### Abstract

In this paper we combine kinesthetic demonstrations and dynamical systems to enable a humanoid robot to imitate constrained reaching gestures directed toward a target.
Using a learning algorithm based on Gaussian Mixture Regression, the task constraints are extracted from several demonstrations. Those constraints take the form of desired velocity profiles of the end-effector and joint angle variables. The velocity profiles are then used to modulate a dynamical system which has the reaching target as attractor. This way, the reaching trajectory can be reshaped in order to satisfy the constraints of the task, while preserving the adaptability and robustness provided by the dynamical system. In particular, the system can adapt to changes in the initial conditions and to target displacements occurring during the movement execution. We first evaluate the potential of this method on experiments involving the Hoap3 humanoid robot putting an object into a box. We then show how a manipulation tasks can be executed as sequences of such constrained reaching movement. This is illustrated on a packaging task performed by the robot.

### Bibtex reference

@inproceedings{Hersch06,
author = "M. Hersch and F. Guenter and
S. Calinon and A.G. Billard",
title = "Learning Dynamical System Modulation for Constrained Reaching Tasks",
booktitle = "Proceedings of the {IEEE-RAS} International Conference on Humanoid Robots ({H}umanoids)",
year = "2006",
month="December",
location="Genova, Italy",
pages="444--449"
}

### Video

Handling of dynamic perturbations during the reproduction attempts. The robot first learns how to generalize a skill by observing several demonstrations of a task. When trying to reproduce the skill (here, dropping an object in a box), the robot automatically adapts its motion if someone is moving the box during the reproduction attempt.