Sparsification for Fast Optimal Multi-Robot Path Planning in Lazy Compilation Schemes

TL;DR

This paper introduces a sparsification technique for SAT-based multi-robot path planning, reducing problem size and solving time while maintaining optimality guarantees.

Contribution

It proposes a novel sparsification method for candidate paths in SAT-based MRPP, improving efficiency without sacrificing optimal solutions.

Findings

Smaller Boolean formulas lead to faster solving times.

Sparsification maintains optimality guarantees.

Enhanced approach outperforms previous methods in efficiency.

Abstract

Path planning for multiple robots (MRPP) represents a task of finding non-colliding paths for robots through which they can navigate from their initial positions to specified goal positions. The problem is usually modeled using undirected graphs where robots move between vertices across edges. Contemporary optimal solving algorithms include dedicated search-based methods, that solve the problem directly, and compilation-based algorithms that reduce MRPP to a different formalism for which an efficient solver exists, such as constraint programming (CP), mixed integer programming (MIP), or Boolean satisfiability (SAT). In this paper, we enhance existing SAT-based algorithm for MRPP via spartification of the set of candidate paths for each robot from which target Boolean encoding is derived. Suggested sparsification of the set of paths led to smaller target Boolean formulae that can be constructed and solved faster while optimality guarantees of the approach have been kept.