Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
Art gallery theorems and algorithms
Art gallery theorems and algorithms
The Art Gallery theorem for polygons with holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Introduction to Algorithms
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
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In this paper, we present a novel near-optimal art gallery-based algorithm for placing a small (but sufficient) number of robot configurations to plan its path in a 2D environment cluttered with obstacles. The solution of the problem is inspired from the well-known art gallery problem (AGP) which asks to position the minimum number of guards required to cover a gallery that is represented as a simple polygon with n vertices and h holes. The proposed algorithm efficiently computes the placement of guards in simple polygons with holes, which runs in O(n log n) time and requires a linear storage complexity. The proposed algorithm can be useful in a variety of applications such as 3D model construction of a workspace, navigation and inspection tasks, medical surgery, and virtual reality exploration systems. It can also be used to solve the robot motion planning problem for an autonomous mobile robot in a global environment. A 2D workspace for an autonomous robot can be modeled as a gallery and the obstacles are presented as holes. The proposed placement guarantees to compute the near-optimal distribution of guards that fully cover the entire free space. Such guards can then be used as milestones along the path of the robot. The proposed algorithm is not only offering a better performance in terms of computational cost but also ease in implementation. Simulation results demonstrate the efficiency, robustness, and potential of the proposed algorithm compared to other visibility-based techniques.