Wireless charging technology might be the best way to extend the lifetime of sweep coverage networks, as sensors are required to move to ensure periodic target coverage constantly. However, few studies have considered the energy constraint in the sweep coverage problem. This paper studies the sweep coverage facilitated by rechargeable sensors, which persistently navigate between target nodes and charging stations to fulfill the periodic coverage demands of the targets while ensuring they return to the charging stations before their energy runs out. For the first time, this paper proposes a general definition of the Chargeable Sweep Coverage (CSC) problem and studies the CSC problem by examining various constraints. We also propose one CSC problem subject to a special constraint where the sensors must return to their initial charging stations to recharge. The CSC problem under constrain is also NP-hard. In this paper, the problem is modeled as Maximum nodes inclusion problem with unbound candidate paths. We discuss the effective paths of the problems by situation, bound the candidate paths to certain lengths using discretization technology, and employ existing approximation algorithms to get the approximation solutions. When the charging period is greater than the sweep period, we get a 2 5approximation algorithm. For the opposite, we get 1 6 -approximation algorithms for it. The validity and scalability of the proposed algorithms are proved by theoretical proofs and experimental simulations.