# Robotics: Science and Systems II

### Learning Operational Space Control

*J. Peters, S. Schaal*

**Abstract:** While operational space control is of essential importance
for robotics and well-understood from an analytical
point of view, it can be prohibitively hard to achieve accurate
control in face of modeling errors, which are inevitable in
complex robots, e.g., humanoid robots. In such cases, learning
control methods can offer an interesting alternative to analytical
control algorithms. However, the resulting learning problem is
ill-defined as it requires to learn an inverse mapping of a usually
redundant system, which is well known to suffer from the
property of non-covexity of the solution space, i.e., the learning
system could generate motor commands that try to steer the
robot into physically impossible configurations. A first important
insight for this paper is that, nevertheless, a physically correct
solution to the inverse problem does exits when learning of the
inverse map is performed in a suitable piecewise linear way.
The second crucial component for our work is based on a
recent insight that many operational space controllers can be
understood in terms of a constraint optimal control problem.
The cost function associated with this optimal control problem
allows us to formulate a learning algorithm that automatically
synthesizes a globally consistent desired resolution of redundancy
while learning the operational space controller. From the view
of machine learning, the learning problem corresponds to a
reinforcement learning problem that maximizes an immediate
reward and that employs an expectation-maximization policy
search algorithm. Evaluations on a three degrees of freedom
robot arm illustrate the feasability of our suggested approach.

**Bibtex:**

@INPROCEEDINGS{ Peters-RSS-06, AUTHOR = {J. Peters and S. Schaal}, TITLE = {Learning Operational Space Control}, BOOKTITLE = {Proceedings of Robotics: Science and Systems}, YEAR = {2006}, ADDRESS = {Philadelphia, USA}, MONTH = {August}, DOI = {10.15607/RSS.2006.II.033} }