Technology Category
Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsSearch and Optimization: Adversarial SearchReasoning under Uncertainty: Stochastic Optimization
Adversarial Obstacle Placement with Spatial Point Processes for Optimal Path Disruption
🤖 AI Summary
This paper addresses the Optimal Obstacle Placement (OOP) problem under uncertainty—strategically deploying obstacles to maximize disruption to traversal paths, formulated as the dual of optimal path planning in stochastic obstacle environments. Methodologically, it introduces the Strauss point process (to model regular spatial distributions) and the Matérn cluster process (to model clustered distributions) into adversarial obstacle layout design, establishing a unified stochastic geometric modeling framework. On an 8-connected grid-based geographic network, path traversal cost is quantified via Monte Carlo simulation coupled with a reset-based debiasing algorithm. Results show that regular obstacle configurations increase traversal cost by up to 40%, whereas clustered layouts create navigable corridors, reducing cost by up to 25%. Moreover, increasing the true obstacle presence ratio from 30% to 70% nearly doubles average traversal cost. These findings reveal the intrinsic mechanism by which spatial configuration governs navigation robustness.
Technology Category
Application Category
📝 Abstract
We investigate the Optimal Obstacle Placement (OOP) problem under uncertainty, framed as the dual of the Optimal Traversal Path problem in the Stochastic Obstacle Scene paradigm. We consider both continuous domains, discretized for analysis, and already discrete spatial grids that form weighted geospatial networks using 8-adjacency lattices. Our unified framework integrates OOP with stochastic geometry, modeling obstacle placement via Strauss (regular) and Matérn (clustered) processes, and evaluates traversal using the Reset Disambiguation algorithm. Through extensive Monte Carlo experiments, we show that traversal cost increases by up to 40% under strongly regular placements, while clustered configurations can decrease traversal costs by as much as 25% by leaving navigable corridors compared to uniform random layouts. In mixed (with both true and false obstacles) scenarios, increasing the proportion of true obstacles from 30% to 70% nearly doubles the traversal cost. These findings are further supported by statistical analysis and stochastic ordering, providing rigorous insights into how spatial patterns and obstacle compositions influence navigation under uncertainty.
Problem
Research questions and friction points this paper is trying to address.
Investigating optimal obstacle placement under uncertainty for path disruption
Modeling obstacle distributions using Strauss and Matérn spatial processes
Analyzing traversal cost variations across different obstacle configurations
Innovation
Methods, ideas, or system contributions that make the work stand out.
Modeling obstacle placement with Strauss and Matérn processes
Evaluating traversal using Reset Disambiguation algorithm
Extensive Monte Carlo experiments for performance analysis
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