Hierarchical Decision Mamba-Liquid Architecture for Multi-Embodiment Continuous Robotic Control

High-dimensional continuous control in multi-articulated robotic systems—ranging from quadrupeds and 3D humanoids to serpentine and bipedal mechanisms—faces a fundamental multi-scale challenge: reconciling long-horizon macro-cognitive reasoning over temporal state-action trajectories with high-frequency, continuous-time motor execution on physical actuators. While discrete Transformer-based sequence models capture long-term behavioral dependencies, they incur quadratic computational complexity O(T^2), exhibit severe vulnerability to distribution shifts under physical perturbations, and suffer from high-frequency torque chatter. To overcome these limitations, we propose HDML (Hierarchical Decision Mamba-Liquid), a generalist multi-embodiment foundation architecture. HDML couples an 8-layer Selective State Space Model (Mamba-3) augmented with Rotary Position Embeddings (RoPE) for O(1) streaming inference with a continuous-time Closed-Form Continuous-Time (CfC) Neural ODE motor filter for smooth, chatter-free actuator control. Pre-trained across 11 diverse robotic morphologies comprising exactly 1,735,673 physical transitions, HDML demonstrates rapid few-shot transfer: freezing 95.9%–97.0% (11.99M) of core backbone parameters while adapting lightweight universal adapters (376k–516k parameters) in under 30 seconds yields an action loss of 0.00602 on a 12-DoF Unitree A1 quadruped and 0.02579 on a 17-DoF 3D Humanoid. Under physical force impulse and sensor noise perturbations, HDML achieves a 16x higher Interquartile Mean (IQM) reward over Decision Transformers (18.88 vs. 1.17) while maintaining a pure model inference latency of 12.81 ms (78.0 Hz) and an end-to-end closed-loop control frequency of 43.2 Hz (23.1 ms total cycle including physics simulation and PACE safety monitoring).