Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems
SIAM Journal on Computing
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots
SIAM Journal on Computing
Convergence of Autonomous Mobile Robots with Inaccurate Sensors and Movements
SIAM Journal on Computing
Gathering Problem of Two Asynchronous Mobile Robots with Semi-dynamic Compasses
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Using eventually consistent compasses to gather memory-less mobile robots with limited visibility
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
Byzantine-Resilient Convergence in Oblivious Robot Networks
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Optimal Byzantine Resilient Convergence in Asynchronous Robots Networks
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
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
Characterizing geometric patterns formable by oblivious anonymous mobile robots
Theoretical Computer Science
On the feasibility of gathering by autonomous mobile robots
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Convergence of mobile robots with uniformly-inaccurate sensors
SIROCCO'09 Proceedings of the 16th 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
Asynchronous pattern formation by anonymous oblivious mobile robots
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Price of asynchrony in mobile agents computing
Theoretical Computer Science
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Anonymous mobile robots are often classified into synchronous, semi-synchronous, and asynchronous robots when discussing the pattern formation problem. For semi-synchronous robots, all patterns formable with memory are also formable without memory, with the single exception of forming a point (i.e., the gathering) by two robots. (All patterns formable with memory are formable without memory for synchronous robots, and little is known for asynchronous robots.) However, the gathering problem for two semi-synchronous robots without memory (called oblivious robots in this paper) is trivially solvable when their local coordinate systems are consistent, and the impossibility proof essentially uses the inconsistencies in their coordinate systems. Motivated by this, this paper investigates the magnitude of consistency between the local coordinate systems necessary and sufficient to solve the gathering problem for two oblivious robots under semi-synchronous and asynchronous models. To discuss the magnitude of consistency, we assume that each robot is equipped with an unreliable compass, the bearings of which may deviate from an absolute reference direction, and that the local coordinate system of each robot is determined by its compass. We consider two families of unreliable compasses, namely, static compasses with (possibly incorrect) constant bearings and dynamic compasses the bearings of which can change arbitrarily (immediately before a new look-compute-move cycle starts and after the last cycle ends). For each of the combinations of robot and compass models, we establish the condition on deviation $\phi$ that allows an algorithm to solve the gathering problem, where the deviation is measured by the largest angle formed between the $x$-axis of a compass and the reference direction of the global coordinate system: $\phi