README.md

---
license: other
task_categories:
  - tabular-regression
  - time-series-forecasting
language:
  - en
pretty_name: Dynamics Simulation Dataset
size_categories:
  - 1K<n<10K
tags:
  - dynamics
  - simulation
  - multibody-systems
  - natural-coordinate-method
  - robotics
  - time-series
---

# Dynamics Simulation Dataset

## Dataset Summary

This dataset contains dynamics simulation trajectories computed with the Natural Coordinate Method (NCM). It is organized by benchmark case. Each case provides a training split and a test split, and each split contains multiple simulation runs with different initial conditions.

The dataset is intended for learning and evaluating dynamics models, trajectory prediction methods, control-aware models, and surrogate models for multibody mechanical systems.

## Directory Structure

Each top-level directory follows this naming pattern:

```text
<case_name>_<split>/
```

where `<split>` is either `train` or `test`.

Each split directory contains numbered subdirectories. Each numbered subdirectory corresponds to one simulation condition with a distinct initial state.

```text
2p2d_train/
  1/
    dt.csv
    q.csv
    u.csv
    t.csv
    tu.csv
  2/
    dt.csv
    q.csv
    u.csv
    t.csv
    tu.csv
```

All simulation subdirectories contain:

- `dt.csv`: time step size.
- `q.csv`: natural coordinate trajectory.
- `u.csv`: driving input at each time step.

Some simpler benchmark cases additionally contain:

- `t.csv`: minimal coordinate trajectory, such as joint angles.
- `tu.csv`: driving input represented in the corresponding minimal coordinates.

## Benchmark Cases

| Case name   | Description                           |
| ----------- | ------------------------------------- |
| `2p2d`      | Two-link planar structure             |
| `3p2d`      | Three-link planar structure           |
| `4p2d`      | Four-link planar structure            |
| `disT_2p2d` | Dissipative two-link planar structure |
| `3arm2d`    | Three-section planar robotic arm      |
| `7arm2d`    | Seven-link planar structure           |
| `3Sp3d`     | Three-section 3D spine-like structure |
| `5Sp3d`     | Five-section 3D spine-like structure  |

## Splits

Each benchmark case has two splits:

- `train`: 64 simulation runs with different initial conditions.
- `test`: 100 simulation runs with different initial conditions.

The top-level directories are:

```text
2p2d_train/        2p2d_test/
3p2d_train/        3p2d_test/
4p2d_train/        4p2d_test/
disT_2p2d_train/   disT_2p2d_test/
3arm2d_train/      3arm2d_test/
7arm2d_train/      7arm2d_test/
3Sp3d_train/       3Sp3d_test/
5Sp3d_train/       5Sp3d_test/
```

## Data Files

The CSV files store time-series simulation data. Rows correspond to time steps. The columns correspond to the coordinate components or input components used by the corresponding benchmark system.

Because the systems have different numbers of bodies, joints, and coordinates, the dimensionality of `q.csv`, `u.csv`, `t.csv`, and `tu.csv` may differ across benchmark cases.

## Dataset Creation

The trajectories were generated from dynamics simulations computed using the Natural Coordinate Method. Each numbered run corresponds to a different initial condition for the same benchmark case and split.

## Intended Use

This dataset may be useful for:

- training neural dynamics models;
- evaluating trajectory prediction accuracy;
- comparing natural-coordinate and minimal-coordinate representations;
- studying control inputs for simulated multibody systems;
- benchmarking data-driven models on planar and spatial mechanical systems.

## Limitations

The dataset contains simulated trajectories rather than real-world measurements. Model performance on this dataset may not directly transfer to physical systems without accounting for modeling assumptions, numerical integration details, sensing noise, actuation limits, and unmodeled dynamics.

## Citation

If you use this dataset in academic work, please cite the associated project, paper, or repository when available.