Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Selected writings on computing: a personal perspective
Selected writings on computing: a personal perspective
Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems
SIAM Journal on Computing
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Stably computable predicates are semilinear
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Computation in networks of passively mobile finite-state sensors
Distributed Computing - Special issue: PODC 04
Local spreading algorithms for autonomous robot systems
Theoretical Computer Science
Arbitrary pattern formation by asynchronous, anonymous, oblivious robots
Theoretical Computer Science
Distributed algorithms for partitioning a swarm of autonomous mobile robots
Theoretical Computer Science
Characterizing geometric patterns formable by oblivious anonymous mobile robots
Theoretical Computer Science
On the computational power of oblivious robots: forming a series of geometric patterns
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Boundary patrolling by mobile agents with distinct maximal speeds
ESA'11 Proceedings of the 19th European conference on Algorithms
Observe and remain silent (communication-less agent location discovery)
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Localization for a system of colliding robots
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Hi-index | 0.00 |
A collection of n anonymous mobile robots is deployed on a unit-perimeter ring or a unit-length line segment. Every robot starts moving at constant speed, and bounces each time it meets any other robot or segment endpoint, changing its walk direction. We study the problem of position discovery, in which the task of each robot is to detect the presence and the initial positions of all other robots. The robots cannot communicate or perceive information about the environment in any way other than by bouncing. Each robot has a clock allowing it to observe the times of its bounces. The robots have no control on their walks, which are determined by their initial positions and the starting directions. Each robot executes the same position detection algorithm, which receives input data in real-time about the times of the bounces, and terminates when the robot is assured about the existence and the positions of all the robots. Some initial configuration of robots are shown to be infeasible -- no position detection algorithm exists for them. We give complete characterizations of all infeasible initial configurations for both the ring and the segment, and we design optimal position detection algorithms for all feasible configurations. For the case of the ring, we show that all robot configurations in which not all the robots have the same initial direction are feasible. We give a position detection algorithm working for all feasible configurations. The cost of our algorithm depends on the number of robots starting their movement in each direction. If the less frequently used initial direction is given to k≤n/2 robots, the time until completion of the algorithm by the last robot is $\frac{1}{2}\lceil \frac{n}{k} \rceil$. We prove that this time is optimal. By contrast to the case of the ring, for the unit segment we show that the family of infeasible configurations is exactly the set of so-called symmetric configurations. We give a position detection algorithm which works for all feasible configurations on the segment in time 2, and this algorithm is also proven to be optimal.