The Beachcombers’ Problem: Walking and Searching with Mobile Robots

We introduce and study a new problem concerning the exploration of a geometric domain by mobile robots. Consider a line segment [0,I] and a set of n mobile robots r 1,r 2,…, r n placed at one of its endpoints. Each robot has a searching speed s i and a walking speed w i , where s i  < w i . We assume that every robot is aware of the number of robots of the collection and their corresponding speeds.