### Abstract

We present a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper systems acting in multiple frames of reference. Each candidate coordinate system observes a set of demonstrations from its own perspective, by extracting an attractor path whose variations depend on the relevance of the frame at each step of the task. This information is exploited to generate new attractor paths in new situations (new position and orientation of the frames), with the predicted covariances used to estimate the varying stiffness and damping of the spring-damper systems, resulting in a minimal intervention control strategy. The approach is tested with a 7-DOFs Barrett WAM manipulator whose movement and impedance behavior need to be modulated in regard to the position and orientation of two external objects varying during demonstration and reproduction.

### Bibtex reference

@inproceedings{Calinon14ICRA,
author="Calinon, S. and Bruno, D. and Caldwell, D. G.",
title="A task-parameterized probabilistic model with minimal intervention control",
booktitle="Proc. {IEEE} Intl Conf. on Robotics and Automation ({ICRA})",
year="2014",
month="May-June",
pages="3339--3344"
}

### Video

This video presents a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper systems acting in multiple frames of reference. Each candidate coordinate system observes a set of demonstrations from its own perspective, by extracting an attractor path whose variations depend on the relevance of the frame at each step of the task.

This information is exploited to generate new attractor paths in new situations (new position and orientation of the frames), with the predicted covariances used to estimate the varying stiffness and damping of the spring-damper systems, resulting in a minimal intervention control strategy.

The approach is tested with a 7-DOFs Barrett WAM robot whose movement and impedance behavior are modulated in regard to the position and orientation of two external objects varying during demonstration and reproduction.

### Source codes

Demonstration a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper systems acting in multiple frames of reference. Each candidate coordinate system observes a set of demonstrations from its own perspective, by extracting an attractor path whose variations depend on the relevance of the frame through the task. This information is exploited to generate a new attractor path corresponding to new situations (new positions and orientation of the frames), while the predicted covariances are exploited by a linear quadratic regulator (LQR) to estimate the stiffness and damping feedback terms of the spring-damper systems, resulting in a minimal intervention control strategy.