Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Wireless integrated network sensors
Communications of the ACM
Robot Motion Planning
Planning Algorithms
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Simple Robots in Polygonal Environments: A Hierarchy
Algorithmic Aspects of Wireless Sensor Networks
Bitbots: simple robots solving complex tasks
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Counting targets with mobile sensors in an unknown environment
ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
Exploring Polygonal Environments by Simple Robots with Faulty Combinatorial Vision
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
A polygon is determined by its angles
Computational Geometry: Theory and Applications
Exploring and triangulating a region by a swarm of robots
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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
Reconstructing visibility graphs with simple robots
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
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
Reconstructing visibility graphs with simple robots
Theoretical Computer Science
Perspective: Simple agents learn to find their way: An introduction on mapping polygons
Discrete Applied Mathematics
Unsolved problems in visibility graphs of points, segments, and polygons
ACM Computing Surveys (CSUR)
Intensity-based navigation with global guarantees
Autonomous Robots
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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 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.