Agile Locomotion & Manipulation via Reversible Flow Adaptation

System Architecture

flowchart TB
    %% Styling Classes
    classDef pretrain fill:#e3f2fd,stroke:#1e88e5,stroke-width:2px,color:#0d47a1
    classDef deploy fill:#e8f5e9,stroke:#43a047,stroke-width:2px,color:#1b5e20
    classDef hardware fill:#ffebee,stroke:#e53935,stroke-width:2px,color:#b71c1c
    classDef adapt fill:#fff3e0,stroke:#fb8c00,stroke-width:2px,color:#e65100

    subgraph Pretraining ["1. Offline Distillation"]
        direction LR
        O[("Oracle RL Teacher")] 
        F1["Flow Matching Student<br/>(O(1) Vector Field)"]
        V1["ViT Auxiliary<br/>Physics Head"]
        
        O -->|Optimal Transport| F1
        O -->|Supervised Loss| V1
    end

    subgraph Deployment ["2. Online 50Hz Control Loop"]
        direction TB
        S(["State: Vision + Proprioception"])
        V2["ViT Auxiliary Head"]
        F2["Flow Matching Student"]
        A["Action: Commanded Torque"]
        R{{"Robot Hardware"}}
        E{"Tracking Error > τ"}
        PD["PD Reflex Stabilizer"]
        P["Invertible Projection Mapping"]

        S --> V2
        V2 --> F2
        F2 --> A
        A --> R
        R --> E
        E -->|Yes: OOD Event| PD
        PD -->|a_corr| P
    end

    subgraph Adaptation ["3. Asynchronous 2Hz Thread"]
        direction TB
        I["Hutchinson Trace Estimator<br/>(Invertible ODE)"]
        L["LoRA Weight Update"]
        
        I -->|Gradient Descent| L
    end

    %% Cross-Subgraph Connections
    F1 -.->|Deploy Weights| F2
    V1 -.->|Deploy Weights| V2
    
    P -->|Trigger Adaptation| I
    L -.->|Atomic Swap| V2

    %% Apply Styles
    class O,F1,V1 pretrain
    class S,V2,F2,A,P deploy
    class R,E,PD hardware
    class I,L adapt

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