# ⚛  L1 Principle — Vehicle Dynamics (Bicycle Model)

**ID:** `L1-453` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Robotics — *Autonomous vehicles*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** vehicle state vector
> **📡 Carrier:** N/A · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555278

---

## 🧠 1. Introduction

**Vehicle Dynamics (Bicycle Model)** is a **parameter-estimation problem** whose unknown lives in **vehicle state vector** space, within the **Autonomous vehicles** sub-domain of **Robotics**.

Measurements consist of N/A via a **vehicle state estimation** sensing mechanism.

The forward operator applies, in order: time evolution of the state; S · tire · pacejka model operator; O · ekf · vehicle state operator.

Observations are corrupted by additive Gaussian noise. Existence of the recovered vehicle_state_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); tire_force_saturation 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 · tire · pacejka model → O · ekf · vehicle state → **y** (detector).

```
y = `O.ekf.vehicle_state` `S.tire.pacejka_model` ∂_t x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `D.time` | Time evolution of the state |
| `S.tire.pacejka_model` | S · tire · pacejka model operator |
| `O.ekf.vehicle_state` | O · ekf · vehicle state operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Robotics |
| Sub domain | Autonomous vehicles |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | vehicle_state_vector |
| Noise model | gaussian |
| Integration axis | time |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered vehicle_state_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); tire_force_saturation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | yaw_rate_RMSE_deg_s |
| Secondary | side_slip_angle_RMSE_deg |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `vehicle_state_estimation`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Road mu | — | 0.8 |
| Speed m s | s | 20 |
| Vehicle mass kg | kg | 1500 |
| Lateral acceleration m s2 | — | 3 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Road mu | — | 0.3 – 1.2 |
| Speed m s | s | 5 – 50 |
| Vehicle mass kg | kg | 500 – 5000 |
| Lateral acceleration m s2 | — | 0.5 – 10.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1.0 yaw_rate_RMSE_deg_s

| Metric | Range |
|---|---|
| Yaw rate rmse deg s | 0.1 – 10.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **yaw_rate_RMSE_deg_s**, with κ = `2000` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xc079116e269d4400b1e08b23e98cfacd962ca5f3d799db830a3c0c80b5339c60`
- **Chain tx hash:** `0x96bc7f9c7d1a5b61c977fc9baccc0d68aaa3c34c9fccdfc81b6e2b8d132e9333`
- **Chain block:** `41555278`

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## File Mapping

This bundle consists of: `L1-453.md`, `L1-453.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-453.md` | Source of truth — edit this | Human or LLM |
| `L1-453.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 `L1-453`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._