### Abstract

We propose to formulate the problem of representing a distribution of robot configurations (e.g. joint angles) as that of approximating a product of experts. Our approach uses variational inference, a popular method in Bayesian computation, which has several practical advantages over sampling-based techniques. To be able to represent complex and multimodal distributions of configurations, mixture models are used as approximate distribution. We show that the problem of approximating a distribution of robot configurations while satisfying multiple objectives arises in a wide range of problems in robotics, for which the properties of the proposed approach have relevant consequences. Several applications are discussed, including learning objectives from demonstration, planning, and warm-starting inverse kinematics problems. Simulated experiments are presented with a 7-DoF Panda arm and a 28-DoF Talos humanoid.

### Bibtex reference

@inproceedings{Pignat20ICRA,
author="Pignat, E. and Lembono, T. S. and Calinon, S.",
title="Variational Inference with Mixture Model Approximation for Applications in Robotics",
booktitle="Proc. IEEE Intl Conf. on Robotics and Automation (ICRA)",
year="2020",
pages="3395--3401"
}


### Video

Need to find all the solutions of a multi-objective inverse kinematics problem? In this work, we reformulated this problem as a product of experts approximation using variational inference. A python/tensorflow library, with jupyter notebook examples, are provided to facilitate the exploitation of this approach in other problems (by providing a URDF file).

### Source codes

Source codes related to this publication are available as part of PbDlib.