Toward Hardware-Agnostic Quadrupedal World Models via Morphology Conditioning

1. Problem Statement

Current World Models (WMs) in robotics suffer from the "Hardware Lottery": they are highly specialized to the specific kinematic and dynamic properties of the robot they were trained on.

• The Bottleneck: A model trained on a Boston Dynamics Spot fails catastrophically on a Unitree Go1 because it overfits to specific embodiment constraints (limb lengths, mass distribution, actuator limits) rather than learning universal locomotion dynamics.
• The Limitation of Current Solutions: Existing multi-task approaches often rely on implicit system identification, where the model attempts to infer physical properties (like mass or limb length) solely from the history of interactions (latent state $h_t$).
  • Adaptation Lag: This requires the robot to move (potentially dangerously) to generate enough data to "identify" itself before effective control is possible.
  • Entanglement: The latent state must simultaneously encode static physical properties and dynamic states (velocity, orientation), leading to capacity issues and interference.
• Goal: To create a Generalizable Quadrupedal World Model (QWM) that can control unseen robots with zero-shot transfer (no fine-tuning, no warm-up) by explicitly disentangling environmental dynamics from robot morphology.

2. Methodology

The authors propose QWM, a framework built upon the DreamerV3 architecture (Recurrent State-Space Model or RSSM) but modified to explicitly condition on physical structure. The core innovation is treating morphology not as a latent variable to be inferred, but as a known engineering specification provided as an input.

A. Explicit Physical Morphology Encoding (PME)

Instead of inferring morphology from history, the system extracts a static feature vector $\mu$ directly from the robot's Unified Scene Description (USD) or URDF files. This vector is normalized and includes:

• Kinematics & Topology: Limb segment lengths ($l_{hip}, l_{thigh}, l_{shank}$) and knee configuration style (e.g., "X-config" vs. "dog-like").
• Geometry: Stance footprint dimensions and aspect ratios (stability polygon).
• Dynamics: Log-scaled total mass and trunk mass ratio (inertia distribution).
• Actuation: Torque density (force capacity relative to mass).
  These features are min-max normalized to ensure numerical stability.

B. Morphology-Conditioned Architecture

The standard RSSM is modified with three key components:

1. Dual-Tower Encoder:
   • Dynamic Tower: Processes high-frequency proprioceptive data (joint positions, velocities, base velocity) via a deep MLP.
   • Static Tower: Processes the morphology vector $\mu$ via a separate, shallower MLP.
   • Fusion: The outputs are concatenated before entering the latent space, ensuring static structural context is not "washed out" by dynamic noise.
2. Explicit Recurrent Conditioning:
   • The morphology vector $\mu$ is injected directly into the recurrent transition function at every time step: $h_t = f_\phi(h_{t-1}, z_{t-1}, a_{t-1}, \mu)$.
   • Benefit: This relieves the recurrent state $h_t$ from the burden of memorizing static physical properties, allowing it to focus purely on the dynamic state evolution.
3. Adaptive Reward Normalization (ARN):
   • Different robots have vastly different reward scales (e.g., Spot rewards $\approx 350$, Unitree $\approx 40$).
   • ARN uses an Exponential Moving Average (EMA) of the 5th and 95th percentiles of returns for each robot type to dynamically scale rewards. This prevents high-reward robots from dominating the gradient updates and ensures stable multi-robot training.

C. Training Infrastructure

The authors developed Hetero-Isaac, a simulation environment built on NVIDIA Isaac Lab that supports heterogeneous batches. Unlike standard vectorized training (thousands of identical clones), Hetero-Isaac manages a single batch containing different robot types (ANYmal, Unitree, Spot) simultaneously, each with its own USD path and physics parameters.

3. Key Contributions

1. First Zero-Shot Morphology Generalization: The first World Model capable of deploying a single frozen policy to entirely unseen quadrupeds without online system identification or fine-tuning.
2. Explicit vs. Implicit Conditioning: Demonstrates that explicitly providing physical specifications (USD-derived features) is superior to implicit inference, eliminating the dangerous "adaptation lag."
3. Architectural Innovations: Introduction of the Dual-Tower Encoder and Explicit Recurrent Conditioning to disentangle static morphology from dynamic state.
4. Heterogeneous Training Framework: A novel simulation setup (Hetero-Isaac) and reward normalization scheme (ARN) enabling stable training across robots with different scales and reward functions.

4. Experimental Results

The model was trained on a cohort of 7 diverse quadrupeds (ANYmal B/C/D, Unitree A1/Go1/Go2/B2, Boston Dynamics Spot) and evaluated on held-out robots.

• Multi-Morphology Mastery: QWM significantly outperformed baselines (Vanilla PPO, DreamerV3, PWM, TWISTER) in convergence speed and stability. Baselines suffered from "mean-dynamics collapse," failing to distinguish between robots.
• Long-Horizon Prediction: QWM maintained tight synchronization with ground-truth physics over 45-step open-loop rollouts across diverse scales, whereas baselines diverged rapidly.
• Zero-Shot Generalization (Simulation):
  • Interpolation: On robots structurally similar to the training set (e.g., Unitree Go1, ANYmal-D), QWM achieved performance comparable to specialist policies trained only on that specific robot.
  • Extrapolation: On extreme outliers (Unitree B2, which is 4x heavier), performance degraded, confirming the model acts as a distribution-bounded interpolator rather than a universal physics engine.
• Real-World Deployment:
  • The frozen zero-shot policy was deployed on Unitree Go1 and ANYmal-D (robots excluded from training).
  • Result: Both robots achieved stable, high-frequency locomotion immediately. Tracking errors were within ~10% of specialist baselines, with zero falls across 20 trials.
• Ablation Studies:
  • Removing ARN caused total training failure (gradient domination by high-reward robots).
  • Removing PME (reverting to implicit ID) allowed learning but resulted in suboptimal gaits and lower rewards.
  • Removing Recurrent Conditioning led to catastrophic collapse in later training stages.

5. Significance

This work represents a paradigm shift from hardware-specific specialists to physics-grounded generalists in robotic control.

• Safety & Efficiency: It eliminates the need for dangerous real-world warm-up periods where robots must "learn" their own physical constraints through trial and error.
• Scalability: It enables the deployment of a single "brain" across a heterogeneous fleet of robots, drastically reducing the computational cost of training individual experts for every robot variation.
• Foundational Step: While currently limited to quadrupeds within a specific distribution, the framework (explicit morphology conditioning) provides a blueprint for building Universal World Models capable of controlling any articulated rigid body, from bipeds to manipulators.