SCG '86 Proceedings of the second annual symposium on Computational geometry
On the computational geometry of pocket machining
On the computational geometry of pocket machining
How to learn an unknown environment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Watchman routes under limited visibility
Computational Geometry: Theory and Applications
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
On-line search in a simple polygon
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for lawn mowing and milling
Computational Geometry: Theory and Applications
The Polygon Exploration Problem
SIAM Journal on Computing
Improved exploration of rectilinear polygons
Nordic Journal of Computing
On the Competitive Complexity of Navigation Tasks
Revised Papers from the International Workshop on Sensor Based Intelligent Robots
Competitive exploration of rectilinear polygons
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Exploring simple grid polygons
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Observe and remain silent (communication-less agent location discovery)
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Hi-index | 0.00 |
A mobile robot, represented by a point moving along a polygonal line in the plane, has to explore an unknown polygon and return to the starting point. The robot has a sensing area which can be a circle or a square centered at the robot. This area shifts while the robot moves inside the polygon, and at each point of its trajectory the robot ''sees'' (explores) all points for which the segment between the robot and the point is contained in the polygon and in the sensing area. We focus on two tasks: exploring the entire polygon and exploring only its boundary. We consider several scenarios: both shapes of the sensing area and the Manhattan and the Euclidean metrics. We focus on two quality benchmarks for exploration performance: optimality (the length of the trajectory of the robot is equal to that of the optimal robot knowing the polygon) and competitiveness (the length of the trajectory of the robot is at most a constant multiple of that of the optimal robot knowing the polygon). Most of our results concern rectilinear polygons. We show that optimal exploration is possible in only one scenario, that of exploring the boundary by a robot with square sensing area, starting at the boundary and using the Manhattan metric. For this case we give an optimal exploration algorithm, and in all other scenarios we prove impossibility of optimal exploration. For competitiveness the situation is more optimistic: we show a competitive exploration algorithm for rectilinear polygons whenever the sensing area is a square, for both tasks, regardless of the metric and of the starting point. Finally, we show a competitive exploration algorithm for arbitrary convex polygons, for both shapes of the sensing area, regardless of the metric and of the starting point.