RL² — Real Life & Real Learning Lab

BeJEPA: A Goal-Conditioned Humanoid Behavior World Model via Unsupervised RL

1RL² Lab, Shanghai Jiao Tong University 2Shanghai Innovation Institute 3Zhejiang University 4Tongji University 5Fudan University 6Robotics Lab, Lenovo Research, Lenovo Group Limited

† Corresponding author

Code Before mid-November arXiv Link forthcoming

World-anchored whole-body control on the Unitree G1.

Abstract

BeJEPA learns a goal-conditioned behavior world model for humanoid control through unsupervised reinforcement learning from human motion priors and robot interaction. It represents whole-body posture, world position, and heading in a shared latent space. A Dynamic Predictor models immediate action consequences, while a Successor Predictor summarizes expected long-term behavior. Their composition guides policy learning without long imagined rollouts, and Dynamic further refines actions at inference time. BeJEPA improves world-coordinate motion tracking and enables a physical Unitree G1 to reach joint posture and world-pose goals, stand up from the ground, and return after disturbances and goal changes.

BeJEPA combines world-goal tracking, a behavior world model with Dynamic and Successor predictors, and online action refinement.
One shared representation connects posture, world placement, and goal-conditioned behavior.

Method

The shared encoder, actor, Dynamic Predictor, and Successor Predictor, with transition and behavioral learning objectives.

A goal in the shared latent space

The shared encoder maps the current state and target to embeddings ztz_t and zgz_g, capturing posture, world position, and heading. Normalizing them to radius d\sqrt d makes similarity reward equivalent to proximity to the goal:

rg(st)=⟨zt,zg⟩=d−12∥zt−zg∥22r_g(s_t)=\langle z_t,z_g\rangle=d-\tfrac{1}{2}\lVert z_t-z_g\rVert_2^2

One physical step, one long-term summary

Dynamic predicts an action's next latent state, independently of the goal. Successor summarizes future embeddings under the goal-conditioned policy, with discount factor γ\gamma:

z^t+1=Dν(zt,at)≈Eϕ(st+1)\widehat z_{t+1}=D_\nu(z_t,a_t)\approx E_\phi(s_{t+1})
Sξ(zt,zg)≈(1−γ) Eπg ⁣[∑k=0∞γkzt+k | st]S_\xi(z_t,z_g)\approx(1-\gamma)\,\mathbb{E}_{\pi_g}\!\left[\sum_{k=0}^{\infty}\gamma^k z_{t+k}\,\middle|\,s_t\right]

Both train the shared encoder from robot transitions: Dynamic uses observed next states, while Successor uses a vector Bellman target to learn long-term continuation without long imagined rollouts.

Compose the predictions to choose actions

Combining Dynamic's predicted next state with Successor yields a goal-aligned action value. Gradients through both predictors guide the actor toward useful long-term behavior:

Q^g(zt,at)=⟨(1−γ)zt+γSξ(z^t+1,zg), zg⟩\widehat Q_g(z_t,a_t)=\big\langle(1-\gamma)z_t+\gamma S_\xi(\widehat z_{t+1},z_g),\,z_g\big\rangle

A fixed goal enables reaching; successive goals enable tracking. At deployment, an observation-history encoder supplies the state representation, and Dynamic supports short-horizon MPC refinement with frozen network weights.

Key results

Coordinating whole-body posture, world placement, and execution timing.

Whole-body motion tracking

BeJEPA-MPC (Balanced) achieves the lowest global body-position and root errors among the compared methods on both datasets. Local posture and wrist errors are reported alongside them to show the trade-offs in world-coordinate tracking.

AMASS

Lower is better ↓
Whole-body motion tracking on selected 20-second AMASS segments.
MethodGlobal MPJPEmm ↓Local MPJPEmm ↓Root error↓Wrist error↓
BFM-Zero (world)573.497.10.80132.4
SONIC531.549.70.57115.3
Humanoid-GPT832.4115.71.10727.5
BeJEPA278.082.30.37725.9
BeJEPA-MPC (Balanced)219.563.90.25516.3

LAFAN

Lower is better ↓
Whole-body motion tracking on selected 20-second LAFAN segments.
MethodGlobal MPJPEmm ↓Local MPJPEmm ↓Root error↓Wrist error↓
BFM-Zero (world)797.189.31.02025.8
SONIC887.577.80.97123.6
Humanoid-GPT1433.1127.91.72029.7
BeJEPA584.581.90.71624.3
BeJEPA-MPC (Balanced)543.875.30.63920.1

Bold and underline mark the best and second-best values. Root error = xy error (m) + 0.01 × yaw error (degrees); wrist error = local position error (cm) + 0.5 × orientation error (degrees).

Evaluation uses selected, non-interactive 20-second AMASS and LAFAN segments with the 29-actuator G1 in MuJoCo at 50 Hz. Trajectories with large spatial deviations are retained.

More precise execution, the same pretrained model

Dynamic-based MPC refines actions at inference time without retraining. The Balanced setting reduces all six tracking errors, with a mean relative reduction of 31.2% on AMASS and 13.4% on LAFAN over BeJEPA. Changing the MPC cost shifts priority toward root translation or wrist orientation.

AMASS radar plot comparing six normalized tracking errors across BeJEPA and three MPC settings, alongside mean signed lag of 94.8, 21.2, 45.5, and 50.0 milliseconds respectively.
Tracking priorities and temporal alignment on AMASS. Left: errors normalized by BeJEPA; outward is better. Right: mean signed joint-tracking lag. View full size ↗
Closer to the reference clock. Balanced MPC reduces mean signed lag from 94.8 to 21.2 ms on AMASS, and from 97.2 to 51.0 ms on LAFAN, using the same pretrained weights.

World-anchored control on the physical G1

On the physical robot, BeJEPA coordinates posture with a persistent world reference: returning after an external kick, standing up from the ground, and switching between goals before returning to the starting location.

Physical G1 experiments: (a) returning to a marked floor location after a kick, (b) standing up from the ground, and (c) moving from a T-pose through kneeling, advancing, turning, and returning.
(a) Disturbance recovery. (b) Ground recovery. (c) Sequential goal switching. Gold rings identify floor reference marks. View full size ↗

Citation