---
license: apache-2.0
library_name: lerobot
pipeline_tag: robotics
tags:
  - robotics
  - lerobot
  - imitation-learning
  - act
  - b-spline
  - so101
  - bspline_act
datasets:
  - aryankakad/CUPSTACKING
model_name: cupstack_bspline_act_v2
---

# cupstack_bspline_act_v2

An [ACT](https://huggingface.co/papers/2304.13705) policy that predicts **B-spline
trajectory segments** instead of discrete action chunks, trained on SO-101 cup stacking.
This is the "Reg.+BSP" variant from
[B-spline Policy: Accelerating Manipulation Policies via B-spline Action Representations](https://arxiv.org/abs/2607.09648).

The practical consequence: **you can run this checkpoint faster without retraining it.**
The policy outputs a curve, so executing `a(n·t)` replays the same trajectory geometry
n times faster. Speed-up is an inference flag, and it is exact — verified to
0.000e+00 deviation at 2× and 4×.

This supersedes `cupstack_bspline_act`. Two things changed: idle frames were trimmed
from the demonstrations, and **5 episodes were held out for validation**, so for the
first time there are held-out numbers for this task.

> [!IMPORTANT]
> **Read the [Evaluation](#evaluation) section before trusting any number here.**
> Held-out error is ~19°, against 2.1° on training data. The policy is clearly
> reading the scene — it beats the inter-demonstration spread by 42% — but it has
> **never been run on hardware**, and task success rate is unknown. Keep the e-stop
> within reach.

## Download

```bash
hf download Dimios45/cupstack_bspline_act_v2 --local-dir ./cupstack_bspline_act_v2
```

The repository root holds the recommended checkpoint, so `--policy.path` also accepts
the repo id directly. Individual checkpoints live under `checkpoints/<step>/`.

## Run it

```bash
lerobot-rollout \
    --strategy.type=base \
    --policy.path=./cupstack_bspline_act_v2/checkpoints/040000/pretrained_model \
    --policy.speed_up=1.0 \
    --device=cuda \
    --robot.type=so101_follower \
    --robot.port=/dev/ttyACM0 --robot.id=FOLLOWER \
    --robot.cameras='{front: {type: opencv, index_or_path: 0, width: 640, height: 480, fps: 30}, gripper: {type: opencv, index_or_path: 4, width: 640, height: 480, fps: 30}}' \
    --task="Cup stacking" \
    --fps=30 --duration=60
```

`--policy.path` takes either a Hub repo id (`namespace/name`) or a **local directory
containing `config.json`** — which is the `pretrained_model/` subdirectory, not the
step directory above it. There is no `--policy.subfolder` flag.

To try the speed-up, raise `--policy.speed_up` to 2.0 or 4.0. Start at 1.0 and step up
only once the task succeeds. Retiming does not make the arm stronger — past the
low-level controller's tracking limit it overshoots rather than stopping. The paper
reaches 4× on cube picking but only 2× on speed stacking, and cup stacking is the same
precise-placement regime.

If the control loop can't keep up, drop `--display_data` (Rerun can saturate its
channel at two 640×480 streams) rather than assuming the policy is too slow — a
B-spline policy runs the network only when a segment is exhausted, roughly every
0.76 s, so most control ticks are just spline evaluation.

### Camera naming is not optional

The `--robot.cameras` dict keys must be **`front`** and **`gripper`**, lowercase:

| Key | Shape |
|---|---|
| `observation.images.front` | `(3, 480, 640)` |
| `observation.images.gripper` | `(3, 480, 640)` |
| `observation.state` | `(6,)` |

Joint order is `shoulder_pan, shoulder_lift, elbow_flex, wrist_flex, wrist_roll, gripper`,
in degrees. Swapping the two cameras produces confident but wrong behaviour rather
than an error.

### Requirements

This policy type is not in upstream LeRobot. You need a checkout containing the
`bspline_act` policy, installed with the scipy extra:

```bash
uv pip install -e ".[feetech,bspline]"
```

`scipy>=1.15` is required for `interpolate.generate_knots`.

Unnormalization statistics are stored as buffers inside `model.safetensors`, so each
checkpoint is self-contained — you do not need the training dataset on the robot machine.

## Checkpoints

| Step | Epoch | Train error | **Held-out error** | Eval loss | |
|---|---|---|---|---|---|
| 10000 | 17 | 6.56° | 19.20° | 0.3074 | |
| 20000 | 33 | 4.95° | 19.36° | 0.3072 | |
| 30000 | 50 | 3.89° | 19.33° | 0.3060 | |
| **40000** | 67 | 2.63° | **19.06°** | 0.3084 | **recommended** |
| 45000 | 75 | 2.49° | **18.72°** | 0.3005 | best, within noise of 40k |
| 50000 | 83 | 2.28° | 19.05° | 0.3088 | |
| 60000 | 100 | 2.08° | 19.22° | 0.3121 | final |

All twelve checkpoints of the run span 18.72–19.36° held-out (mean 19.03, sd 0.22), so
**every checkpoint here performs the same on unseen data**. 45000 is nominally best and
is included for that reason, but its margin over 40000 is a quarter of the run's own
noise. Pick 40000 unless you have a reason not to.

Error is mean absolute joint error in degrees, worst joint, over each predicted
segment's horizon (~0.76 s), measured by decoding the spline and comparing against
ground-truth actions.

## Training

| | |
|---|---|
| Steps | 60,000 |
| Batch size | 32 |
| Epochs | 100 |
| Dataset | [`aryankakad/CUPSTACKING`](https://huggingface.co/datasets/aryankakad/CUPSTACKING) → idle-trimmed → B-spline converted |
| Episodes | **45 train / 5 held out** |
| Frames | 20,956 (from 24,044; 12.9% boundary idle removed) |
| Optimizer | AdamW, lr 2e-5 (backbone 1e-5), wd 1e-4 |
| Precision | bf16 autocast + `channels_last` |
| Hardware | 1× RTX 4090, 3 h 16 min |
| Seed | 1000 |
| Augmentation | none |

### Preprocessing

Leading and trailing motionless frames were removed from every episode — 77 s of
lead-in and 26 s of trailing idle across 50 episodes. Interior pauses were kept
(only 0.3% of frames, and they are real behaviour).

Motion is measured as peak-to-peak joint range over a ±0.5 s window rather than
frame-to-frame delta. A single jittery sample inside a dead stretch defeats a delta
test, which silently leaves the idle in.

Leading idle matters more than it looks: it maps the opening observation to
"don't move", and since executing a stay-still segment doesn't change the scene, the
policy can re-predict it indefinitely and never start.

## Architecture

Standard ACT with one change: the decoder emits a B-spline **parameter matrix** rather
than an action chunk.

```
(n_knots, 1 + action_dim) = (16, 7) = 112 values per prediction
   column 0   knot vector, in source-frame units, 0 = "now"
   columns 1: control points, one per joint
```

| | |
|---|---|
| Params | 51.6 M |
| Vision backbone | ResNet18 (ImageNet init, fine-tuned) |
| dim_model / chunk_size | 512 / 16 |
| VAE | enabled, kl_weight 10.0 |
| B-spline degree | 3 (cubic, C² continuous) |
| bspline_chunk_size | 10 |
| Fitting tolerance ε | 0.2 (degrees) |
| Max knot span | 6 frames |

Knot spacing is fitted adaptively, so a fixed 16 rows covers a **variable** time
horizon — 0.50 s to 1.03 s per segment, 0.76 s mean. The network runs only when a
segment is exhausted, which decouples policy rate from control rate.

### On the fitting tolerance

ε = 0.2 is not the paper's value. The paper uses 0.002 for metre-scale end-effector
actions; SO-101 stores joint targets in **degrees** (~±120), roughly 100× larger.
At ε = 0.002 compression is 1.06× — one knot per frame, which defeats the
representation. At 0.2 the fit compresses 2.41× and reconstructs to 0.187° p99, well
below servo resolution.

`max_knot_span` caps how wide a single knot interval may be, bounding open-loop
exposure at `chunk_size × 6` frames. On this dataset it is nearly a no-op (uncapped
p95 span is already 1.17 s); it matters on recordings with long pauses, where uncapped
fitting produced 18-second segments.

## Evaluation

**Offline only. No hardware evaluation has been performed.**

| | Train (45 eps) | **Held-out (5 eps)** |
|---|---|---|
| Best checkpoint | 2.49° | **18.72°** |
| Recommended (40k) | 2.63° | 19.06° |

Two reference points for the held-out number:

- **Inter-demonstration spread: 32.27°** — how far apart two different human
  demonstrations of this task are, phase-aligned. At 18.7° the policy predicts an
  unseen episode's trajectory substantially better than another demonstration would.
  It is reading the scene, not replaying an average.
- **Hold-still baseline: 17.59°** — emitting the current action for the next 0.76 s.
  The policy scores near this, but the comparison flatters a do-nothing policy: over a
  short horizon on a slow task, "don't move" is a decent *predictor* while being a
  useless *policy*. Do not read this as "no better than nothing".

**Held-out performance was fixed after step ~3,000.** Across twelve checkpoints and
55,000 steps it moved 0.6°, while training error fell from 8.00° to 2.08°. Everything
after the first few thousand steps went into fitting the training episodes harder.

> The predecessor model card reported "2.10° open-loop error at 100k" without a
> validation split. This run reproduces that figure (2.08° at 60k) and shows the
> held-out number underneath it is ~19°. That was a training-data measurement, not a
> generalization result.

Temporal rescaling is **exact**: on a real predicted segment, `a(2t)` and `a(4t)`
reproduce the 1× samples to 0.000e+00, consuming the segment in 24 / 12 / 6 control
ticks.

## Limitations

- **No hardware evaluation.** Task success rate is unknown.
- **Held-out split is the last 5 episodes**, not a random sample. Episodes were largely
  cut from a continuous teleoperation stream (40 of 49 boundaries are contiguous to
  under 1°), so adjacent episodes are correlated and an interleaved split would leak.
  The tail split avoids leakage at the cost of possible session drift.
- **Single task, single scene.** No robustness to lighting, camera placement, or cup
  position changes should be assumed.
- **Speed-up has a hardware ceiling.** Expect degradation near 2× on this task.
- **Camera assignment is silent when wrong.** Swapped views degrade behaviour without
  raising an error.

## Citation

```bibtex
@article{han2026b,
  title={B-spline Policy: Accelerating Manipulation Policies via B-spline Action Representations},
  author={Han, Xiaoshen and Xiong, Haoyu and Chen, Haonan and Liu, Chaoqi and
          Torralba, Antonio and Zhu, Yuke and Du, Yilun},
  journal={arXiv preprint arXiv:2607.09648},
  year={2026}
}
```