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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).

no assumptions›+ point›+ unlimited visibility, + transparent›+ no faults›ASYNC, + internal light (FSTA), + \(n = 2\)

Rendezvous, internal light (FSTA), ASYNC

verified

Time: unknownColours: unknown

Whether robots with internal lights can meet in ASYNC is open.

Assumed (added on the last edge are outlined)

+Bodypoint robots+Visibilityunlimited+Opacitytransparent: every robot sees every robot within range+Faultsno faults+Lights (persistent memory)internal light only (FSTA): a robot sees its own light, not the others'+Number of robots\(n = 2\) (rendezvous)

Not assumed

Schedulerasynchronous (ASYNC)Agreement on coordinatesno agreement on local coordinate systemsMovementnon-rigid: the adversary may stop a move after some minimum distance \(\delta\)Multiplicity detectionnone: a point with several robots looks like one robotRandomnessdeterministicIdentifiersanonymous: all robots are identical

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: no faults: All robots follow the algorithm forever.
Scheduler: ASYNC: ASYNC: each robot's Look, Compute and Move phases take finite but unbounded, adversarially chosen time; a robot may look while others move, and compute on an outdated snapshot. Time is counted in epochs: an epoch is an interval of time in which every robot completes at least one full Look–Compute–Move cycle; it need not be the shortest such interval. The execution is divided into consecutive epochs, and a bound of \(X\) epochs holds for every such division. In FSYNC and SSYNC time is counted in rounds. Called Corda by Prencipe Prencipe 2007. Intermediate variants restrict interleavings: LC-atomic (no Look by another robot between a robot's Look and its Compute), Move-atomic (no Look during another robot's Move) and CM-atomic Flocchini et al. 2023.
Lights (persistent memory): internal light (FSTA): FSTA: each robot has a light with \(c\) colours that only it can see; it persists between cycles (constant persistent memory, no communication). Also called an internal light.
Agreement on coordinates: disoriented: Each robot \(r\) observes in its own coordinate system, obtained from the global one by an unknown similarity (translation, rotation, uniform scaling, and possibly reflection); systems may differ between robots and, in some models, between cycles. Papers that call robots disoriented do not always mean this: Défago and Souissi use the word while assuming chirality Défago & Souissi 2008. Some papers also let the adversary change a robot's rotation, reflection and unit at every Look (variable disorientation) Flocchini et al. 2023 Masuzawa et al. 2026.
Movement: non-rigid: In a Move phase the adversary may stop a robot before its destination, but only after it has travelled at least \(\delta>0\) (a constant unknown to the robots) or reached the 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).

What is known

Time · rounds (FSYNC, SSYNC) or epochs (ASYNC) until the task is done; "finite" when only solvability is known

unknown

Open.

lower boundnone known

introductory—

current best—

Colours · colours of the light per robot (0 for oblivious robots)

unknown

Open.

lower bound

\(3\) Otaka et al. 2026

bottleneckmemory

holds when

SSYNC bound (Theorem 1), hence also in ASYNC

introductory—

current best—

Results, in order of publication

No result recorded yet.

Open questions

Can robots with internal lights solve rendezvous in ASYNC Flocchini et al. 2016 Masuzawa et al. 2026?

Notes

If no robot looks while another moves (Move-atomic ASYNC), 4 colours suffice with rigid moves (Theorem 9 of Masuzawa et al. 2026, a preprint). Checked against the full texts.

What carries over from neighbouring settings

Read off the order of assumptions, not checked case by case: results may carry extra assumptions (shown on their pages), and asynchronous time is measured in epochs.

Algorithms from weaker settings work here

No catalogued weaker setting.

Lower bounds from stronger settings hold here

Rendezvous, full lights (LUMI), ASYNC, non-rigid

Colours \(2\)

Rendezvous, internal light (FSTA), SSYNC, non-rigid

Colours \(3\)

Know a better result for this setting, or found a mistake? Suggest a result · Report an error. Accepted contributions are acknowledged.