A Space-Efficient Algebraic Approach to Robotic Motion Planning

TL;DR

This paper introduces a memory-efficient algebraic method for robotic route planning, specifically addressing the Graph Inspection problem, by improving monomial detection techniques and demonstrating practical efficiency.

Contribution

It develops a novel algebraic approach using tree certificates for monomial detection and recovery, enhancing memory efficiency in robotic motion planning algorithms.

Findings

Circuit-based algorithms are memory-efficient in practice.

The algebraic pipeline effectively solves Graph Inspection tasks.

The approach broadens the application of algebraic tools in robotics.

Abstract

We consider efficient route planning for robots in applications such as infrastructure inspection and automated surgical imaging. These tasks can be modeled via the combinatorial problem Graph Inspection. The best known algorithms for this problem are limited in practice by exponential space complexity. In this paper, we develop a memory-efficient approach using algebraic tools related to monomial testing on the polynomials associated with certain arithmetic circuits. Our contributions are two-fold. We first repair a minor flaw in existing work on monomial detection using a new approach we call tree certificates. We further show that, in addition to detection, these tools allow us to efficiently recover monomials of interest from circuits, opening the door for significantly broadened application of related algebraic tools. For Graph Inspection, we design and evaluate a complete algebraic pipeline. Our engineered implementation demonstrates that circuit-based algorithms are indeed memory-efficient in practice, thus encouraging further engineering efforts.