stephane-caron/koopman_dcm

Koopman DCM

Datasets of the CoRL 2026 paper Koopman DCM: Unstable Eigenfunctions as Data-driven Representations for Legged Balancing.

Files

File	Content	Paper results
cookie/cookie.h5	Cookie wheeled biped, real robot, closed-loop balancing data at 100 Hz	Training data of the Cookie DCM, Section 4
cookie/cookie-ood.h5	Cookie wheeled biped, real robot, tracking at out-of-distribution periods	Sections 4.4 and 4.5
cookie/pybullet-cookie.h5	Cookie wheeled biped in PyBullet, closed-loop balancing data at 100 Hz	Training data of the Cookie simulation DCM, Table 2
cookie/cookie-evaluation.h5	Per-trial results of the Cookie evaluation, 270 trials	Table 2, Cookie wheeled biped
g1/pybullet-g1.h5	Unitree G1 in PyBullet, closed-loop balancing data at 240 Hz	Training data of the G1 DCM, Table 2
g1/g1-evaluation.h5	Per-trial results of the G1 evaluation, 270 trials	Table 2, G1 humanoid

All files are HDF5. Lateral coordinates are normalized along the line between the two feet (G1) or wheel contacts (Cookie).

Cookie training data

cookie/cookie.h5 was collected on the real Cookie robot on 2026-05-26 and 2026-05-27: 330,000 steps at 100 Hz, that is, 55 minutes. The robot balances laterally under proportional DCM feedback with the kinematic LIP DCM, while tracking sinusoidal ZMP references o + A sin(2π t / T) whose amplitude A ∈ {0, 0.1, 0.2, 0.4, 0.8}, offset o ∈ {0, ±0.2, ±0.5} and period T ∈ {0.3, 0.7, 1.0, 1.2, 1.4} s are drawn at random every 10 seconds (Section 4.1 of the paper). A new episode starts after a fall or a manual reset: 91 episodes end with a fall and 102 are truncated.

cookie/pybullet-cookie.h5 was collected in PyBullet on 2026-08-10 with the same controller and reference distribution: 360,000 steps at 100 Hz, that is, 60 minutes of simulated time, with 39 episodes ending with a fall and 8 truncated.

Both files have the same layout, with N the number of steps:

Dataset	Shape	Content
Y	N × 20	Measurements, see below
U	N	Action: commanded lateral ZMP, normalized
amplitude, offset, period	N	Parameters of the ZMP reference, period in s
terminated	N	Episode ended by a fall
truncated	N	Episode ended without a fall

File attributes: dt (control period in s), frequency (control rate in Hz) and chunk_duration (duration of a reference in s).

Columns of Y, in order:

• joint angles of the 6 actuated joints, in rad, ordered [left_hip, left_knee, left_wheel, right_hip, right_knee, right_wheel] (6 columns);
• CoM position in the anchor frame, centered at the midpoint between the two wheel contacts and aligned with the robot's heading, in m (3 columns);
• lateral CoM coordinate, normalized (1 column);
• joint torques of the 6 actuated joints, in N·m, same order (6 columns);
• ZMP position in the anchor frame, in m (3 columns);
• lateral ZMP coordinate, normalized (1 column).

The DCM observable only takes the first 10 columns of Y as input, together with U.

Cookie out-of-distribution data

cookie/cookie-ood.h5 was recorded on the real robot on 2026-08-11: 25,800 steps at 100 Hz of ZMP tracking at amplitude A = 0.3 and periods T ∈ {0.5, 1.8, 2.0} s, outside the training grid, with three trials per period for both the kinematic LIP DCM and the Koopman DCM dcm-cookie.onnx. Each trial lasts ten periods, and the paper discards the first two as settling. It has the same datasets and Y columns as the training files, plus:

Dataset	Shape	Content
cycle	N	Trial index, from 1 to 3
model	N	Index of the DCM in the models file attribute

The models attribute uses internal names: kinematics for the kinematic LIP DCM, and dcm-cookie-0527 for dcm-cookie.onnx.

None of this file was used for training. Section 4.4 of the paper reports tracking at these periods, and Section 4.5 scrambles the inputs of the learned DCM on this data.

Cookie evaluation results

cookie/cookie-evaluation.h5 holds the results behind the Cookie column of Table 2, from a run in PyBullet on 2026-08-10 with the model dcm-pybullet-cookie.onnx. The three controllers are the same as for G1. Each one tracks ZMP references over amplitudes {0.2, 0.4, 0.6}, offsets {0, 0.5} and periods {1.0, 1.2, 1.4} s, with five seeds per cell. Each trial is 14 s of tracking after a 3 s warmup. Each dataset has one row per trial, with the same columns as the G1 evaluation below, plus:

Dataset	Content
fell_in_warmup	Whether the robot fell during the warmup, before tracking started
rmse_zmp_cmd_last_2T	RMSE of the commanded rather than measured ZMP, over the same window
dcm_constraint_rate, zmp_constraint_rate	Fraction of control cycles with an active DCM or ZMP constraint in the MPC, NaN for dcm
predicted_peak_max	Largest predicted DCM over the MPC horizon, NaN for dcm

The dcm_model file attribute holds the internal name dcm-pybullet-0810 of dcm-pybullet-cookie.onnx. Falls are detected from the tilt of the IMU, above 1 rad. A fall during the warmup counts as a fall and contributes no tracking error.

G1 training data

g1/pybullet-g1.h5 was collected on 2026-05-28: 1,008,000 steps at 240 Hz, that is, 70 minutes of simulated time. The G1 stands in static double support and balances laterally under the DCM MPC, while tracking sinusoidal ZMP references o + A sin(2π t / T) with amplitude A ∈ {0, 0.2, 0.4, 0.8}, offset o ∈ {−0.5, 0.5} and period T ∈ {0.3, 0.7, 1.2} s. The collection code was meant to draw a new reference every 10 seconds, but a bug at the time, since fixed, kept the first one: each of the four parallel workers tracked a single reference, so the file holds four references in total. The collect-data task of the code release draws a new reference every 10 seconds. A new episode starts after a fall: 55 episodes end with a fall and 4 are truncated.

Dataset	Shape	Content
Y	1,008,000 × 66	Measurements, see below
U	1,008,000	Action: commanded lateral ZMP, normalized
amplitude, offset, period	1,008,000	Parameters of the ZMP reference, period in s
terminated	1,008,000	Episode ended by a fall
truncated	1,008,000	Episode ended without a fall

Columns of Y, in order:

• joint angles of the 29 actuated joints, in rad (29 columns);
• CoM position relative to the anchor point, the low-pass filtered midpoint between the feet, in m, with world-aligned axes (3 columns);
• lateral CoM coordinate, normalized (1 column);
• joint torques of the 29 actuated joints, in N·m (29 columns);
• ZMP position relative to the anchor point, in m (3 columns);
• lateral ZMP coordinate, normalized (1 column).

The DCM observable only takes the first 33 columns of Y as input, together with U.

G1 evaluation results

g1/g1-evaluation.h5 holds the results behind the G1 column of Table 2, from a run on 2026-08-10 with the model dcm-pybullet-g1.onnx. Three controllers use the same learned DCM: proportional DCM feedback (dcm), the MPC with viability constraint (mpc) and the same MPC without this constraint (viability-less-mpc). Each one tracks ZMP references over amplitudes {0.3, 0.6, 0.9}, offsets {0, 0.5} and periods {1.3, 1.6, 1.9} s, with five seeds per cell, for trials of 19 s. Each dataset has one row per trial:

Dataset	Content
amplitude, offset, period, seed	Trial parameters
controller	Controller name
did_fall	Whether the robot fell
fall_time	Time of the fall in s, NaN without fall
rmse_zmp_last_2T	ZMP tracking RMSE over the last two periods of the trial

A trial stops when the robot falls, so for fallen trials rmse_zmp_last_2T covers the two periods before the fall, falling motion included. Use did_fall to select standing trials when comparing tracking errors.

Usage

From the cookie_balancer directory of the code release, where tasks download the files they need:

pixi run train-dcm     # train a DCM observable on cookie.h5
pixi run evaluate-mpc  # run the Cookie evaluation of Table 2

From the g1_evaluation directory, with both files copied to data/:

pixi run train-dcm    # train a DCM observable on pybullet-g1.h5
pixi run print-table  # print the G1 column of Table 2 from g1-evaluation.h5

Citation

@inproceedings{caron2026koopman,
    title = {Koopman {DCM}: Unstable Eigenfunctions as Data-driven Representations for Legged Balancing},
    author = {Caron, St{\'e}phane},
    booktitle = {Conference on Robot Learning (CoRL)},
    url = {https://openreview.net/pdf?id=mday00WZFr},
    month = nov,
    year = {2026},
}