  Sweep coverage is to realize the periodic coverage of targets by planning the
periodic sweeping paths of mobile sensors. It is difficult for sensors to
reduce energy consumption by reducing the moving distances. Therefore, charging
technology is the best way to extend the lifetime of the sweep coverage
network. This paper studies the sweep coverage of rechargeable sensors: the
sensors are rechargeable, constantly sweep between the target points and the
charging stations not only tp meet the periodic coverage requirement of the
target points, but also need to return to the charging stations during the
charging period to avoid running out of energy. This paper proposes the general
definition of Chargeable Sweep Coverage (CSC) problem for the first time, and
studies the complexity of the CSC problem by analyzing CSC problems under
different constraints, and then proposes two kinds of CSC problems under
special constraints: 1) The sensors need to return to their original charging
stations for charging; 2) The sensors can go to different charging stations for
charging, and the number of charging stations is 2. Both of these problems are
NP-hard. In this paper, these two problems are modeled as the maximum set
coverage problem, and the approximation algorithms are obtained by reducing the
number of candidate paths to polynomials. The validity and scalability of the
proposed algorithms is proved by theoretical proof and experimental simulation.
