  Multi-Robot-Arm Motion Planning (M-RAMP) is a challenging problem featuring
complex single-agent planning and multi-agent coordination. Recent advancements
in extending the popular Conflict-Based Search (CBS) algorithm have made large
strides in solving Multi-Agent Path Finding (MAPF) problems. However,
fundamental challenges remain in applying CBS to M-RAMP. A core challenge is
the existing reliance of the CBS framework on conservative "complete"
constraints. These constraints ensure solution guarantees but often result in
slow pruning of the search space -- causing repeated expensive single-agent
planning calls. Therefore, even though it is possible to leverage domain
knowledge and design incomplete M-RAMP-specific CBS constraints to more
efficiently prune the search, using these constraints would render the
algorithm itself incomplete. This forces practitioners to choose between
efficiency and completeness.
  In light of these challenges, we propose a novel algorithm, Generalized ECBS,
aimed at removing the burden of choice between completeness and efficiency in
MAPF algorithms. Our approach enables the use of arbitrary constraints in
conflict-based algorithms while preserving completeness and bounding
sub-optimality. This enables practitioners to capitalize on the benefits of
arbitrary constraints and opens a new space for constraint design in MAPF that
has not been explored. We provide a theoretical analysis of our algorithms,
propose new "incomplete" constraints, and demonstrate their effectiveness
through experiments in M-RAMP.
