Coordination of Communication in Robot Teams by Reinforcement Learning - Foundations on Natural and Artificial Computation - page 156

meanings (i.e. the objects, states of the environment and self-states) into symbols
or signals . According to a long and well-established line of thought culminating
with the work of Ferdinand de Saussure [9] and Charles S. Peirce [8], the pioneer
of Semiotics, the association of the symbols of a language to their meanings are
(1) arbitrary and (2) conventional.
In this paper we use arbitrarily (in fact, randomly) initialized association ma-
trices, for each robot and through an dynamic process based on communicative
or linguistic interactions implemented by means of the Reinforcement Learning
paradigm, the team converges to an optimum consensus state. 1

2 Formal Definitions

2.1 Multi-Robot Communication System

We define a Communication System, CS , in a team of robots as the triple:

CS M, Σ, A i (1)

where M =

{ m 1 ,...,m p }

is the set of meanings (i.e. the objects or states in the
environment that can be of relevance for communication in the team of robots),
Σ =

is the set of symbols or signals used by the robots in their
communication acts and which represent the actual meanings, A i ( i =1 ,...,N )
are the association matrices of the robots defining their specific associations
between meanings and symbols:

{ s 1 ,...,s n }

A i =( a rj ) i ; i =1 ,...,N agents (2)

in which the entries a rj of the matrix A are non negative real numbers such that
0

1, ( r =1 ,...,p ; j =1 ,...,n ). These entries a rj give the strength
of the association of meaning m r to symbol s j ; such that a rj = 0 indicates
no association at all and a rj = 1 indicates total association. Note that these
quantitative associations have a deterministic and non probabilistic nature so
that the associations between meanings and symbols are based on the maximum
principle, which means that the maximum value of the entries in a row (column)
gives the valid association. An ideal, optimum association matrix is purely binary
(the entries are either 0 or 1) and also have the additional restriction of having
in each row only one 1 (i.e. no synonyms are allowed) and having a unique 1 in
each column, too (no homonyms are allowed).
Optimum association matrices are also known as permutation matrices as
they are equal to their transpose matrix, a very important property from the
communication eciency point of view (see paragraph 2.2 below).

≤ a rj ≤

1 Some authors, inspired in the ideas of Ludwig Wittgenstein, have called them lan-
guage games [7,10,2], although we believe a more founded denomination should be
communication or signaling games as defined by David K. Lewis [3].