A General Formal Framework for Pathfinding Problems with Multiple Agents

Abstract

Pathfinding for a single agent is the problem of planning a route from an initial location to a goal location in an environment, going around obstacles. Pathfinding for multiple agents also aims to plan such routes for each agent, subject to different constraints, such as restrictions on the length of each path or on the total length of paths, no self-intersecting paths, no intersection of paths/plans, no crossing/meeting each other. It also has variations for finding optimal solutions, e.g., with respect to the maximum path length, or the sum of plan lengths. These problems are important for many real-life applications, such as motion planning, vehicle routing, environmental monitoring, patrolling, computer games. Motivated by such applications, we introduce a formal framework that is general enough to address all these problems: we use the expressive high-level representation formalism and efficient solvers of the declarative programming paradigm Answer Set Programming. We also introduce heuristics to improve the computational efficiency and/or solution quality. We show the applicability and usefulness of our framework by experiments, with randomly generated problem instances on a grid, on a real-world road network, and on a real computer game terrain.

Model-Based Diagnosis of Multi-Agent Systems: A Survey

“…A known research field that considers the synchronization challenge is Multi-Agent Path Finding problem (MAPF) (Pallottino et al 2007;Erdem et al 2013;Surynek et al 2016;Švancara et al 2019;Barták et al 2019;Barták, Švancara, and Krasičenko 2020;Li, Ruml, and Koenig 2021). MAPF describes the problem of moving agents to destinations while avoiding collisions.…”

Optimal and Bounded-Suboptimal Multi-Goal Task Assignment and Path Finding

“…MAPF: The MAPF problem is NP-hard to solve optimally for flowtime (the sum of the finish times of all agents in the last goal locations of their assigned tasks) minimization [8] and even NP-hard to approximate within any constant factor less than 4/3 for makespan (the maximum of the finish times of all agents in their pre-assigned goal locations) minimization [9], [10]. MAPF algorithms include reductions to other well-studied optimization problems [11]- [13] and specialized rule-based, search-based and hybrid algorithms [14]- [20]. In particular, Conflict-Based Search (CBS) [19] is a popular two-level optimal MAPF algorithm that computes time-optimal paths for individual agents on the low level and performs a best-first tree search to resolve collisions among the paths on the high level.…”

Graph-Based Multi-Robot Path Finding and Planning

“…Reduction-Based MAPF Algorithms Reduction-based MAPF algorithms reduce MAPF to other well-studied combinatorial problems, such as Boolean Satisfiability [29], Integer Linear Programming [30], and Answer Set Programming [31,32]. They are complete for all MAPF problem instances.…”