Pushing the Envelope: From Discrete to Continuous Movements in Multi-Agent Path Finding via Lazy Encodings
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Multi-agent path finding in continuous space and time with geometric agents MAPF^R is addressed in this paper. The task is to navigate agents that move smoothly between predefined positions to their individual goals so that they do not collide. We introduce a novel solving approach for obtaining makespan optimal solutions called SMT-CBS^R based on satisfiability modulo theories (SMT). The new algorithm combines collision resolution known from conflict-based search (CBS) with previous generation of incomplete SAT encodings on top of a novel scheme for selecting decision variables in a potentially uncountable search space. We experimentally compare SMT-CBS^R and previous CCBS algorithm for MAPF^R.
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