International Journal of Swarm Intelligence Research, 1(4), 17-45, October-December 2010 17
A Theoretical Framework for
Estimating Swarm Success
Probability Using Scouts
Antons Rebguns, The University of Wyoming, USA
Diana Spears, Swarmotics LLC, USA
Richard Anderson-Sprecher, University of Wyoming, USA
Aleksey Kletsov, East Carolina University, USA
ABSTRACT
This paper presents a novel theoretical framework for swarms of agents. Before deploying a swarm for a task,
it is advantageous to predict whether a desired percentage of the swarm will succeed. The authors present
a framework that uses a small group of expendable “scout” agents to predict the success probability of the
entire swarm, thereby preventing many agent losses. The scouts apply one of two formulas to predict – the
standard Bernoulli trials formula or the new Bayesian formula. For experimental evaluation, the framework
is applied to simulated agents navigating around obstacles to reach a goal location. Extensive experimental
results compare the mean-squared error of the predictions of both formulas with ground truth, under varying
circumstances. Results indicate the accuracy and robustness of the Bayesian approach. The framework also
yields an intriguing result, namely, that both formulas usually predict better in the presence of (Lennard-Jones)
inter-agent forces than when their independence assumptions hold.
Keywords:
Bayesian, Sampling, Scouts, Success Rate, Swarm of Agents
INTRODUCTION
This paper presents a novel theoretical framework for swarm risk assessment. The framework
is applied to a scenario consisting of a swarm of
agents that needs to travel from an initial location to a goal location, while avoiding obstacles.
Before deploying the entire swarm, we would
like to have a certain level of confidence that
DOI: 10.4018/jsir.2010100102
a desired portion of the swarm will successfully reach the goal. If not, then perhaps the
swarm should not be deployed. For example,
for a swarm of moving robots, the environment
itself can pose a significant risk (rough terrain,
sudden changes in elevation that agents are not
equipped to handle, water, etc.) and, as with
any hardware, circuit and mechanical failures
can prevent agents from successfully reaching
their destination. It is alternatively plausible that
the swarm consists of software agents trying to
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18 International Journal of Swarm Intelligence Research, 1(4), 17-45, October-December 2010
achieve a more abstract goal, such as a successful transaction, while avoiding obstacles, such
as provisions or constraints. For simplicity, in
our simulation agents are modeled as robots
and obstacles are modeled as physical objects.
The environment in which the agents are
deployed is assumed to be static, though it
may be completely or partially unknown. This
environment can be highly unstructured as
well, as in Mondada et al. (2005). Additionally,
deployment of the entire swarm is potentially
hazardous, e.g., due to the possible loss or
corruption of agents – for example, some of
the obstacles might contain explosives, agents
could fall into inescapable holes as in Dorigo
et al. (2006), or there could be environmental
hazards as in Tatomir and Rothkrantz (2006).
In these and many similar situations it is advantageous to do a preliminary phase of risk
assessment before deploying the full swarm. The
information gained from this phase will help the
practitioner decide what deployment strategy
to use, e.g. what starting location works best,
how many agents to deploy in order to ensure
a desired success rate, and whether the task at
hand is worth the risk of losing a possibly large
portion of the swarm.
The solution proposed here is the use of a
group of expendable agent “scouts” to predict
the success probability for the swarm, during
the risk assessment phase. For practical reasons,
only a few (less than 20) scouts are sent from
the swarm, which may consist of hundreds of
agents. A human or artificial agent, called the
“sender,” deploys the scouts. Then, an agent
(e.g., a person, an artificial scout, or a sensing
device), called the “receiver,” counts the fraction of scouts that arrive at the goal successfully. The sender and receiver must be able to
communicate with each other – to report the
scout success rate, but no other agents require
the capability of communicating messages.
Using the fraction of scouts that successfully
reach the goal, we apply a formula that predicts
the probability that a desired percentage of the
entire swarm will reach the goal. Based on this
probability, the sender can decide whether or not
to deploy the full swarm. Alternatively, based
on this probability the sender can decide how
many agents to deploy in order to yield a high
probability that a desired number of agents will
reach the goal.
Our theoretical framework is based on two
formulas that use agent scouts as “samples”
for making predictions regarding the success
probability of a swarm. The first approach is
the standard Bernoulli trials formula, and the
second is a novel Bayesian formula. We report
conclusions regarding the predictive accuracy
of these formulas, based on an extensive set
of experiments during which parameters were
varied methodically. Our measure of predictive
accuracy is the mean squared error (MSE) of
each formula’s predictions versus “ground
truth.” Experimental conclusions include the
value of a uniform prior for the Bayesian formula
in knowledge-lean situations, and the accuracy
and robustness to changes in the environment of
the Bayesian approach. This paper also reports
an intriguing result, namely, that both formulas
usually predict better in the presence of interagent forces (when a Lennard-Jones inter-agent
force law is used) than when their independence
assumptions hold. Inter-agent forces are useful
for initiating and sustaining multi-agent formations while traveling to a target location. We
conclude that these formulas, and especially our
Bayesian formula, provide extremely practical
solutions for solving “the swarm success rate
prediction problem” in a variety of real-world
situations. Additionally, this paper provides
conclusions which lead to advice on selecting
the values of controllable parameters in order
to help the practitioner apply our framework.
The most notable contributions of this
research are:
•
A novel theoretical framework for swarm
risk assessment, using very few scouts to
predict the swarm success probability, is
presented. For the first time, scouts are used
to predict the probability that a given portion of a swarm will achieve its objective.
Although our framework has been applied
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