Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Fault-tolerant gathering algorithms for autonomous mobile robots
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems
SIAM Journal on Computing
Impossibility of gathering by a set of autonomous mobile robots
Theoretical Computer Science
Local spreading algorithms for autonomous robot systems
Theoretical Computer Science
Gathering few fat mobile robots in the plane
Theoretical Computer Science
Randomized Gathering of Mobile Robots with Local-Multiplicity Detection
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Self-stabilizing Deterministic Gathering
Algorithmic Aspects of Wireless Sensor Networks
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A local O(n2) gathering algorithm
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Collisionless gathering of robots with an extent
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Gathering asynchronous mobile robots with inaccurate compasses
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Gathering autonomous mobile robots with dynamic compasses: an optimal result
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Local, self-organizing strategies for robotic formation problems
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Continuous local strategies for robotic formation problems
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Gathering of robots on anonymous grids without multiplicity detection
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Collecting information by power-aware mobile agents
DISC'12 Proceedings of the 26th international conference on Distributed Computing
How to gather asynchronous oblivious robots on anonymous rings
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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Given a set of n mobile robots in the d-dimensional Euclidean space, the goal is to let them converge to a single not predefined point. The challenge is that the robots are limited in their capabilities. Robots can, upon activation, compute the positions of all other robots using an individual affine coordinate system. The robots are indistinguishable, oblivious and may have different affine coordinate systems. A very general discrete time model assumes that robots are activated in arbitrary order. Further, the computation of a new target point may happen much earlier than the movement, so that the movement is based on outdated information about other robot's positions. Time is measured as the number of rounds, where a round ends as soon as each robot has moved at least once. In [6], the Center of Gravity is considered as target function, convergence was proven, and the number of rounds needed for halving the diameter of the convex hull of the robot's positions was shown to be O(n2) and Ω(n). We present an easy-to-check property of target functions that guarantee convergence and yields upper time bounds. This property intuitively says that when a robot computes a new target point, this point is significantly within the current axes aligned minimal box containing all robots. This property holds, e.g., for the above-mentioned target function, and improves the above O(n2) to an asymptotically optimal O(n) upper bound. Our technique also yields a constant time bound for a target function that requires all robots having identical coordinate axes.