MSc Defence: Multi-Agent Disk Inspection

MSc Candidate: James Conley

Supervisor: Dr. Konstantinos Georgiou

Abstract

Consider n unit-speed mobile agents initially positioned at the centre of a unit disk, tasked with inspecting all points on the disk’s perimeter. A perimeter point is considered inspected if an agent positioned outside the disk’s interior has unobstructed viability of it, treating the disk itself as an obstacle. For n = 1, this problem was proposed as a variant of Bellman’s famous lost-in-the-forest problem [9]. Isbell [26] derived an optimal trajectory that minimizes the worst-case inspection time for that problem. For n ≥ 2 agents, worst-case optimal trajectories were shown in [1, 17]. Our contributions are threefold. First, we extend Isbell’s findings by deriving worst-case optimal trajectories for partial inspection of the disk. Second, we analyze the average-case inspection time. Using spacial discretization and Nonlinear Programming (NLP), we propose feasible solutions to the continuous problem and evaluate their effectiveness compared to NLP solutions. Third, we establish Pareto-optimal bounds for the multi-objective problem of jointly minimizing the worst-case and average-case inspection times.