  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 {\em searching speed} $s_i$ and a {\em walking speed} $w_i$, where $s_i
<w_i$. We assume that each robot is aware of the number of robots of the
collection and their corresponding speeds. At each time moment a robot $r_i$
either walks along a portion of the segment not exceeding its walking speed
$w_i$ or searches a portion of the segment with the speed not exceeding $s_i$.
A search of segment $[0,I]$ is completed at the time when each of its points
have been searched by at least one of the $n$ robots. We want to develop {\em
mobility schedules} (algorithms) for the robots which complete the search of
the segment as fast as possible. More exactly we want to maximize the {\em
speed} of the mobility schedule (equal to the ratio of the segment length
versus the time of the completion of the schedule).
  We analyze first the offline scenario when the robots know the length of the
segment that is to be searched. We give an algorithm producing a mobility
schedule for arbitrary walking and searching speeds and prove its optimality.
Then we propose an online algorithm, when the robots do not know in advance the
actual length of the segment to be searched. The speed $S$ of such algorithm is
defined as $S = \inf_{I_L} S(I_L)$ where $S(I_L)$ denotes the speed of
searching of segment $I_L=[0,L]$. We prove that the proposed online algorithm
is 2-competitive. The competitive ratio is shown to be better in the case when
the robots' walking speeds are all the same.
