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
Gathering Multiple Robotic Agents with Crude Distance Sensing Capabilities
ANTS '08 Proceedings of the 6th international conference on Ant Colony Optimization and Swarm Intelligence
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Dynamic compass models and gathering algorithms for autonomous mobile robots
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Connectivity-preserving scattering of mobile robots with limited visibility
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
A tight runtime bound for synchronous gathering of autonomous robots with limited visibility
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Convergence with limited visibility by asynchronous mobile robots
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Gathering asynchronous mobile robots with inaccurate compasses
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
A continuous, local strategy for constructing a short chain of mobile robots
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Gathering autonomous mobile robots with dynamic compasses: an optimal result
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Continuous local strategies for robotic formation problems
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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We consider a scenario in which n mobile robots with a limited viewing range are distributed arbitrarily in the plane, such that the visibility graph of the robots is connected. The goal is to gather the robots in one (not predefined) point. Each robot may base its decision where to move only on the current relative positions of the robots which are in its viewing range. That is, besides having a limited viewing range, the robots are oblivious (they do not use information from the past), they do not have IDs, and they do not have a common sense of direction. On the other hand side, we assume that they are points, i.e., have no extent. Variants of this problem have been studied extensively in different discrete time models. In this paper, we study the gathering problem in a continuous time model. That is, the robots continuously sense the positions of their neighboring robots within their viewing range, and continuously adapt speed and direction, according to a local rule. We assume a speed limit normalized to 1, so that the maximum distance traveled by any robot is smaller or equal to the runtime. Gordon, Wagner and Bruckstein have proposed a simple and intuitive continuous algorithm in ANTS '04, and they showed that their algorithm gathers the robots in finite time. But the runtime of this algorithm has been open since then. We present a runtime analysis for their algorithm and show two runtime bounds. The first one is an optimal worst case bound O(n), the second one shows the log(OPT)-competitiveness in the sense that if OPT is the runtime of an optimal global algorithm, the local algorithm is at most by a factor of log(OPT) slower than the global algorithm. Best previous bounds on the distance traveled by the robots are obtained for discrete time models and are O(n^2) in the worst case and only O(n) competitive.