MAC versus PC: Determinism and randomness as complementary approaches to robotic exploration of continuous unknown domains

Three methods are described for exploring a continuous unknown planar regio n by a group of robots having limited sensors and no explicit communication . We formalize the problem, prove that its off-line version is NP-hard, and show a lower bound on the length of any solution. Then a deterministic mar k and cover (MAC) algorithm is described for the on-line problem using shor t-lived navigational markers as a means of navigation and indirect communic ation. The convergence of the algorithm is proved, and its cover time is sh own, to be the asymptotically optimal O(A/a), where A is the total area and a is the area covered by the robot in a single step. The MAC algorithm is tested against an alternative randomized probabilistic covering (PC) method which does not rely on sensors but is still able to cover an unknown regio n in an expected time that depends polynomially on the dimensions of the re gion. Both, algorithms enable cooperation of several robots to achieve fast er coverage. Finally, we show that the two methods can be combined to yield a third, hybrid algorithm with a better trade-off between performance and robustness.