Device control, which aims to find full-coverage sets of active sensors as much as possible, has been considered as an effective strategy to save energy and extend lifetime of wireless sensor networks (WSNs). In this paper, we intend to address a more general form of the WSN device control problem with non-disjoint set coverage, probability sensing and connectivity constraints. With these considerations, the problem model can better simulate the reality of sensor heterogeneousness, signal attenuation and network connectivity in multi-sink WSNs. As the problem is challenging, an ant colony optimization (ACO) approach is introduced with the objective to prolong the operational working time of WSNs. Different from the existing ACO and evolutionary computation approaches, the proposed ACO utilizes a global optimization approach that finds the sensor assignments for all time slots in a single run. Furthermore, a novel criterion is introduced to find out the short boards in restricting the working time of the whole system. Aided by the Cannikin Law, artificial ants in ACO pay more attention to the short boards, so that the assignment of sensors can be more instructional. To validate the proposed approach, simulations are done on 36 networks with up to 2000 sensors. Experimental results show that the proposed ACO is effective.