shot optimization-based adaptation. Unlike prior on-policy reinforcement learning (RL) frameworks, BFM-Zero builds upon recent advancements in unsupervised RL and Forward-Backward (FB) models, which offer an objective-centric, explainable, and smooth latent representation of whole-body motions. We further extend BFM-Zero with critical reward shaping, domain randomization, and history-dependent asymmetric learning to bridge the sim-to-real gap. Those key design choices are quantitatively ablated in simulation. A first-of-its-kind model, BFM-Zero establishes a step toward scalable, promptable behavioral foundation models for whole-body humanoid control.

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Behavioral foundation models (BFMs) have recently shown that a single humanoid policy can support diverse whole-body control, but extending such generality to physical interaction remains challenging. We introduce I-BFM, to our knowledge the first BFM for humanoid-object interaction. Rather than relying on task-specific policies or reference tracking, I-BFM learns a shared representation of the coupled dynamics among the humanoid, objects, and their contacts using forward-backward representations and unsupervised reinforcement learning. Given a downstream task reward, the same policy can be directly conditioned on a latent command to execute closed-loop interaction without task-specific policy optimization. To improve interaction control over different time scales, we further train the policy with both short-horizon interaction targets and longer-horizon goal targets. A single I-BFM policy performs carrying, pushing, and kicking, while also supporting goal reaching, motion tracking, stylistic control, and long-horizon task chaining. More importantly, it remains effective after large deviations from nominal execution: on Carry, I-BFM achieves 94.3% nominal success and retains 89.3% success after robot falls, compared with 1.3% for a planning-based baseline. Real-world experiments on a Unitree G1 further demonstrate diverse loco-manipulation behaviors, rapid recovery from interaction failures and external disturbances, and task chaining without task-specific retraining.

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