L1 ⚛ L1-448 ⊙ Testnet

Forward Dynamics

Robotics · Robot dynamics

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⬇ L1-448.md

# ⚛ L1 Principle — Forward Dynamics **ID:** `L1-448` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Robotics — *Robot dynamics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** joint acceleration vector > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555260 --- ## 🧠 1. Introduction **Forward Dynamics** is a **parameter-estimation problem** whose unknown lives in **joint acceleration vector** space, within the **Robot dynamics** sub-domain of **Robotics**. Measurements consist of N/A via a **torque to acceleration** sensing mechanism. The forward operator applies, in order: time evolution of the state; S · articulated body · aba operator; O · ode · integration operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered joint_acceleration_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); inertia_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Time derivative → S · articulated body · aba → O · ode · integration → **y** (detector). ``` y = `O.ode.integration` `S.articulated_body.aba` ∂_t x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `S.articulated_body.aba` | S · articulated body · aba operator | | `O.ode.integration` | O · ode · integration operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Robotics | | Sub domain | Robot dynamics | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | joint_acceleration_vector | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered joint_acceleration_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); inertia_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | joint_trajectory_RMSE_deg | | Secondary | energy_conservation_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `torque_to_acceleration` **Center point:** | Parameter | Unit | Value | |---|---|---| | N joints | — | 6 | | Total mass kg | kg | 10 | | Simulation time s | s | 1 | | Friction coefficient | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N joints | — | 2 – 10 | | Total mass kg | kg | 0.5 – 1000 | | Simulation time s | s | 0.1 – 100 | | Friction coefficient | — | 0.0 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.0 joint_trajectory_RMSE_deg | Metric | Range | |---|---| | Joint trajectory rmse deg | 0.01 – 10.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **joint_trajectory_RMSE_deg**, with κ = `2000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x007249d71bb962a4a0d435aba3e4dd4602bc1650028ead53d67963ff9ca20761` - **Chain tx hash:** `0x9a348e02c700c44ccf825997b0c15b2df5361ddd20f4150f53d8c72d555a5fa8` - **Chain block:** `41555260` --- ## File Mapping This bundle consists of: `L1-448.md`, `L1-448.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-448.md` | Source of truth — edit this | Human or LLM | | `L1-448.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-448`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-448.md).
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L2-448-001 Forward Dynamics — Nominal + Mismatch Specs

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📋 JSON metadata

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  "artifact_id": "L1-448",
  "chain_block": 41555260,
  "chain_hash": "0x007249d71bb962a4a0d435aba3e4dd4602bc1650028ead53d67963ff9ca20761",
  "chain_tx_hash": "0x9a348e02c700c44ccf825997b0c15b2df5361ddd20f4150f53d8c72d555a5fa8",
  "domain": "Robotics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 2000,
    "metric": "joint_trajectory_RMSE_deg",
    "type": "epsilon_fn"
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  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "joint_trajectory_RMSE_deg",
    "regime": "Existence of the recovered joint_acceleration_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); inertia_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "energy_conservation_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Robotics",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "D.time",
      "S.articulated_body.aba",
      "O.ode.integration"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "torque_to_acceleration",
    "solution_space": "joint_acceleration_vector",
    "sub_domain": "Robot dynamics",
    "title": "Forward Dynamics"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "torque_to_acceleration"
    ],
    "allowed_omega_dimensions": [
      "N_joints",
      "total_mass_kg",
      "friction_coefficient",
      "simulation_time_s"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.0 joint_trajectory_RMSE_deg",
      "forward_operator": "torque_to_acceleration",
      "input_format": "measurement_only",
      "omega": {
        "N_joints": 6,
        "friction_coefficient": 0.1,
        "simulation_time_s": 1.0,
        "total_mass_kg": 10
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "joint_trajectory_RMSE_deg": [
        0.01,
        10.0
      ]
    },
    "omega_bounds": {
      "N_joints": [
        2,
        10
      ],
      "friction_coefficient": [
        0.0,
        1.0
      ],
      "simulation_time_s": [
        0.1,
        100
      ],
      "total_mass_kg": [
        0.5,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Robot dynamics",
  "title": "Forward Dynamics"
}

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