Localization of Unknown Odor Source Based on
Shannon’s Entropy Using Multiple Mobile Robots
Qiang Lu, Yang He, and Jian Wang
School of Automation, Hangzhou Dianzi University, Hangzhou, 310018, China
Email: lvqiang@hdu.edu.cn
Abstract—This paper deals with the problem of odor source
localization by designing a collective decision-making mechanism
based on Shannon’s entropy and using two finite-time motion
control algorithms for multiple mobile robots. Specifically, for
the collective decision-making mechanism, a discrete grid map is
first used to model the search environment. Then, the posteriori
probability distribution for the position of the odor source on
the discrete grid map is recursively updated by the detection
events and non-detection events. Next, the Shannon’s entropy
for the probability distribution is employed to collectively make
the decision on the movement direction of the robot group.
For the motion control, the finite-time parallel motion control
algorithm and the finite-time circular motion control algorithm
are described. Moreover, two motion control algorithms are
further extended in order to enable the robot group to avoid
obstacles. Finally, the effective of the collective decision-making
mechanism and two finite-time motion control algorithms is
illustrated for the problem of odor source localization.
Index Terms—odor source localization; Shannon’s entropy;
multiple mobile robots; posteriori p robability distribution
I. INTRODUCTION
In the last two decades, the problem of odor source local-
ization has been widely studied based on a single robot in
the science and engineering field [1], [3]. On the other hand,
using the multiple mobile robots to locate the odor source has
also received much attention from researchers due to a major
advantage, i.e. a wider detection range, which can enable the
robot group to better capture the time-varying plume.
There exist two classes of solutions for controlling the
multi-robot systems: one is the the particle swarm optimization
(PSO) algorithm [2], [4]–[7], [10] while another is decision-
control solution [8], [9]. For example, Jatmiko et al. (2007)
[2] proposed the charged PSO algorithm (CPSO) to coordinate
the multiple mobile robots where two types of robots (neutral
and charged robots) are used to search for the odor source.
On the basis of the CPSO algorithm, Jatmiko et al. (2007) [2]
further gave two wind utility algo rithms: one is the WUI-45
algorithm while the other is the WUII algorithm. For the WUI-
45 algorithm and the WUII algorithm, the wind information
is simply employed to guide the movement direction of the
robot group. By analyzing the PSO algorithm, Lu and Han
(2011) [6] put forth a probability particle swarm optimization
with information-sharing mechanism (PPSO-IM) algorithm to
control the robot group such that the robot group is guided
to search for the approp riate rang e with a higher probability.
However, the wind information is still not better utilized
in the above solutions, which results in appearance of the
“soft sensor” [4], [5]. By the “soft sensor”, the position of
the odor source can be “observed”. In terms of the “soft
sensor”, Lu and Han (2014) [7] proposed a finite-time particle
swarm optimization algorithm (FPSO) algorithm such that
the odor clues can be quickly captured. By summarizing the
aforementioned research results, Lu and Han (2013,2014) [8],
[9] gave the decision-control solution where the “soft sensor”
and the decision mechanism applied in PSO algorithms are
used to make decision on movement direction and the finite-
time motion controllers are employed to coordinate the multi-
robot systems to quickly and orderly track the time-varying
plume. It should be pointed out that the “soft sensor” only
works when the robot detects the odor clues, which implies
that non-detection events are not fully taken into account and
two issues arise. One issue is that how to use the non-detection
events to improve the observation results of the “soft sensor”
while the other issue is how to utilize the observation results
to orient the movement direction of the robot group in order
to collect the much odor information. Therefore, how to deal
with the two issues is the motivation of the current study.
In this paper, we will deal with the problem of odor
source localization by designing a collective decision-making
mechanism based on Shannon’s entropy and using two finite-
time motion control algorithms for multiple mobile robots. For
the collective decision-making mechanism, we will first make
use of a discrete grid map to model the search environment
such that the updating methods of probability distribution on
the position of the odor source can be established. Second, by
means of the Shannon’s entropy for the probability distribution
on the position of the odor source, we will plan the movement
direction of the robot group. Third, we will describe the finite-
time parallel motio n control algorithm and the finite-time
circular motion control algorithm. Finally, we will illustrate
the effectiveness of the collective decision-making mechanism
and two finite-time motion control algorithms for odor source
localization.
II. C
OLLECTIVE DECISION-MAKING BASED ON
SHANNON’S ENTROPY
In this section, we first make use of a discrete map to model
the search env ironment, and then derive a posteriori probability
distribution on the position of the odor source. Finally, based
on the Shannon’s entropy, we give the movement direction of
the robot group.
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