Swarms of Mobile Agents: From Discrete to Continuous Movements in Multi-Agent Path Finding

Abstract

A variant of multi-agent path finding in continuous space and time with geometric agents ${\text{MAP}}{{\text{F}}^{\mathcal{R}}}$ 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 ${\text{SMT - CB}}{{\text{S}}^{\mathcal{R}}}$ 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 ${\text{SMT - CB}}{{\text{S}}^{\mathcal{R}}}$ and the previous CCBS algorithm for ${\text{MAP}}{{\text{F}}^{\mathcal{R}}}$.