Gathering
Robots must meet at a single point that is not fixed in advance, and stay there.
Problem statement and measuresexpand
\(n\) robots start at distinct points and must all reach the same point in finite time and remain there. For \(n = 2\) the problem is called rendezvous. Time is counted in rounds (FSYNC, SSYNC) or in epochs (ASYNC: intervals in which every robot completes at least one full Look–Compute–Move cycle); colours count light colours.
Measures: Time, rounds (FSYNC, SSYNC) or epochs (ASYNC) until the task is done; "finite" when only solvability is known; Colours, colours of the light per robot (0 for oblivious robots).
Rendezvous, full lights, a crash, SSYNC
verifiedIf the correct robot must reach a crashed one, two robots cannot meet in SSYNC, even with unboundedly many colours, rigid moves and a common coordinate system.
Assumed (added on the last edge are outlined)
Not assumed
Formal definitions of this setting
- Body: point
- Each robot is a point of the plane: several robots may share a point (multiplicity), and a robot hides only what lies exactly behind it on a line of sight.
- Visibility: unlimited visibility
- A robot sees all robots (subject to opacity).
- Opacity: transparent
- Robots do not obstruct each other's view.
- Faults: crash faults
- Up to \(f\) robots stop forever at adversarial times and remain visible at their last position.
- Scheduler: SSYNC
- SSYNC: time is divided into rounds; in each round a non-empty subset of robots, chosen by a fair adversary, executes one atomic Look–Compute–Move cycle. Called Atom by Prencipe Prencipe 2007.
- Lights (persistent memory): lights (LUMI)
- LUMI: each robot has a light with \(c\) colours, set at the end of Compute, visible to all robots including itself; it is both memory and communication. Also called luminous robots, or a full light.
- Agreement on coordinates: compass
- All robots agree on the directions and orientations of both axes (a common compass); they may still disagree on origin and unit. Called full compass by Efrima and Peleg, who also use half compass (both axis directions, the positive sense of one axis, no chirality), direction-only and axes-only Efrima & Peleg 2009. Agreement on one axis together with common chirality is equivalent: the orientation of the second axis then follows from handedness.
- Movement: rigid
- Every Move phase ends at the computed destination.
- Multiplicity detection: no multiplicity detection
- A snapshot is a set of points: a point occupied by several robots looks like a single robot.
- Randomness: deterministic
- The destination computed in a cycle is a function of the snapshot (and the light, if any).
- Identifiers: anonymous
- Robots are indistinguishable and run the same algorithm.
- Number of robots: \(n = 2\)
- Exactly two robots (rendezvous).
Statement for this variant
Stand-up indulgent rendezvous: if one robot crashes, the other must reach the crashed robot's position.
What is known
- Theorem 1: SSYNC
- holds with full lights of infinitely many colours, rigid moves and a common coordinate system
Results, in order of publication
No result recorded yet.
Open questions
None recorded for this variant.
Notes
With mobility faults, where a faulty robot stops moving but its light keeps working, 3 colours are necessary and sufficient for two robots in ASYNC Pramanick et al. 2025, a preprint. Checked against the full texts.
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