Physically Consistent GMM and DS Learning

Abstract

We propose a physically-consistent Bayesian non-parametric approach for fitting Gaussian Mixture Models (GMM) to trajectory data. Physical-consistency of the GMM is ensured by imposing a prior on the component assignments biased by a novel similarity metric that leverages locality and directionality. The resulting GMM is then used to learn globally asymptotically stable Dynamical Systems (DS) via a Linear Parameter Varying (LPV) re-formulation. The proposed DS learning scheme accurately encodes challenging nonlinear motions automatically. Finally, a data-efficient incremental learning approach is introduced that encodes a DS from batches of trajectories, while preserving global stability. Our contributions are validated on 2D datasets and a variety of tasks that involve single-target complex motions with a KUKA LWR 4+ robot arm.

This new DS formulation and learning approach has been further used to learn navigation tasks for a semi-autonomous wheelchair and for a humanoid robot to navigate and co-manipulate and object as shown in the videos below.

Video of Approach and Robot Experiments

• Robot Manipulation Experiments

• Wheelchair Navigation Simulation

• iCub Navigation and Co-Manipulation Simulation

Code

Following we list all of the code repositories made available for this project, including:

• Code for Learning GMM and DS in MATLAB:
  https://github.com/nbfigueroa/phys-gmm
  https://github.com/nbfigueroa/ds-opt

• Code for Executing Learned DS models in C++:
  https://github.com/nbfigueroa/lpvDS-lib

• Code for Executing Learned DS models in ROS:
  https://github.com/epfl-lasa/ds_motion_generator

• Code for Executing Manipulation Tasks on a KUKA-LWR 4+/Gazebo (in ROS):
  https://github.com/epfl-lasa/kuka-lpvds-tasks

• Code for Executing Navigation Tasks on Gazebo (ROS) simulation of Quickie Salsa-M Wheelchair:
  https://github.com/epfl-lasa/wheelchair-ds-motion

• Code for Recording Kinesthetic Demonstrations in ROS (arm states, sensors and gripper states):
  https://github.com/nbfigueroa/easy-kinesthetic-recording

References

[1] Figueroa, N. and Billard, A. (2018) “A Physically-Consistent Bayesian Non-Parametric Mixture Model for Dynamical System Learning”. In Proceedings of the 2nd Conference on Robot Learning (CoRL). [pdf]

Contact

Nadia Figueroa (nadia.figueroafernandez AT epfl dot ch)

Acknowledgments

This work was supported by the EU project Cogimon H2020-ICT-23-2014.