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Song et al. proposed a Distributed Bidirectional Auction algorithm for multi-
robot systems coordination. A task is divided into
n
sub-tasks, a robot can only
run a sub-task, the allocation of sub-tasks is decided by both the auctioneer and
bidder; the auctioneer chooses the pre-winners ordering the prices of offer, while
the bidders chosen all tasks that pre-won the sub-task which has the lowest price.
After the first round, the sub-tasks that were not chosen by any bidder enters
a second round of auction depending on the initial price auction, this process is
repeated until all sub-tasks have been completed [14].
In [15] Lim et al. presented an architecture based on the auction market for
the cooperation of a team of robots. On this platform, each team of robots is
controlled by a respective MRS Client program and communicating through Zig-
Bee Wireless Personal Area Network (WPAN). Each WPAN is assigned whit a
different identity (ID) so the data security of communicated information be pre-
served. A client program that acts as a buyer is used to deliver the tasks for users
in the market. Then, a server program of tasks coordination is used to compare
the buyers' demand matches the supply from sellers. These programs are based
on client/server architecture and are connected through Local Area Network
(LAN) using Transmission Control Protocol (TCP) and Internet Protocol (IP).
3 Response Threshold Model
Insect societies are characterized by the division of labor, communication be-
tween individuals and the ability to solve complex problems [16], and these
characteristics have long been a source of inspiration and subject of numer-
ous studies, acquiring great relevance for many researchers both in the field of
robotics as in biology. On the one hand, the biologists trying to prove their
theories of social insects on robots, and on the other hand, researchers in the
discipline of robotics seek solutions to problems that cannot be solved by a single
robot.
Seeley et al. [17] have considered the following experiment to study the col-
lective behavior in a colony of insects, focusing on the work performed by bees
to get honey. Two food sources are presented to the colony at 8:00 A.M. at the
same distance from the hive: source A is characterized by a sugar concentration
of 1.0 mol/1 and source B by a concentration of 2.5 mol/1. Between 8:00 A.M.
and noon, source A has been visited 12 times and source B, 91 times. At noon,
the sources are modified: source A is now characterized by a sugar concentration
of 2.5 mol/1 and source B 0.75 mol/1. Between noon and 4:00 P.M., source A
has been visited 121 times and source B only 10 times. Have shown that a bee
has a relatively high probability of going to a good food source and abandon a
poor food source.
Based on these observations, these simple rules of behaviors allow the bees
to select the best quality source; Eric Bonabeau et al. have proposed a simple
mathematical model of response thresholds for the regulation of division of labor
in insect societies [18]. In this model assume that each task is associated with a
stimulus or set of stimuli, so that individuals can detect information on each of
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