Designing emergent behaviors: from local interactions to collective intelligence
Proceedings of the second international conference on From animals to animats 2 : simulation of adaptive behavior: simulation of adaptive behavior
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
Gathering few fat mobile robots in the plane
Theoretical Computer Science
Optimal strategies for maintaining a chain of relays between an explorer and a base camp
Theoretical Computer Science
Self-stabilizing Deterministic Gathering
Algorithmic Aspects of Wireless Sensor Networks
A local O(n2) gathering algorithm
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
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
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
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
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Energy-efficient strategies for building short chains of mobile robots locally
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
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
Optimal and competitive runtime bounds for continuous, local gathering of mobile robots
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Continuous local strategies for robotic formation problems
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Energy-efficient strategies for building short chains of mobile robots locally
Theoretical Computer Science
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We are given an arbitrarily shaped chain of n robots with fixed end points in the plane. We assume that each robot can only see its two neighbors in the chain, which have to be within its viewing range. The goal is to move the robots to the straight line between the end points. Each robot has to base the decision where to move on the relative positions of its neighbors only. Such local strategies considered until now are based on discrete rounds, where a round consists of a movement of each robot. In this paper, we initiate the study of continuous local strategies: The robots may perpetually observe the relative positions of their neighbors, and may perpetually adjust their speed and direction in response to these observations. We assume a speed limit for the robots, that we normalize to one, which corresponds to the viewing range. Our contribution is a continuous, local strategy that needs time ${\mathcal O}(min\{n, (OPT+d) \log(n)\})$. Here d is the distance between the two stationary end points, and OPT is the time needed by an optimal global strategy. Our strategy has the property that the robot which reaches its destination last always moves with maximum speed. Thus, the same bound as above also holds for the distance travelled.