Art gallery theorems and algorithms
Art gallery theorems and algorithms
Navigating in unfamiliar geometric terrain
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
How to learn an unknown environment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Searching for a mobile intruder in a polygonal region
SIAM Journal on Computing
Walking an unknown street with bounded detour
Computational Geometry: Theory and Applications
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Competitive searching in a generalized street
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
An optimal algorithm for finding the edge visibility polygon under limited visibility
Information Processing Letters
Searching for the kernel of a polygon—a competitive strategy
Proceedings of the eleventh annual symposium on Computational geometry
Optimal on-line algorithms for walking with minimum number of turns in unknown streets
Computational Geometry: Theory and Applications
Localizing a robot with minimum travel
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
On-line search in a simple polygon
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Navigating Mobile Robots: Systems and Techniques
Navigating Mobile Robots: Systems and Techniques
Directed Sonar Sensing for Mobile Robot Navigation
Directed Sonar Sensing for Mobile Robot Navigation
Exploration of polygonal environments using range data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Polygon exploration with time-discrete vision
Computational Geometry: Theory and Applications
Minimum Covering with Travel Cost
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Survey: Online algorithms for searching and exploration in the plane
Computer Science Review
Minimum covering with travel cost
Journal of Combinatorial Optimization
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This paper integrates constraints from visual processing and robot navigation into the well-studied computational geometry problem of exploring unknown polygonal environments with obstacles. In particular, we impose two constraints. First, we consider a robot with limited visibility, which can reliably "see" its environment only within a certain range R. Second, we allow the computation of visibility only from discrete number of points on the path. Both these constraints arise from real life cost constraints associated with robotic exploration and robot vision processing. We present an online algorithm for exploration under such constraints and show that the maximum number of views needed to explore the unknown polygon (with obstacles) P, is bounded by 驴2脳Perimeter(P)/R驴 + 驴2脳Area(P)/R2驴 + 3n, where n is the number of sides of the polygon. We also show that the competitive ratio of the algorithm is 6驴 + 4r+3n/ma(驴Area(P)/驴R2驴, 驴Perimeter(P) - 2Rr/2驴R)驴.