\section{Autonomous Walking Results}
  \label{sec:results}

%!

The Ambler autonomous walking system has been tested extensively over
the past several years, in both indoor and outdoor trials.  This section
presents results from a representative sample of the many trials,
including indoor navigation over rugged terrain and outdoor,
long-distance, long-endurance autonomous walking.

A typical trial begins by executing perception, planning, and control
processes on the on-board computers.  
For convenience, the standard outputs of these processes are displayed on
windows on off-board workstations.
A human operator enters a path as a sequence
of arcs of circles, and issues the command to start walking.
The Ambler then operates autonomously,
planning and executing every footfall, leg move, body
move, leveling maneuver, and other action or reaction.

To date, the Ambler has walked autonomously a total of over 4 km,
much of it over rugged, difficult terrain.
Table \ref{tbl:walking} reports statistics of several 
walking trials, which were selected to indicate
the progressive escalation of challenges and capability.

In the table, the column labeled ``planar travel'' indicates the horizontal
distance traveled by the Ambler body, but does not include body lifts
and lowers.
The ``leg travel'' column reports the sum of the planar distances traveled by
the legs, measured from pick-up to set-down.  The total leg distance can
be greater than six times the body travel during trials in which the
Ambler is executing many point turns, since in that maneuver some legs
travel in retrograde motion (see Section~\ref{sec:gait}).
Most of the leg travel occurs during circulation.
Walking time includes the time required for movement, sensing, mapping,
planning, and all processing; it excludes idle time due, for instance, to
debugging.  Average walking speed over all types of terrain is 35
cm/minute, with the speed for straight-line, benign terrain about 40 cm/minute.

\begin{table}
\begin{center}
\begin{tabular}{c r r r r r r}
Date	& Terrain		& Body	& Planar	& Body		& Leg 	& 
Total \\
 	&			& Moves	& Travel	& Rotation	& Travel & Time \\
	& 			& 	& (m)		& (rad)		& (m)	& (hr)	\\ \hline
1990	& Indoor obstacle course& 27	& 11		& 2		& ?  		& 0.7 \\ 
1991	& Outdoor obstacle course& 100	& 25		& 2		& ?  		& 
3.5  \\
1992	& Indoor obstacle course& 397	& 107		& 55		& 901 	
	& 7.0  \\
1992	& Outdoor field		& 151	& 46		& ?		& ?  		& 
?   \\ 
1992	& Outdoor field		& 1219	& 527		& 20		& 3330  
	& 20.8 \\ \hline
\end{tabular}
\end{center}
\caption{Statistics from selected walking trials}
\label{tbl:walking}
\end{table}


\subsection{Indoor Trials}

For indoor trials, the Ambler operated on obstacle courses fashioned
from 40 tons of sand, 20 tons of boulders, a $30^{\rm o}$ wooden ramp,
and various other objects (Figure \ref{fig:PRB}).  The courses typically
include rolling, sandy terrain with several boulders one meter or
taller, approximately ten boulders one-half meter tall, a ditch, and a
ramp.  The largest of the boulders
is 1.5 m tall, 4 m long, and 2 m wide.  With such
materials, the obstacle courses pose significant barriers to locomotion.
We know of no other robot that could surmount all of the obstacles in
the course.

\begin{figure}
\vspace{1 in}
\caption{Ambler traversing indoor obstacle course}
{\small Ambler on sandy terrain with meter-tall boulders (under legs and
body), ditches (the center leg on the far stack is standing in one), and
ramp (lower right).}
\label{fig:PRB}
\end{figure}

Traversing a variety of these obstacle courses,
the Ambler has demonstrated long-term autonomous walking.
In one trial, 
the Ambler took 397 steps and traveled about 107 meters 
following a figure-eight pattern,
each circuit of which covers about 35 m and 550 degrees of turn 
(Figure \ref{fig:bowTie}).  
In the figure, the thin line indicates the course followed by the center of the
Ambler's body for one complete circuit.
The triangle indicates one randomly selected body pose obtained during the trial.
Other trials typically result in somewhat different courses, due to
changes in the terrain and exact starting location of the robot.

Completing more than two circuits during the trial,
the Ambler turned nearly 9 complete revolutions, 
thus devoting a significant fraction of the trial to turning
rather than to advancing.
The two circuits were different in the sense that the robot 
did not take the same step twice.

\begin{figure}
\vspace{4 in}
% \special{psfile=fig/navFig8.ps hscale=0.6 vscale=0.6 hoffset=0 voffset=0}
\caption{Top view of figure-eight circuit}
{\small Boulders are drawn grey;  units are meters.}
\label{fig:bowTie}
\end{figure}

\subsection{Outdoor Trials}

A number of trials were performed outdoors.  These differed from the
indoor trials primarily in that we were able to test the ability of the
Ambler to traverse significant slopes and to operate autonomously for
long distances (up to half a kilometer at a time). 

For one set of outdoor trials,
the Ambler operated in a parking lot strewn with wooden obstacles such as
boxes, pyramids, and ramps.
In one of these trials, 
the Ambler took 100 steps along a gently curving arc,
traveling about 25 m over a variety of obstacles.
In another of these trials, 
the Ambler walked in the parking lot at night, without lights, 
since the laser rangefinder does not require ambient illumination.
In fact, we observed the range images to be noisier during the day, 
because the signal-to-noise ratio is higher without ambient illumination.

For another set of outdoor trials, 
the Ambler operated on rolling, grassy terrain (Figure \ref{fig:wstc}).
The site is a field cleared in a hilly, wooded area at an industrial park.
Although it does not contain obstacles like those encountered in the
indoor trials, the site poses its own challenges:  steeper slopes and
side-slopes, and soft ground.

\begin{figure}
\vspace{1 in}
\caption{Ambler walking 527 m in field}
\label{fig:wstc}
\end{figure}

In the longest of the outdoor trials, 
the Ambler took 1219 steps, traveling 527 m horizontally
and 25 m vertically.
It followed a meandering course 
that included first climbing a hill and descending from it,
then roughly following an iso-elevation contour for 250 m,
executing a point turn of roughly $\pi$ radians,
climbing a bit to a higher elevation,
and then following an iso-elevation contour back to the starting region.
While this course is simpler
than the indoor figure-eight pattern (Figure \ref{fig:bowTie}),
since it involves less turning and no boulders, it is notable for both
the length and duration (over 20 hours) of autonomous operation.
In addition, the Ambler traversed rather steep slopes: it ascended and
descended a 30 percent grade, and traversed side-slopes of up to 15
percent grades.

\subsection{Remarks}

Average walking speed over these trials, including all computation, is 35 cm/min 
(typical body moves travel about 50 cm).  
Moving the mechanism is the main limitation to the speed.  
During operation, the real-time controller is active about 80\% of the time,
while the planners and perception subsystems are each active about 50\% of
the time, and the centralized task-level controller is active only about 3\%
of the time (the total is greater than 100\% because operations occur
concurrently).  


The results of the indoor and outdoor walking trials show that the
approach meets the challenges identified in Section \ref{sec:intro}:
\begin{enumerate}

\item Self-reliant control.
The approach meets this challenge, since the integrated walking system
exhibits a high level of autonomy in planning and executing
motions (e.g., traversing a specified path), reacting to unsafe conditions
(e.g., leveling), learning good footfalls on the basis of experience, and
operating for extended periods.
Still, there was some manual intervention in the form of restarting
processes and  occasionally over-riding a default value.

\item Limited power.
The approach meets this challenge by reducing unwanted terrain contact to a
negligible (but non-zero) level.
Thus, the system transfers far less energy to the terrain than would a
purely reactive or purely randomized robot.

\item Rugged terrain traversal.
The approach enables locomotion over
challenging obstacle courses, soft ground, and significant slopes and
side-slopes.

\end{enumerate}

