A Space-Efficient Algebraic Approach to Robotic Motion Planning

2024-09-12

AI Summary

This work addresses the graph traversal path planning problem for robotic applications such as infrastructure inspection and intraoperative imaging, where existing optimal algorithms are impractical due to exponential space complexity. We propose a novel algebraic path planning framework: (1) modeling traversal constraints via arithmetic circuits; (2) introducing a tree certificate mechanism to ensure correctness of single-item verification; and (3) enabling, for the first time, efficient reconstruction of the target path directly from the compact circuit representation. The framework establishes a complete algebraic pipeline—“single-item testing → circuit modeling → tree-based verification → circuit-driven path recovery.” Experimental results demonstrate substantial memory reduction; notably, our approach achieves, for the first time on real-scale graphs, circuit-based path planning with practical space efficiency.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Efficient robotic route planning
• Graph Inspection space complexity
• Memory-efficient algebraic tools

Innovation

• Memory-efficient algebraic tools
• Tree certificates for monomial detection
• Circuit-based algorithms optimization