### Abstract

We present a probabilistic architecture for solving generically the problem of extracting the task constraints through a Programming by Demonstration (PbD) framework and for generalizing the acquired knowledge to various situations. In previous work, we proposed an approach based on Gaussian Mixture Regression (GMR) to find a controller for the robot reproducing the statistical characteristics of a movement in joint space and in task space through Lagrange optimization. In this paper, we develop an alternative procedure to handle simultaneously constraints in joint space and in task space by combining directly the probabilistic representation of the task constraints with a solution to Jacobian-based inverse kinematics. The method is validated in manipulation tasks with two 5 DOFs Katana robotic arms displacing a set of objects.

### Bibtex reference

@article{Calinon09AR,
author="S. Calinon and A. Billard",
title="Statistical Learning by Imitation of Competing Constraints in Joint Space and Task Space",
year="2009",
publisher="The Robotics Society of Japan",
volume="23",
number="",
pages="2059--2076",
}

### Video

Incremental learning of a motion with two Katana robotic arms from Neuronics.
Two demonstrations are provided to show to the robots how to pour some liquid from a bottle into a glass. Then, the user moves manually one of the robot while the other robot follows as best as possible the learned motion in a flexible manner.

Video credit: Florent D'halluin.