A self-stabilizing marching algorithm for a group of oblivious robots

We propose a self-stabilizing marching algorithm for a group of oblivious robots in an obstacle-free workplace. To this end, we develop a distributed algorithm for a group of robots to transport a polygonal object, where each robot holds the object at a corner, and observe that each robot can simulate the algorithm, even after we replace the object by an imaginary one; we thus can use the algorithm as a marching algorithm. Each robot independently computes a velocity vector using the algorithm, moves to a new position with the velocity for a unit of time, and repeats this cycle until it reaches the goal position. The algorithm is oblivious, i.e., the computation depends only on the current robot configuration, and is constructed from a naive algorithm that generates only a selfish move, by adding two simple ingredients. For the case of two robots, we theoretically show that the algorithm is self-stabilizing, and demonstrate by simulations that the algorithm produces a motion that is fairly close to the time-optimal motion. For cases of more than two robots, we show that a natural extension of the algorithm for two robots also produces smooth and elegant motions by simulations as well.