\section{Introduction and Previous Work} \figgp{robot_whitebg}{.44}{simulator_screenshot_crop}{.55}{The 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} %\seclabel{problemDefinition} % %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 % %\be %\vec{x} = g(t) %\ee % %\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.