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exercise1_learning

This package includes GUI simulations and demo scripts for learning stable non-linear Dynamical Systems (DS) from demonstrations using LPV-DS [1] and SEDS [2] approaches developed in LASA-EPFL.

Installing the exercise

Run the script setup_demo.m

Compatibility: These exercise scripts have been tested in Matlab versions 2015a - 2018a.

Running the gui for exercise sessions

  • gui_lpvDS.m: Brings up a GUI for estimation of Globally Asymptotically Stable Dynamical Systems focused on Linear Parameter Varying formulation with GMM-based mixing function and different Lyapunov candidate functions as proposed in [1], where a non-linear DS formulated as:

is learned from demonstrations in a decoupled manner. Where the GMM parameters used to parametrize are estimated via the physically-consistent GMM approach proposed in [1] and provided in phys-gmm and the DS parameters are estimated via semi-definite optimization problem that ensures global asymptotic stability of the system via constraints derived from either a:

  • (O1)-QLF (Quadratic Lyapunov Function):

  • (O2)-P-QLF (Parametrized QLF):

with different GMM estimation options:

  • Manual K selection
  • Model Selection with BIC
  • PC-GMM [1]

A guided video explaining how to use the GUI, can be found in this link

  • [Optional] gui_seDS.m: Brings up a GUI for estimation of Globally Asymptotically Stable Dynamical Systems with the SEDS (constrained-GMR) [2] where a non-linear DS formulated as:

Whith the probability distribution being estimated with a Gaussian Mixture Model (GMM). This GUI also includes robot simulation as above.

A guided video explaining how to use the GUI, can be found in this link

Using algorithms on own data

Within the ds_opt folder, we provide demo scripts for using any of the presented learning algorithms on test 2D and 3D data. These scripts are useful if you want to learn DS with your own datasets.

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).
[2] Khansari Zadeh, S. M. and Billard, A. (2011) Learning Stable Non-Linear Dynamical Systems with Gaussian Mixture Models. IEEE Transaction on Robotics, vol. 27, num 5, p. 943-957.

Contact: Nadia Figueroa (nadia.figueroafernandez AT epfl dot ch)