  In multi-agent path finding (MAPF) the task is to navigate agents from their
starting positions to given individual goals. The problem takes place in an
undirected graph whose vertices represent positions and edges define the
topology. Agents can move to neighbor vertices across edges. In the standard
MAPF, space occupation by agents is modeled by a capacity constraint that
permits at most one agent per vertex. We suggest an extension of MAPF in this
paper that permits more than one agent per vertex. Propositional satisfiability
(SAT) models for these extensions of MAPF are studied. We focus on modeling
capacity constraints in SAT-based formulations of MAPF and evaluation of
performance of these models. We extend two existing SAT-based formulations with
vertex capacity constraints: MDD-SAT and SMT-CBS where the former is an
approach that builds the model in an eager way while the latter relies on lazy
construction of the model.
