Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Wireless integrated network sensors
Communications of the ACM
Robot Motion Planning
Planning Algorithms
Bitbots: simple robots solving complex tasks
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Simple Robots in Polygonal Environments: A Hierarchy
Algorithmic Aspects of Wireless Sensor Networks
Counting targets with mobile sensors in an unknown environment
ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
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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 particular vertex is convex. Finally, we show that 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) 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 by Ganguli et al.