A Novel Metric for Evaluating Human-Robot Navigation Performance

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It is frequently desirable to quantitatively evaluate perfor-mance in human-robot interaction. In this research, we in-troduce a novel use of fractal based performance measures to evaluate robot navigation. It can be difficult to use simple measurements such as path length and task timing due to large amounts of individual variability along these metrics. This shortcoming makes these measures particularly unsuit-able for evaluating human/robot navigation performance in a complex environment with multiple tasks. Herein we out-line a class of novel metrics for evaluating navigation perfor-mance using fractal geometry. This class of space and time invariant metrics allows us to better analyze human-robot exploration, interpret valuable behavioral information for analysis of movement, measure the handler/robot's search efficiency, path tortuosity, and overall space utilization in relation to handler goals and overall characteristics of the environment. We present techniques for computation and empirical results from our own navigation interface studies.
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A Novel Metric for Evaluating Human-Robot Navigation
Flip Phillips
Skidmore College
Psychology & Neuroscience
Vision Laboratories
Saratoga Springs, New York 12866
Martin Voshell
The Ohio State University
College of Engineering
Cognitive Systems Engineering Laboratory
Columbus, Ohio 43210
It is frequently desirable to quantitatively evaluate perfor-
mance in human-robot interaction. In this research, we in-
troduce a novel use of fractal based performance measures to
evaluate robot navigation. It can be difficult to use simple
measurements such as path length and task timing due to
large amounts of individual variability along these metrics.
This shortcoming makes these measures particularly unsuit-
able for evaluating human/robot navigation performance in
a complex environment with multiple tasks. Herein we out-
line a class of novel metrics for evaluating navigation perfor-
mance using fractal geometry. This class of space and time
invariant metrics allows us to better analyze human-robot
exploration, interpret valuable behavioral information for
analysis of movement, measure the handler/robot’s search
efficiency, path tortuosity, and overall space utilization in
relation to handler goals and overall characteristics of the
environment. We present techniques for computation and
empirical results from our own navigation interface studies.
Categories and Subject Descriptors
H.4 [Information Systems Applications]: Miscellaneous;
D.2.8 [Software Engineering]: Metrics—complexity mea-
sures, performance measures
General Terms
Fractal dimension, Tortuosity, Human-Robot Coordination
Consider the following scenario— a teleoperated robot nav-
igates through a collapsed building and encounters a large,
fallen beam. In a search and rescue mission the operator
faces multiple task-critical decisions— for example, can the
robot fit through a small opening, is the robot able to travel
over the obstacle, or should they simply backtrack and find
another way to the target area? Several constraints frame
decisions of these sorts. For example, resources are at a
Human Robot Interaction ’06 Salt Lake City, Utah USA
premium with respect to onboard power, time is critical in
rescue missions, and cognitive mapping and machine oper-
ation performance varies widely between operators. When
evaluating mission performance, the complexity of the afore-
mentioned constraints suggests that relatively simple met-
rics may not adequately capture the nature of these noisey
relationships on performance.
When exploring a disaster environment with Urban Search
and Rescue (USAR) robots or when monitoring autonomous
military vehicles, energy conservation and battery life are
at a premium and human-robot handlers and supervisors
need meaningful ways to measure and assess the perfor-
mance of the deployed platforms. The human operator (or
the onboard autonomy) is tasked with controlling and reg-
ulating a remote robot platform to fulfill stakeholder and
handler goals in a dynamic and changing world. The result-
ing human-robot behaviors displayed stem from this agent-
environment interaction. In a Gibsonian sense, we are in-
vestigating the constraints that perceptually mediated inter-
faces for remote robot control have on human perception ev-
ident in goal-driven spatial exploration. The interfaces and
hardware used are the constraints placed on a human opera-
tor’s (and therefore the robot’s) actions and limit or expand
the functional coupling between the human, the robot, and
the environment. Any mediated problem of this nature fun-
damentally becomes an issue of coordinating these various
facets to perform a task in an environment. Performance
measures are needed that can better capture these relation-
ships and how they change when introducing new operator
interfaces, new levels of autonomy, and new levels of super-
visory control to the human-robot system.
Teleoperation has the potential to create many perceptual
ambiguities and, with differing levels of visual access, oper-
ators tend to employ a variety of different navigation strate-
gies. People learn and adapt and change their search strate-
gies constantly. When researchers and engineers introduce
new system component designs, gauging the responses are
quite complex and simple outcome measures such as target
‘hits’ and completion time are not likely to be very effec-
tive. Evaluating navigation and exploration in such settings
presents many challenges when it comes to analyzing per-
formance data. This holds equally true for measuring au-
tonomous robot behavior. Similar to Smithers’ [14] lament
over the state of quantitative assessment of computational
algorithms, there are still no meaningful quantitative or
DRAFT COPY- Flip Phillips, Martin Voshell, 2006
Figure 1: Paths shown with increasing fractal dimensions. The top path is fairly direct and, as such, has a
very low fractal dimension. The bottom path has several areas that have been traveled over multiple times.
Using a strict time or distance based measure would overestimate the amount of the space explored in this
case. A fractal measure is more conservative.
qualitative indications of how well a robot is carrying out
its navigation tasks, how well a robot avoids obstacles, or
generally how well a robot keeps from getting stuck.
In the robotics and human factors literature, analysis met-
rics have a difficult time capturing the intricacy and com-
plexity involved in the domain of practice, especially when
it comes to bridging metric representations with cognitive
work from each field. Fong et al. [5] emphasize the need for
a standardized framework of metrics that span across the
application space between humans, robots, and the human-
robot systems. The most significant problem they cite in
utilizing common metrics lay in the fundamental issue that
that human-robot teams simply are utilized in many diverse
In our previous research designing interfaces for teleoperated
robots in USAR settings [15, 16], one of the central compo-
nents of analysis was navigation. Investigators looking at
such navigation performance data tend to employ multiple
combinations of measures usually within three dimensional
space and time. Chronometric and tally measures collect
task completion times, rest periods, and mean number of
stops. Other metrics tend to look at Cartesian properties
of the exploration, looking at distance traveled, distance
backtracked, number of turns, and number of stops. Many
measurments are entirely task specific, keeping track of tar-
gets located and identified, missiles fired, mines defused, etc.
Others seek more descriptive measures such as smoothness
of trajectory, mean absolute error in pointing direction, and
number of collisions. Clearly, there are many potential met-
rics available, however none of these tell a complete story.
Such traditional measures for analyzing the robot handlers
performance in a complex environment with multiple tasks
were not very informative and it proved very difficult to
pull out different individual search strategies in what can be
seemingly random exploration behavior with high levels of
interoperator variance. Simple first order tabulations tend
not to tell much about complex processes nor capture the
intricacies and problems inherent in search and rescue in
remote exploration. We propose using scale invariant fractal
techniques to be able to help meaningfully understand such
complex performance.
Different types of relational measures were needed to be able
to look at goal-oriented paths in relation to environmental
characteristics and challenges. To this end, we adapt frac-
tal measures from their uses in experimental biology, phys-
iology, and entomology. Whereas traditional quantification
and comparison measures focus on what sources are produc-
ing observed variation, fractal describes the variation itself.
Deviations in the fractal dimension of the robot/handler’s
goal directed path through a complex environment in rela-
tion to various ambiguities and obstacles provide a metric
that captures a very rich set of descriptive behaviors allow-
ing performance evaluation across many applications.
How can we gauge how well a human/robot system is cur-
rently performing? In many ways search and rescue is anal-
ogous to a foraging task in an unknown environment. For
any animal, human, or robot, a complex environment struc-
ture constrains movement. When functioning under these
constraints, searching for distributed information in a given
area becomes challenging. In many biological settings track-
ing exploratory behavior is quite complex and seemingly
random. What could we learn from these and could it be
applied to the data we were finding in simulated teleopera-
Dicke and Burrough [4] first utilized fractal metrics to ex-
plain spontaneous locomotion data in insects with respect
DRAFT COPY- Flip Phillips, Martin Voshell, 2006
Figure 2: The images on the right show god’s-eye-views of two paths taken by subjects in two different
interface configurations. The top shows a multi-camera ’folded’ interface and its respective fractal dimension,
D= 1.03 and the bottom shows a traditional single camera interface with D= 1.18. The second human /
robot team faced significant trouble navigating around the fallen beam in the illustration on the left since
they could not adequately determine if they could fit the robot through the available opening.
to their position. Initially, this motion appeared to be ran-
dom but, when analyzed with a sensitive nonlinear measure,
turns out to be structured in a more complex domain. In
these measures, the fractal dimension, D, as proposed by
Mandelbrot [8], provides a measure of this hidden regular-
Briefly, Dprovides a measure of path complexity that is
totally scale- and time-invariant. Imagine traveling on a
path between two discrete locations, AB, on a two-
dimensional plane P. When traveling in a straight line be-
tween them D= 1.0, the same as its Euclidian counterpart.
If, on the other hand, you were to systematically explore
every location on Pin an effort to find Byou will cover the
two-dimensional area of Pand thus, D= 2. Totally ran-
dom (i.e. Brownian) motion through the space results in a
D= 1.5. This suggests that, when applied to position of
a robot vehicle, this measure provides a useful indication of
degree of exploration independent of the time or path length
taken (See Figure 1).
In the natural world, ecological objects tend to be highly
fragmented and irregular and individual behavioral differ-
ences are often large enough to make quantifying such be-
havior quite difficult. In the animal behavior research such
individual variation may provide valuable information about
what components are leading toward specific behavioral se-
lections [11, 6]. Many species and many behaviors have
been described in 2-D and 3-D as fractal. From the many
scales of variation inherent in the spontaneous locomotion
trails of spider mite spatial exploration described by Dicke
and Burrough [4], to foraging patterns of minnows [1], hawk
prey vigilance [7] and even in analyzing social behavior se-
quences in chimpanzees [2], fractal measures provide a mean-
ingful and therefore useful metric. When describing goldfish
swimming, Neumister explains that fish often swim in highly
organized spatial patterns consisting of coordinated motor
activity where individual activity is often explained with
socio-biological descriptors with little concern for those in-
dividual differences [11]. Persistence (repeating squences)
and redundancy (uncertainty to length) in fish swimming
are two such nonlinear operationally defined patterns that
Neumeister used different fractal approaches to quantify.
Human/robot pairs must explore highly irregular terrain,
they might have to go around corners, over or under de-
bris and rubble, and the optimal path is seldom a straight
line. From our own work [15, 16] we have seen there are
large amounts of interoperator variability in path explo-
ration and Nehmzow and Walker [10] show that some au-
tonomous pathing exploration tends to exhibit determinis-
tic chaos. Quantifying such complex and seemingly random
data while taking into account behavior, task, and locomo-
tion, fractal measures serve as a promising nonlinear mea-
sure to characterize such human-robot exploration.
2.1 Applications
An application of interest to us concerns assessing the qual-
ity of navigation performance in order to compare several
teleoperation interfaces in the USAR domain [15, 16] . A
simulation of a teleoperated robot-assisted search and res-
cue mission was carried out in an urban environment (based
DRAFT COPY- Flip Phillips, Martin Voshell, 2006
Figure 3: Exploring a disaster area results: path length and fractal D when navigating around a fallen beam.
In the first group, using the ”folded” interface, the path length and fractal dimension increase concomitantly.
In the ”single” trials the relationship between path length and fractal dimension is no longer systematic. In
the case of SM the path lengh is almost 2×the more spatially complex path of JG. This indicates that SM
spent a larger amount of time backtracking on the same path rather than exploring as JG did. Additionally,
the mean distance traveled is significantly longer in the single-camera interface condition, yet the fractal
dimension remains the same, suggesting that the amount of area explored overall remains constant regardless
of interface.
on [13]). The task scenario was based on interactions with
disaster specialists and mimicked the role of a structural
triage team assessing the general condition, type of occu-
pancy, and the collapse mechanism of a building disaster.
The robot-handler navigated a virtual robot through the
disaster area and had to gather as much information as pos-
sible about the incident site to both evaluate the need for
specific specialists as well as to ensure rescuer safety prior
to sending in a reconnaissance team. The disaster envi-
ronment was broken into specific transit and special stages.
Special stages were essentially probe areas and consisted of
particular perceptual ambiguities and cognitive challenges
for the robot-handler. Analysis was focused on the fractal
dimension, path length, and velocity in these special stages
to better understand the implications various interfaces had
on robot-handler environment exploration. In Figure 2, two
of the interface concepts we examined are illustrated — A
single small field of view camera versus an array of multiple
As interface designers we are attempting to improve han-
dler/robot behavior by making display data meaningful. The
fractal analysis captures the relationship between the han-
dler and their understanding of the environment evident
through their locomotion in the environment relative to ob-
stacles, apertures, and other perceived affordances. The
fractal dimension provides an affordance-centered metric that
captures the efficiency of the space explored and is a rich in-
dication of how well an individual is performing with a given
interface. The initial findings from this work suggest that
when interfaces are catered to specific environmental condi-
tions, the operators’ robots have less tortuous paths.
During testing, the fractal dimension was used to character-
ize the tortuosity of the handler/robot paths. Our virtual
robot collected telemetry information in the form of x, y, z
position at the rate of 2Hz. Subsequent to each run we com-
puted a fractal Dfor the path’s spatial component using a
custom Mathematica [17] package. The computation was
performed using a plurality of methods as outlined in [9] to
check for convergent results. Our final method was a hybrid
of the the box method combined with the caliper method,
using multiple scales of interpolated analytic representations
of the path covered. In the biological literature, ‘tortuosity’
refers to how erratic and contorted an animal’s path is and
fractal models have been used to describe the shape of these
goal-directed paths in regard to how directional (D= 1.0)
or random they are (D1.5). Figure 3 show results for
six subjects spilt across the two different experimental con-
ditions — three subjects using an interface consisting of an
array of cameras and three subjects using a traditional sin-
gle camera view. Our results show that the mean distance
traveled is significantly longer in the single-camera interface
condition, yet the fractal dimension remains the same. sug-
gesting that the extent of overall exploration remains con-
stant regardless of interface, but the multi-camera interface
cuts down on revisiting the same locations.
Fractal analysis is not merely restricted to the spatial do-
main. Van Orden, Holden, and Turvey [12] suggest that
temporal properties of human performance also obey highly
non-linear rules. Seemingly random or noisy performance
in time-domain tasks reveal regularities when measured us-
ing fractal metrics. (See [3] for a survey of methods used
in physiological measurements.) Figure 4 shows the speed
of the robot throughout the course of a trial for two sub-
jects. A visual examination of the speed profile suggests a
rather noisy performance but again, the fractal results of
D= 1.16 for Subject A (on the left) and D= 1.33 for
Subject B (on the right) suggest that B’s performance with
respect to speed was less consistent than the performance
of A. Even though Subject B may have completed the task
in a shorter amount of time, the acceleration / deceleration
patterns may have required more energy utilization than
Subject A’s run. More to the point, this analysis can be
continued with higher derivatives of position as well, such
DRAFT COPY- Flip Phillips, Martin Voshell, 2006
100 200 300 400 500
Fractal D = 1.16 Fractal D = 1.33
0 50 100 150 200 250 300
Figure 4: Speed profiles for two Subjects, A (left) and B (right). Both performances are visually ’noisy’
but Subject B’s performance is significantly more-so according to the fractal metric. Even though Subject B
may have completed the task in a shorter amount of time, the acceleration / deceleration patterns may have
required more energy utilization than Subject A’s run.
as acceleration. Furthermore, this analysis could be done
directly on energy utilization, even providing warnings to
the operator as their utilization becomes more ‘fractal’ and
Assessing complex performance data in remote teleopera-
tion and observation is a difficult problem. Performance
tends to be extremely complicated and before we can assess
effective ways to deal with remote perception we have to
develop methods and performance metrics that capture the
interactions between the human, the robot, and the envi-
ronment to better evaluate human-robot team performance.
When designing new interfaces or testing new autonomous
navigation systems, it is imperative to utilize metrics that
capture how well a platform team is doing in spite of what
can appear to be highly variable and random data.
In this paper, we have proposed using fractal techniques
as quantitative estimates of overall human-robot navigation
behavior. We can look at these performance measures in
other spaces rather than strictly time, space, and we can
calculate a scale-invariant measure that is useful integration
of space-time. The fractal approach allows us to specify a di-
mensionality independent of scale and allows us to compare
and contrast it with other simpler scale dependent measures
to help elucidate the true nature of the operator/robot’s per-
formance. This analysis can be extended beyond the spatial
domain to temporal measurements such as speed and energy
As onboard navigation improves, the robot handler role will
slowly translate to one of supervisory control as teleopera-
tion gives way to the need to coordinate many agents with
mixed levels of autonomy. At this point, supervisory con-
trol intervention and the ability to ascertain if a platform
is underperforming becomes critical. Integrating such per-
formance metrics as a robot’s instantaneous fractal dimen-
sion into a supervisor’s interface puts the robot performance
data into context and could give valuable cues to status at
a glance telling a supervisor when to intervene, or adjust
control. Fractal can be adapted across many scales- from
a small UGV to a USAR robot, a micro UAV to Predator
drone UAV, we have a means to start looking how to adapt
different classes of general robot behaviors at different spa-
tial scales. Our current experiments further examine the
efficiency and veridicality of mental representations built up
in exploration, as a function of the fractal dimension of the
On a much larger level, such biological approaches have
many potentially useful implications toward ecological robot
design. By treating robot’s telemetry data in such a way,
valuable behavioral information can be interpreted for anal-
ysis of movement and overall environment utilization. Using
fractal to describe such goal-oriented behavior of human op-
erated robot movements in complex environments is a start-
ing point to try to integrate such measures into future op-
erator interfaces, as well as the control systems themselves.
Prepared through collaborative participation in the Advanced
Decision Architectures Consortium sponsored by the U. S.
Army Research Laboratory under the Collaborative Tech-
nology Alliance Program, Cooperative Agreement DAAD19-
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