Optimally Gathering Two Robots
This solves a specific coordination problem in distributed robotics, but it is incremental as it builds on known impossibility results and focuses on a minimal two-robot case.
The paper tackles the problem of gathering two robots in the non-rigid ASYNC model by introducing an algorithm that uses 2-color lights and distance measurements to achieve finite-time gathering, which is optimal since gathering is impossible with only one color.
We present an algorithm that ensures in finite time the gathering of two robots in the non-rigid ASYNC model. To circumvent established impossibility results, we assume robots are equipped with 2-colors lights and are able to measure distances between one another. Aside from its light, a robot has no memory of its past actions, and its protocol is deterministic. Since, in the same model, gathering is impossible when lights have a single color, our solution is optimal with respect to the number of used colors.