Dynamic Compass Models and Gathering Algorithms for Autonomous Mobile Robots

This paper studies a gathering problem for a system of asynchronous autonomous mobile robots that can move freely in a two-dimensional plane. We consider robots equipped with inaccurate (incorrect) compasses which may point a different direction from other robots' compasses. A gathering problem is that the robots are required to eventually gather at a single point which is not given in advance from any initial configuration. In this paper, we propose several inaccurate compass models and give two algorithms which solve the gathering problem on these models. One algorithm is the first result dealing with the compasses whose indicated direction may change in every beginning of execution cycles of robots. It solves the problem when compasses point different at most π/8 from the (absolute) north. The other one solves the problem when the compasses never change its pointed direction and their difference is at most π/3 among robots.