# Robotics: Science and Systems VI

### Variable Impedance Control - A Reinforcement Learning Approach

*J. Buchli, E. Theodorou, F. Stulp and S. Schaal*

**Abstract:**

One of the hallmarks of the performance, versatility,
and robustness of biological motor control is the ability to adapt
the impedance of the overall biomechanical system to different
task requirements and stochastic disturbances. A transfer of this
principle to robotics is desirable, for instance to enable robots
to work robustly and safely in everyday human environments. It
is, however, not trivial to derive variable impedance controllers
for practical high DOF robotic tasks. In this contribution, we accomplish
such gain scheduling with a reinforcement learning approach
algorithm, PI^{2} (Policy Improvement with Path Integrals).
PI^{2} is a model-free, sampling based learning method derived from
first principles of optimal control. The PI^{2} algorithm requires no
tuning of algorithmic parameters besides the exploration noise.
The designer can thus fully focus on cost function design to
specify the task. From the viewpoint of robotics, a particular
useful property of PI^{2} is that it can scale to problems of many
DOFs, so that RL on real robotic systems becomes feasible. We
sketch the PI^{2} algorithm and its theoretical properties, and how
it is applied to gain scheduling. We evaluate our approach by
presenting results on two different simulated robotic systems, a
3-DOF Phantom Premium Robot and a 6-DOF Kuka Lightweight
Robot. We investigate tasks where the optimal strategy requires
both tuning of the impedance of the end-effector, and tuning
of a reference trajectory. The results show that we can use
path integral based RL not only for planning but also to derive
variable gain feedback controllers in realistic scenarios. Thus,
the power of variable impedance control is made available to a
wide variety of robotic systems and practical applications.

**Bibtex:**

@INPROCEEDINGS{ Buchli-RSS-10, AUTHOR = {J. Buchli AND E. Theodorou AND F. Stulp AND S. Schaal}, TITLE = {Variable Impedance Control - A Reinforcement Learning Approach}, BOOKTITLE = {Proceedings of Robotics: Science and Systems}, YEAR = {2010}, ADDRESS = {Zaragoza, Spain}, MONTH = {June}, DOI = {10.15607/RSS.2010.VI.020} }