The agreement power of disagreement
Abstract
We consider the rendezvous problem of two autonomous robots with very weak capacities. This problem is notoriously impossible to solve in the semi-synchronous execution model when robots are deterministic, oblivious, and their ego-centered coordinate system is fully symmetric.
We show that if the robots disagree on the unit distance of their coordinate system, it becomes possible to solve rendezvous and agree on a final common location, without additional assumptions. We also generalize our scheme to solve gathering (that is, rendezvous of n ≥ 2
robots) in the same setting, possibly starting from a bivalent configuration.