This paper establishes a framework based on logic and automata theory in which to model and automatically verify that multiple mobile robots, with sensing abilities, moving asynchronously, correctly perform their tasks. The motivation is from practical scenarios in which the environment is not completely know to the robots, e.g., physical robots exploring a maze, or software agents exploring a hostile network. The framework shows how to express tasks in a logical language, and exhibits an algorithm solving the parameterised verification problem, where the graphs are treated as the parameter. The main assumption that yields decidability is that the robots take a bounded number of turns. We prove that dropping this assumption results in undecidability, even for robots with very limited (“local”) sensing abilities.