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is no direct communication of the agents of opposite groups. T is the upper bound on
the number of time periods in which all the agents reach their distinct assigned targets.
4
Dynamic Online Auction with Mobility
Each robot agent has its own copy of the modified auction algorithm which serves as a
controller of its actions as it moves toward its assigned target in each period. Since the
auction algorithm's structure is equal for all agents, in the following we will present the
version for the agents belonging to the group A but the same reasoning stands for the
agents of the group Θ which negotiate on their targets: agents of the group A .
Each agent a keeps in its memory the value v θa , that is, its most recent knowledge
about the actual value of target θ , for each θ ∈ Θ ,andtheset S a of its most recent
knowledge about all the agents' assignments. Both v θa and S a do not have to coincide
with the actual target value and agents' assignments, respectively; they may also differ
from one agent to another due to the dynamics of their previous communication and
local interaction with the other agents and targets in the environment. Each agent can
be occupied or free depending if there is or there is not present an agent of the opposite
group on the same position.
Initially, i.e., at time t =1and auction iteration h =0, for each robot agent
a ∈ A ,set S a ( t =1 ,h =0)of assignments is assumed empty and all target values
v θ,a (1 , 0) are set to zero.
At the beginning of each time period t ∈ [1 ,...,T ], a new round of iterative auction
is performed, starting from the assignments and target values locally available to the
agents from the end of the round before. In more detail, during iteration h of round t :
each agent broadcasts within its connected component its identity, the assigned
target (if any) and its status on that target (whether it has arrived or not to the
target).
depending on one of the four applied information exchange policies which are mo-
tivated by different communication costs when different amounts of information
are exchanged, each agent sends and receives:
1. all target values v θ,a ( t, h − 1) and assignments S a ( t, h − 1) for all θ ∈ Θ
from/to the agents within the connected component C a ( t ) agent a belongs to;
2. target values v θ C a ( t ) ,a ( t, h− 1) and assignments within S a ( t, h− 1) for targets
θ assigned only within connected component C a ( t ) agent a belongs to on the
beginning of time period t ;
3. target value v θ a ,a ( t, h− 1) and assignment in S a ( t, h− 1) related only to agent
a 's momentary assignment θ a and exchanged only with the agents which share
the same assignment (if any) within the same connected component C a ( t );
4. no information to/from other agents. Each agent keeps its information for itself.
Each agent updates its local list of the assignments S a ( t, h ) and target values
v θ,a ( t, h ) by adopting the largest value v θ ( t, h − 1) among the set of agents C a ( t )
within the connected component for each target of interest θ ∈ Θ and the assign-
ment resulting from this value. However, if the target θ a
is assigned to more than
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