  We consider the problem of approximate consensus in mobile networks
containing Byzantine nodes. We assume that each correct node can communicate
only with its neighbors and has no knowledge of the global topology. As all
nodes have moving ability, the topology is dynamic. The number of Byzantine
nodes is bounded by f and known by all correct nodes. We first introduce an
approximate Byzantine consensus protocol which is based on the linear iteration
method. As nodes are allowed to collect information during several consecutive
rounds, moving gives them the opportunity to gather more values. We propose a
novel sufficient and necessary condition to guarantee the final convergence of
the consensus protocol. The requirement expressed by our condition is not
"universal": in each phase it affects only a single correct node. More
precisely, at least one correct node among those that propose either the
minimum or the maximum value which is present in the network, has to receive
enough messages (quantity constraint) with either higher or lower values
(quality constraint). Of course, nodes' motion should not prevent this
requirement to be fulfilled. Our conclusion shows that the proposed condition
can be satisfied if the total number of nodes is greater than 3f+1.
