Generalizable Motion Policies through Keypoint Parameterization and Transportation Maps (TRO 2025)

This is the code accompaning the paper Generalizable Motion Policies through Keypoint Parameterization and Transportation Maps published in Transaction of Robotics (2025).

In this article, we parameterize the space with keypoints—for example, the shoulder, elbow, wrist, and hand positions of a human during dressing, or keypoints of an object being manipulated and its goal. We then fit a differentiable map $\phi$ to model the transportation between these keypoints. We deform the

We use the map to generalize the original position, velocity and orientation labels. For example, given a circular motion used to clean a table, we can use the transportation map to generalize it to a new surface and also generalize the velocity labels.

Many function approximators are available as transportation methods.

Minimal Example: Generalizing Labels with Transportation Maps

Below is a minimal code example demonstrating how we generalize position and velocity labels using transportation maps and Gaussian Process Regression (GPR) as the function approximator for the map.

# Define the transportation map and kernel
transport = PolicyTransportation()

# Set up the GPR method
k_transport = C(constant_value=10) * RBF([0.1, 5]) + WhiteKernel(0.01)
method = GPR(k_transport)

# Specify which method the transportation should use
transport.set_method(method=method, is_residual=method.is_residual)

# Fit the transportation map between source and target keypoint distributions
transport.fit(source_distribution, target_distribution)

# Generalize position and velocity labels
X_hat, X_hat_std = transport.transport(X)
deltaX_hat, deltaX_hat_var = transport.transport_velocity(X, deltaX)

This example shows how to fit a transportation map and use it to generalize both position (X_hat) and velocity (deltaX_hat) labels for new data together with the associated uncertainty due to the generalization.

The list of available methods to fit the transportation map that are colelcted in policy_tranportation/models are

Method Name	Call it
Gaussian Process	GPR(kernel)
Locally Weighted Regressin	Iterative_Locally_Weighted_Translations(num_iterations=30)
Radial Basis Function Regression	RBFRegression( beta=20, sigma2=0.001)
Ensamble Bijective Flow	EnsembleBijectiveNetwork(num_epochs=200, n_estimators=10)
Ensamble Neural Network	EnsembleNeuralNetwork(num_epochs=200, n_estimators=10)

Installation

This is a simple python package. You can install it in editable mode with.

pip install -e . 

Citation

Franzese, Giovanni, et al. "Generalizable Motion Policies through Keypoint Parameterization and Transportation Maps." IEEE Transactions on Robotics (2025).