In this paper, four PSO based distributed algorithms are presented to attain k-coverage in the target filed. In the first algorithm named K-Coverage Particle Swarm Optimization (KPSO), each static sensor which discovers an event in its sensing range, implements Particle Swarm Optimization (PSO) algorithm in a distributed manner on its mobile sensors. The calculation time is considered as a big bottleneck in PSO, so a second algorithm named K-Coverage Virtual Force directed Particle Swarm Optimization (KVFPSO) is presented, comprised of Virtual Force and KPSO algorithms. In the first and second proposed algorithms, the best experiences of the particles were used to determine their speed. It is possible that these responses might not be the final result and cause extra movements. Another algorithm named KVFPSO-Learning Automata (KVFPSO-LA) is introduced based on which the speed of particles is corrected by using the existing knowledge and the feedback from the actual implementation of the algorithm. To improve performance of the algorithm, Improved KVFPSO-LA is introduced, in which static sensors are equipped with learning automata. Simulation results show that the proposed protocols perform well with respect to balanced energy consumption among nodes, thus maximizing network life-time