Optimal torus exploration by oblivious robots

Abstract

We deal with a team of autonomous robots that are endowed with motion actuators and visibility sensors. Those robots are weak and evolve in a discrete environment. By weak, we mean that they are anonymous, uniform, unable to explicitly communicate, and oblivious. We first show that it is impossible to solve the terminating exploration of a simple torus of arbitrary size with less than 4 or 5 such robots, respectively depending on whether the algorithm is probabilistic or deterministic. Next, we propose in the SSYNC model a probabilistic solution for the terminating exploration of torus-shaped networks of size $$\ell \times L$$ , where $$7 \le \ell \le L$$ , by a team of 4 such weak robots. So, this algorithm is optimal w.r.t. the number of robots.