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\section{Introduction and Previous Work}
open-source, 3D printed QuadraTot robot used for this study. Left:
physical robot \citep{yosinski2011evolving-robot-gaits}. Right:
simulator \citep{Glette2012Evolution}.}
There has been much previous work in the Artificial Life and
Evolutionary Robotics community on automatically generating behaviors
for robots~\citep{nolfi2000evolutionary,
sims1994evolving, hornby2005autonomous, lipson2000automatic}. Much
of this work has focused on learning gaits for legged
robots~\citep{clune2009evolving, clune2011performance,
hornby2005autonomous, hornby2003generative,
Koos2012, bongard2006resilient,
yosinski2011evolving-robot-gaits}. Some previous work
has focused both on evolution directly on a physical
system~\citep{yosinski2011evolving-robot-gaits, zykov2004evolving}, but more
frequently gaits have been evolved in simulation and then transferred
to the physical robot~\citep{lipson2006evolutionary, Koos2012,
hornby2005autonomous, bongard2006resilient}. Whether simulation or
reality is used gait evaluation, a common thread in these
studies is that learning algorithms are able to produce gaits that
outperform those designed by a human
engineer~\citep{yosinski2011evolving-robot-gaits, hornby2005autonomous}.
%\subsection{Problem Definition}
%Before proceeding, we briefly pause to more concretely formulate the
%gait learning problem to avoid any ambiguity. The gait learning
%problem aims to find a \emph{gait} that maximizes some performance
%metric. Mathematically, we define a gait as a function that specifies
%a vector of commanded motor positions for a robot over time. We can
%write gaits without feedback --- also called open-loop gaits --- as
%\vec{x} = g(t)
%\noindent for commanded position vector $\vec{x}$. The function
%depends only on time, and thus it follows that open-loop gaits are
%deterministic, producing the same command pattern each time they are
%run. While the commanded positions will be the same from trial to
%trial, the actual robot motion and measured fitness will vary due to
%the noisiness of trials in the real world.
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