Abstract

We present an approach based on Hidden Markov Model (HMM) and Gaussian Mixture Regression (GMR) to learn robust models of human motion through imitation. The proposed approach allows us to extract redundancies across multiple demonstrations and build time-independent models to reproduce the dynamics of the demonstrated movements. The approach is systematically evaluated by using automatically generated trajectories sharing similarities with human gestures, and by using several metrics to assess the imitation performance. The proposed approach is contrasted with four state-of-the-art methods previously proposed in robotics to learn and reproduce new skills by imitation. An experiment with a 7 DOFs robotic arm learning and reproducing the motion of hitting a ball with a table tennis racket is then presented to illustrate the approach.

Bibtex reference

@inproceedings{Calinon10ICRA,
  author="Calinon, S. and Sauser, E.L. and Billard, A.G. and Caldwell, D.G.",
  title="Evaluation of a probabilistic approach to learn and reproduce gestures by imitation",
  booktitle="Proc. {IEEE} Intl Conf. on Robotics and Automation ({ICRA})",
  year="2010",
  month="May",
  address="Anchorage, Alaska, USA",
  pages="2381-2388"
}

Video

The experiment consists of learning and reproducing the motion of hitting a ball with a table tennis racket by using a Barrett WAM 7 DOFs robotic arm. One objective is to demonstrate that such movements can be transferred using the proposed approach, where the skill requires that the target be reached with a given velocity, direction and amplitude.

This experiment aims at demonstrating that the framework can be used in an unsupervised learning manner, i.e. where several movements can be encoded in a single HMM, without specifying a priori the number of movements, and without having to associate the different motions with a class or label.

Source codes

Download

  Download GMR Dynamics sourcecode

Usage

Unzip the file and run 'demo1' in Matlab.

Reference

• Calinon, S., D'halluin, F., Sauser, E.L., Caldwell, D.G. and Billard, A.G. (2009) A probabilistic approach based on dynamical systems to learn and reproduce gestures by imitation. IEEE Robotics and Automation Magazine.

Demo 1 - Demonstration of a trajectory learning system robust to perturbation based on Gaussian Mixture Regression (GMR)

This program first encodes a trajectory represented through time 't', position 'x' and velocity 'dx' in a joint distribution P(t,x,dx) through Gaussian Mixture Model (GMM) by using Expectation-Maximization (EM) algorithm. Gaussian Mixture Regression (GMR) is then used to estimate P(x,dx|t), which retrieves another GMM refining the joint distribution model of position and velocity.
The learned skill can then be reproduced by combining an estimation of P(dx|x) with an attractor to the demonstrated trajectories.

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