A competitive analysis of nearest neighbor based algorithms for searching unknown scenes

Abstract

We consider problems involving robot motion planning in an initially unknown scene of obstacles. The two specific problems that we examine are mapping the scene and searching the scene for a recognizable target whose location is unknown. We use competitive analysis as a tool for comparing algorithms. In the case of convex obstacles, we show a tight θ(min(k, √α) bound on the competitiveness for these problems, where α and k are aspect ratio and number of objects, respectively. This lower bound also holds for randomized algorithms. We derive an almost tight bound on the competitive ratio for the Nearest Neighbor heuristic. We also propose allowing multiple robots to cooperatively search the scene. For scenes that contain only objects of bounded perimeter and bounded aspect ratio, we show that m robots can achieve a competitive factor of O(√/m), which is optimal. Thus, the robots can cooperate without interference in searching the scene. For general scenes we show that a competitive factor of O((√α log m)/m) is achievable, provided m = O(√/α).