  We propose an approach to solve multi-agent path planning (MPP) problems for
complex environments. Our method first designs a special pebble graph with a
set of feasibility constraints, under which MPP problems have feasibility
guarantee. We further propose an algorithm to greedily improve the optimality
of planned MPP solutions via parallel pebble motions. As a second step, we
develop a mesh optimization algorithm to embed our pebble graph into
arbitrarily complex environments. We show that the feasibility constraints of a
pebble graph can be converted into differentiable geometric constraints, such
that our mesh optimizer can satisfy these constraints via constrained numerical
optimization. We have evaluated the effectiveness and efficiency of our method
using a set of environments with complex geometries, on which our method
achieves an average of 99.0% free-space coverage and 30.3% robot density within
hours of computation on a desktop machine.
