  In this paper, we introduce a new class of potential fields, i.e., meta
navigation functions (MNFs) to coordinate multi-agent systems. Thanks to the
MNF formulation, agents can contribute to each other's coordination via partial
and/or total associations, contrary to traditional decentralized navigation
functions (DNFs). In particular, agents may stimulate each other via their
MNFs. Moreover, MNFs need to be confined which is a weaker condition compared
to the Morse condition of DNFs. An MNF is composed of a confined function and
an attraction kernel. The critical points of the former can be confined in a
safe region around a target critical point. The collision-free trajectory of an
agent and its associations to its peers are governed by a confined function
before reaching its safe region. Then, the attraction kernel drives the agent
to its target in the safe region. MNFs provide faster coordination compared to
DNFs. We illustrate how MNFs may exhibit some social behaviors in the course of
partial and total associations among agents. Our simulations verify the
efficiency of MNFs to coordinate complex swarms of agents.
