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- W2073261719 abstract "We consider problems of geometric exploration and self-deployment for simple robots that can only sense the combinatorial (non-metric) features of their surroundings. Even with such a limited sensing, we show that robots can achieve complex geometric reasoning and perform many non-trivial tasks. Specifically, we show that one robot equipped with a single pebble can decide whether the workspace environment is a simply connected polygon and, if not, it can also count the number of holes in the environment. Highlighting the subtleties of our sensing model, we show that a robot can decide whether the environment is a convex polygon, yet it cannot resolve whether a given vertex is convex. Finally, we show that by using such local and minimal sensing a robot can compute a proper triangulation of a polygon and that the triangulation algorithm can be implemented collaboratively by a group of m such robots, each with Θ(n/m) word memory. As a corollary of the triangulation algorithm, we derive a distributed analog of the well-known Art Gallery Theorem. A group of [n/3] (bounded memory) robots in our minimal sensing model can self-deploy to achieve visibility coverage of an n-vertex art gallery (polygon). This resolves an open question raised recently." @default.
- W2073261719 created "2016-06-24" @default.
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- W2073261719 date "2008-09-01" @default.
- W2073261719 modified "2023-09-23" @default.
- W2073261719 title "Simple Robots with Minimal Sensing: From Local Visibility to Global Geometry" @default.
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- W2073261719 doi "https://doi.org/10.1177/0278364908095833" @default.
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