# On Satisfisfiability Modulo Theories in Continuous Multi-Agent Path Finding: Compilation-based and Search-based Approaches Compared

### Pavel Surynek

#### Abstract

Multi-agent path finding (MAPF) in continuous space and time with geometric agents, i.e. agents of various geometric shapes moving smoothly between predefined positions, is addressed in this paper. We analyze a new solving approach based on satisfiability modulo theories (SMT) that is designed to obtain makespan optimal solutions. The standard MAPF is a task of navigating agents in an undirected graph from given starting vertices to given goal vertices so that agents do not collide with each other in vertices or edges of the graph. In the continuous version (MAPFR ), agents move in a metric space along predefined trajectories that interconnect predefined positions. Agents themselves are geometric objects of various shapes occupying certain volume of the space - circles, polygons, etc. For simplicity, we work with circular omni-directional agents having constant velocities in the 2D plane where positions are interconnected by straight lines. As agents can have different shapes/sizes and are moving smoothly along lines, a movement along certain lines done with small agents can be non-colliding while the same movement may result in a collision if performed with larger agents. Such a distinction rooted in the geometric reasoning is not present in the standard MAPF. The SMT-based approach for MAPFR called SMT-CBSR reformulates the well established Conflict-based Search (CBS) algorithm in terms of SMT. Lazy generation of decision variables and constraints is the key idea behing SMT-CBS. Each time a new conflict is discovered, the underlying encoding is extended with new variables and constraints to eliminate the conflict. We compared SMT-CBSR and adaptations of CBS for the continuous variant of MAPF experimentally.

Download#### Paper Citation

#### in Harvard Style

Surynek P. (2020). **On Satisfisfiability Modulo Theories in Continuous Multi-Agent Path Finding: Compilation-based and Search-based Approaches Compared**.In *Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-395-7, pages 182-193. DOI: 10.5220/0008980101820193

#### in Bibtex Style

@conference{icaart20,

author={Pavel Surynek},

title={On Satisfisfiability Modulo Theories in Continuous Multi-Agent Path Finding: Compilation-based and Search-based Approaches Compared},

booktitle={Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2020},

pages={182-193},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0008980101820193},

isbn={978-989-758-395-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - On Satisfisfiability Modulo Theories in Continuous Multi-Agent Path Finding: Compilation-based and Search-based Approaches Compared

SN - 978-989-758-395-7

AU - Surynek P.

PY - 2020

SP - 182

EP - 193

DO - 10.5220/0008980101820193