The Polygon Exploration Problem
SIAM Journal on Computing
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Planning Algorithms
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Simple Robots with Minimal Sensing: From Local Visibility to Global Geometry
International Journal of Robotics Research
Bitbots: simple robots solving complex tasks
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Localization With Limited Sensing
IEEE Transactions on Robotics
Deterministic rendezvous of asynchronous bounded-memory agents in polygonal terrains
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
A polygon is determined by its angles
Computational Geometry: Theory and Applications
An improved algorithm for reconstructing a simple polygon from its visibility angles
Computational Geometry: Theory and Applications
Reconstructing a simple polygon from its angles
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
How simple robots benefit from looking back
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
An improved algorithm for reconstructing a simple polygon from the visibility angles
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We consider the problem of finding a minimalistic configuration of sensors that enable a simple robot inside an initially unknown polygon $\mathcal{P}$ on n vertices to reconstruct the visibility graph of $\mathcal{P}$. The robot can sense features of its environment through its sensors, and it is allowed to move from vertex to vertex. We aim at understanding which sensorial capabilities are sufficient for the reconstruction of the visibility graph of $\mathcal{P}$. We are able to show that the combinatorial visibilities at every vertex do not contain enough information even when combined with the knowledge of the exact interior angle at each vertex. Using sensors that can put distant vertices into a spatial relation on the other hand can in some cases enable our robot to reconstruct the visibility graph of $\mathcal{P}$. We show that this is true for a sensor that can distinguish whether the angle between two vertices the robot sees is convex or reflex, as long as the robot is capable of identifying the vertex it last visited. We also show that measuring angles exactly is enough, if the robot has a compass.